From 776c9dfeea692f8beda5b4dfcb8a532a2d44eae2 Mon Sep 17 00:00:00 2001
From: antonio-decaro <antonio.decaro99@outlook.it>
Date: Tue, 1 Jul 2025 19:56:16 +0000
Subject: [PATCH 01/69] feat: add bitset and frontier classes with atomic
 operations and tests

---
 cpp/oneapi/dal/backend/primitives/bitset.hpp  |   1 +
 .../dal/backend/primitives/bitset/bitset.hpp  | 112 ++++++++++++++++++
 .../dal/backend/primitives/frontier.hpp       |   1 +
 .../dal/backend/primitives/frontier/BUILD     |  29 +++++
 .../primitives/frontier/frontier_dpc.hpp      | 105 ++++++++++++++++
 .../frontier/test/basic_frontier_ops_dpc.cpp  |  21 ++++
 .../primitives/frontier/test/frontier.hpp     |  43 +++++++
 7 files changed, 312 insertions(+)
 create mode 100644 cpp/oneapi/dal/backend/primitives/bitset.hpp
 create mode 100644 cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier.hpp
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/BUILD
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/test/frontier.hpp

diff --git a/cpp/oneapi/dal/backend/primitives/bitset.hpp b/cpp/oneapi/dal/backend/primitives/bitset.hpp
new file mode 100644
index 00000000000..905603885cb
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/bitset.hpp
@@ -0,0 +1 @@
+#include "oneapi/dal/backend/primitives/bitset/bitset.hpp"
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
new file mode 100644
index 00000000000..453fd35ec1e
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
@@ -0,0 +1,112 @@
+#include "oneapi/dal/backend/memory.hpp"
+
+namespace oneapi::dal::backend::primitives {
+
+/**
+ * @brief A bitset class that provides a set of operations on a bitset.
+ */
+template <typename ElementType = std::uint32_t>
+class bitset {
+public:
+    using element_t = ElementType;
+    static constexpr size_t element_bitsize = sizeof(element_t) * 8; // Number of bits in an element
+
+    bitset(element_t* data) : _data(data) {}
+
+    /// Sets the bit at the specified index to 1.
+    inline void set(std::uint32_t index) {
+        const auto element_index = index / element_bitsize;
+        const auto bit_index = index % element_bitsize;
+        _data[element_index] |= (element_t(1) << bit_index);
+    }
+
+    /// Clears the bit at the specified index to 0.
+    inline void clear(std::uint32_t index) {
+        const auto element_index = index / element_bitsize;
+        const auto bit_index = index % element_bitsize;
+        _data[element_index] &= ~(element_t(1) << bit_index);
+    }
+
+    /// Checks if the bit at the specified index is set.
+    inline bool test(std::uint32_t index) const {
+        const auto element_index = index / element_bitsize;
+        const auto bit_index = index % element_bitsize;
+        return (_data[element_index] & (element_t(1) << bit_index)) != 0;
+    }
+
+    inline bool gas(std::uint32_t index) const {
+        const auto element_index = index / element_bitsize;
+        const auto bit_index = index % element_bitsize;
+        bool set = (_data[element_index] & (element_t(1) << bit_index)) != 0;
+        if (!set) {
+            _data[element_index] &= ~(element_t(1) << bit_index); // Clear
+        }
+        return set;
+    }
+
+    /// Sets the bit at the specified index using atomic operations.
+    template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
+              sycl::memory_scope mem_scope = sycl::memory_scope::device>
+    inline void atomic_set(std::uint32_t index) const {
+        const auto element_index = index / element_bitsize;
+        const auto bit_index = index % element_bitsize;
+        sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
+            atomic_element(_data[element_index]);
+        atomic_element.fetch_or(element_t(1) << bit_index);
+    }
+
+    /// Clears the bit at the specified index using atomic operations.
+    template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
+              sycl::memory_scope mem_scope = sycl::memory_scope::device>
+    inline void atomic_clear(std::uint32_t index) {
+        const auto element_index = index / element_bitsize;
+        const auto bit_index = index % element_bitsize;
+        sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
+            atomic_element(_data[element_index]);
+        atomic_element.fetch_and(~(element_t(1) << bit_index));
+    }
+
+    /// Checks if the bit at the specified index is set using atomic operations.
+    template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
+              sycl::memory_scope mem_scope = sycl::memory_scope::device>
+    inline bool atomic_test(std::uint32_t index) const {
+        const auto element_index = index / element_bitsize;
+        const auto bit_index = index % element_bitsize;
+        sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
+            atomic_element(_data[element_index]);
+        return (atomic_element.load() & (element_t(1) << bit_index)) != 0;
+    }
+
+    template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
+              sycl::memory_scope mem_scope = sycl::memory_scope::device>
+    inline bool atomic_gas(std::uint32_t index) const {
+        const auto element_index = index / element_bitsize;
+        const auto bit_index = index % element_bitsize;
+        sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
+            atomic_element(_data[element_index]);
+        bool set = (atomic_element.load() & (element_t(1) << bit_index)) != 0;
+        if (!set) {
+            atomic_element.fetch_and(~(element_t(1) << bit_index)); // Clear
+        }
+        return set;
+    }
+
+    /// Returns the pointer to the underlying data.
+    inline element_t* get_data() {
+        return _data;
+    }
+
+    inline void set_data(element_t* data) {
+        _data = data;
+    }
+
+    /// Returns the pointer to the underlying data (const version).
+    inline const element_t* get_data() const {
+        return _data;
+    }
+
+private:
+    element_t* _data;
+};
+
+} // namespace oneapi::dal::backend::primitives
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier.hpp
new file mode 100644
index 00000000000..0ce734a968e
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier.hpp
@@ -0,0 +1 @@
+#include "oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp"
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/BUILD b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
new file mode 100644
index 00000000000..d39a3708bcb
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
@@ -0,0 +1,29 @@
+package(default_visibility = ["//visibility:public"])
+load("@onedal//dev/bazel:dal.bzl",
+    "dal_module",
+    "dal_test_suite",
+)
+
+dal_module (
+    name = "frontier",
+    auto = True
+)
+
+dal_test_suite (
+    name = "tests",
+    framework = "catch2",
+    compile_as = [ "dpc++" ],
+    private = True,
+    hdrs = glob([
+        "test/*.hpp",
+    ]),
+    srcs = glob([
+        "test/*_dpc.cpp",
+    ], exclude=[
+        "test/*perf*.cpp",
+    ]),
+    dal_deps = [
+        ":frontier",
+        "@onedal//cpp/oneapi/dal/backend/primitives:rng",
+    ],
+)
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
new file mode 100644
index 00000000000..618e9328192
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -0,0 +1,105 @@
+#pragma once
+
+#include "oneapi/dal/common.hpp"
+#include "oneapi/dal/graph/detail/common.hpp"
+#include "oneapi/dal/graph/detail/container.hpp"
+#include "oneapi/dal/backend/primitives/bitset.hpp"
+#include "oneapi/dal/backend/primitives/ndarray.hpp"
+
+namespace oneapi::dal::backend::primitives {
+
+template <typename ElementType = std::uint32_t>
+struct frontier_view {
+    using bitmap_t = ElementType;
+    static constexpr std::size_t divide_factor = bitset<bitmap_t>::element_bitsize;
+
+    frontier_view() = default;
+    frontier_view(bitmap_t* data_layer,
+                  bitmap_t* mlb_layer,
+                  std::uint32_t* offsets,
+                  std::uint32_t* offsets_size,
+                  size_t num_items)
+            : _num_items(num_items),
+              _data_layer(data_layer),
+              _mlb_layer(mlb_layer),
+              _offsets(offsets),
+              _offsets_size(offsets_size) {}
+
+    inline void insert(std::uint32_t idx) const {
+        if (_mlb_layer.atomic_gas(static_cast<std::uint32_t>(idx / divide_factor))) {
+            _data_layer.atomic_set(idx);
+        }
+    }
+
+    inline void remove(std::uint32_t idx) const {
+        throw dal::domain_error("Frontier does not support remove operation");
+    }
+
+    inline bool check(std::uint32_t idx) const {
+        return _data_layer.atomic_test(idx);
+    }
+
+    size_t _num_items;
+
+    bitset<bitmap_t> _data_layer;
+    bitset<bitmap_t> _mlb_layer;
+
+    std::uint32_t* _offsets;
+    std::uint32_t* _offsets_size;
+};
+
+template <typename ElementType = std::uint32_t>
+class frontier {
+    using bitmap_t = ElementType;
+
+public:
+    frontier(sycl::queue& queue, std::size_t num_items) : _queue(queue) {
+        auto array_size =
+            (num_items + bitset<bitmap_t>::element_bitsize - 1) / bitset<bitmap_t>::element_bitsize;
+        auto mlb_size = (array_size + bitset<bitmap_t>::element_bitsize - 1) /
+                        bitset<bitmap_t>::element_bitsize;
+        _data_layer = ndarray<bitmap_t, 1>::empty(queue,
+                                                  { static_cast<std::int64_t>(array_size) },
+                                                  sycl::usm::alloc::shared);
+        _mlb_layer = ndarray<bitmap_t, 1>::empty(queue,
+                                                 { static_cast<std::int64_t>(mlb_size) },
+                                                 sycl::usm::alloc::shared);
+        _offsets = ndarray<std::uint32_t, 1>::empty(
+            queue,
+            { static_cast<std::int64_t>(mlb_size + 1) },
+            sycl::usm::alloc::shared); /// First offset is to keep the size of the frontier
+    }
+
+    frontier_view<bitmap_t> get_device_view() {
+        return frontier_view<bitmap_t>(this->get_data_layer(),
+                                       this->get_mlb_layer(),
+                                       this->get_offsets(),
+                                       this->get_offsets_size(),
+                                       _data_layer.get_count());
+    }
+
+    bitmap_t* get_data_layer() {
+        return _data_layer.get_mutable_data();
+    }
+
+    bitmap_t* get_mlb_layer() {
+        return _mlb_layer.get_mutable_data();
+    }
+
+    std::uint32_t* get_offsets() {
+        return _offsets.get_mutable_data() + 1;
+    }
+
+    std::uint32_t* get_offsets_size() {
+        return _offsets.get_mutable_data();
+    }
+
+private:
+    sycl::queue& _queue;
+
+    ndarray<bitmap_t, 1> _data_layer;
+    ndarray<bitmap_t, 1> _mlb_layer;
+    ndarray<std::uint32_t, 1> _offsets;
+};
+
+} // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
new file mode 100644
index 00000000000..9d5645d687f
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
@@ -0,0 +1,21 @@
+#include "oneapi/dal/backend/primitives/frontier.hpp"
+
+#include "oneapi/dal/test/engine/common.hpp"
+#include "oneapi/dal/test/engine/fixtures.hpp"
+#include "oneapi/dal/test/engine/dataframe.hpp"
+
+namespace oneapi::dal::backend::primitives::test {
+
+TEST("frontier can be created", "[frontier]") {
+    sycl::queue queue{ sycl::default_selector_v };
+
+    const std::size_t num_items = 100;
+    REQUIRE(num_items > 0);
+    // auto f = frontier<std::uint32_t>(queue, num_items);
+
+    // auto view = f.get_device_view();
+    // view.insert(0);
+
+} // TEST
+
+} // namespace oneapi::dal::backend::primitives::test
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier.hpp
new file mode 100644
index 00000000000..3c6b3bed9bd
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier.hpp
@@ -0,0 +1,43 @@
+#include "oneapi/dal/backend/primitives/frontier.hpp"
+
+#include "oneapi/dal/test/engine/common.hpp"
+#include "oneapi/dal/test/engine/fixtures.hpp"
+#include "oneapi/dal/test/engine/dataframe.hpp"
+
+namespace oneapi::dal::backend::primitives::test {
+
+template <typename Param>
+class frontier_test
+        : public oneapi::dal::test::engine::float_algo_fixture<std::tuple_element_t<0, Param>> {
+public:
+    using float_t = std::tuple_element_t<0, Param>;
+
+    void generate_input(std::int64_t n = -1, std::int64_t p = -1) {
+        if (n == -1 || p == -1) {
+            this->n_ = GENERATE(7, 827, 13, 216);
+            this->p_ = GENERATE(4, 17, 41, 256);
+        }
+        else {
+            this->n_ = n;
+            this->p_ = p;
+        }
+        const auto dataframe = GENERATE_DATAFRAME(
+            oneapi::dal::test::engine::dataframe_builder{ n_, p_ }.fill_uniform(-0.5, 0.5));
+        this->data_ = dataframe.get_table(this->get_homogen_table_id());
+    }
+
+    void measure_time() {
+        // Implement the performance measurement logic here
+    }
+};
+
+TEMPLATE_LIST_TEST_M(frontier_test,
+                     "frontier test",
+                     "[frontier]",
+                     oneapi::dal::test::engine::float_types) {
+    SKIP_IF(this->not_float64_friendly());
+    this->generate_input();
+    this->measure_time();
+}
+
+} // namespace oneapi::dal::backend::primitives::test

From cb957e8e17caf8e51de139b01fcacb304e30d165 Mon Sep 17 00:00:00 2001
From: antonio-decaro <antonio.decaro99@outlook.it>
Date: Mon, 7 Jul 2025 12:39:38 +0000
Subject: [PATCH 02/69] feat: enhance frontier class with additional operations
 and tests; remove obsolete test header

---
 .../dal/backend/primitives/bitset/bitset.hpp  | 32 +++----
 .../dal/backend/primitives/frontier/BUILD     |  6 +-
 .../primitives/frontier/frontier_dpc.hpp      | 76 +++++++++++++---
 .../frontier/test/basic_frontier_ops_dpc.cpp  | 89 +++++++++++++++++--
 .../primitives/frontier/test/frontier.hpp     | 43 ---------
 5 files changed, 165 insertions(+), 81 deletions(-)
 delete mode 100644 cpp/oneapi/dal/backend/primitives/frontier/test/frontier.hpp

diff --git a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
index 453fd35ec1e..110bdaba70a 100644
--- a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
@@ -15,28 +15,28 @@ class bitset {
 
     /// Sets the bit at the specified index to 1.
     inline void set(std::uint32_t index) {
-        const auto element_index = index / element_bitsize;
-        const auto bit_index = index % element_bitsize;
+        element_t element_index = index / element_bitsize;
+        element_t bit_index = index % element_bitsize;
         _data[element_index] |= (element_t(1) << bit_index);
     }
 
     /// Clears the bit at the specified index to 0.
     inline void clear(std::uint32_t index) {
-        const auto element_index = index / element_bitsize;
-        const auto bit_index = index % element_bitsize;
+        element_t element_index = index / element_bitsize;
+        element_t bit_index = index % element_bitsize;
         _data[element_index] &= ~(element_t(1) << bit_index);
     }
 
     /// Checks if the bit at the specified index is set.
     inline bool test(std::uint32_t index) const {
-        const auto element_index = index / element_bitsize;
-        const auto bit_index = index % element_bitsize;
+        element_t element_index = index / element_bitsize;
+        element_t bit_index = index % element_bitsize;
         return (_data[element_index] & (element_t(1) << bit_index)) != 0;
     }
 
     inline bool gas(std::uint32_t index) const {
-        const auto element_index = index / element_bitsize;
-        const auto bit_index = index % element_bitsize;
+        element_t element_index = index / element_bitsize;
+        element_t bit_index = index % element_bitsize;
         bool set = (_data[element_index] & (element_t(1) << bit_index)) != 0;
         if (!set) {
             _data[element_index] &= ~(element_t(1) << bit_index); // Clear
@@ -48,8 +48,8 @@ class bitset {
     template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
               sycl::memory_scope mem_scope = sycl::memory_scope::device>
     inline void atomic_set(std::uint32_t index) const {
-        const auto element_index = index / element_bitsize;
-        const auto bit_index = index % element_bitsize;
+        element_t element_index = index / element_bitsize;
+        element_t bit_index = index % element_bitsize;
         sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
             atomic_element(_data[element_index]);
         atomic_element.fetch_or(element_t(1) << bit_index);
@@ -59,8 +59,8 @@ class bitset {
     template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
               sycl::memory_scope mem_scope = sycl::memory_scope::device>
     inline void atomic_clear(std::uint32_t index) {
-        const auto element_index = index / element_bitsize;
-        const auto bit_index = index % element_bitsize;
+        element_t element_index = index / element_bitsize;
+        element_t bit_index = index % element_bitsize;
         sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
             atomic_element(_data[element_index]);
         atomic_element.fetch_and(~(element_t(1) << bit_index));
@@ -70,8 +70,8 @@ class bitset {
     template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
               sycl::memory_scope mem_scope = sycl::memory_scope::device>
     inline bool atomic_test(std::uint32_t index) const {
-        const auto element_index = index / element_bitsize;
-        const auto bit_index = index % element_bitsize;
+        element_t element_index = index / element_bitsize;
+        element_t bit_index = index % element_bitsize;
         sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
             atomic_element(_data[element_index]);
         return (atomic_element.load() & (element_t(1) << bit_index)) != 0;
@@ -80,8 +80,8 @@ class bitset {
     template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
               sycl::memory_scope mem_scope = sycl::memory_scope::device>
     inline bool atomic_gas(std::uint32_t index) const {
-        const auto element_index = index / element_bitsize;
-        const auto bit_index = index % element_bitsize;
+        element_t element_index = index / element_bitsize;
+        element_t bit_index = index % element_bitsize;
         sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
             atomic_element(_data[element_index]);
         bool set = (atomic_element.load() & (element_t(1) << bit_index)) != 0;
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/BUILD b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
index d39a3708bcb..394618090e5 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/BUILD
+++ b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
@@ -14,9 +14,9 @@ dal_test_suite (
     framework = "catch2",
     compile_as = [ "dpc++" ],
     private = True,
-    hdrs = glob([
-        "test/*.hpp",
-    ]),
+    # hdrs = glob([
+    #     "test/*.hpp",
+    # ]),
     srcs = glob([
         "test/*_dpc.cpp",
     ], exclude=[
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
index 618e9328192..7826f7a82d6 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -26,9 +26,12 @@ struct frontier_view {
               _offsets_size(offsets_size) {}
 
     inline void insert(std::uint32_t idx) const {
-        if (_mlb_layer.atomic_gas(static_cast<std::uint32_t>(idx / divide_factor))) {
+        if (!_data_layer.test(idx)) {
             _data_layer.atomic_set(idx);
         }
+        if (!_mlb_layer.test(idx / divide_factor)) {
+            _mlb_layer.atomic_set(idx / divide_factor);
+        };
     }
 
     inline void remove(std::uint32_t idx) const {
@@ -48,7 +51,7 @@ struct frontier_view {
     std::uint32_t* _offsets_size;
 };
 
-template <typename ElementType = std::uint32_t>
+template <typename ElementType = std::uint32_t, sycl::usm::alloc Alloc = sycl::usm::alloc::shared>
 class frontier {
     using bitmap_t = ElementType;
 
@@ -58,16 +61,23 @@ class frontier {
             (num_items + bitset<bitmap_t>::element_bitsize - 1) / bitset<bitmap_t>::element_bitsize;
         auto mlb_size = (array_size + bitset<bitmap_t>::element_bitsize - 1) /
                         bitset<bitmap_t>::element_bitsize;
-        _data_layer = ndarray<bitmap_t, 1>::empty(queue,
-                                                  { static_cast<std::int64_t>(array_size) },
-                                                  sycl::usm::alloc::shared);
-        _mlb_layer = ndarray<bitmap_t, 1>::empty(queue,
-                                                 { static_cast<std::int64_t>(mlb_size) },
-                                                 sycl::usm::alloc::shared);
-        _offsets = ndarray<std::uint32_t, 1>::empty(
+        auto [data_layer, e1] =
+            ndarray<bitmap_t, 1>::zeros(queue, { static_cast<std::int64_t>(array_size) }, Alloc);
+        auto [mlb_layer, e2] =
+            ndarray<bitmap_t, 1>::zeros(queue, { static_cast<std::int64_t>(mlb_size) }, Alloc);
+        auto [offsets, e3] = ndarray<std::uint32_t, 1>::zeros(
             queue,
             { static_cast<std::int64_t>(mlb_size + 1) },
             sycl::usm::alloc::shared); /// First offset is to keep the size of the frontier
+        _buffer = ndarray<std::uint32_t, 1>::empty(queue, { static_cast<std::int64_t>(10) }, Alloc);
+
+        e1.wait_and_throw();
+        e2.wait_and_throw();
+        e3.wait_and_throw();
+
+        _data_layer = std::move(data_layer);
+        _mlb_layer = std::move(mlb_layer);
+        _offsets = std::move(offsets);
     }
 
     frontier_view<bitmap_t> get_device_view() {
@@ -78,28 +88,68 @@ class frontier {
                                        _data_layer.get_count());
     }
 
-    bitmap_t* get_data_layer() {
+    bitmap_t* get_data_layer() const {
         return _data_layer.get_mutable_data();
     }
 
-    bitmap_t* get_mlb_layer() {
+    size_t get_data_layer_size() const {
+        return _data_layer.get_count();
+    }
+
+    size_t get_mlb_layer_size() const {
+        return _mlb_layer.get_count();
+    }
+
+    bitmap_t* get_mlb_layer() const {
         return _mlb_layer.get_mutable_data();
     }
 
-    std::uint32_t* get_offsets() {
+    std::uint32_t* get_offsets() const {
         return _offsets.get_mutable_data() + 1;
     }
 
-    std::uint32_t* get_offsets_size() {
+    std::uint32_t* get_offsets_size() const {
         return _offsets.get_mutable_data();
     }
 
+    bool empty() const {
+        auto empty_buff = _buffer.slice(0, 1);
+        fill(_queue, empty_buff, bitmap_t(0)).wait();
+        auto empty_buff_ptr = empty_buff.get_mutable_data();
+
+        auto e = _queue.submit([&](sycl::handler& cgh) {
+            const auto range = make_range_1d(_mlb_layer.get_count());
+            auto sum_reduction = sycl::reduction(empty_buff_ptr, sycl::plus<>());
+            auto* f_ptr = this->get_mlb_layer();
+
+            cgh.parallel_for(range, sum_reduction, [=](sycl::id<1> idx, auto& sum_v) {
+                sum_v += f_ptr[idx];
+            });
+        });
+        e.wait_and_throw();
+        auto empty_sum = empty_buff.at_device(_queue, 0, { e });
+        return empty_sum == 0;
+    }
+
+    void insert(bitmap_t idx) {
+        if (idx >= _data_layer.get_count() * bitset<bitmap_t>::element_bitsize) {
+            throw dal::domain_error("Index is out of range");
+        }
+        auto view = this->get_device_view();
+        _queue
+            .single_task([=]() {
+                view.insert(idx);
+            })
+            .wait();
+    }
+
 private:
     sycl::queue& _queue;
 
     ndarray<bitmap_t, 1> _data_layer;
     ndarray<bitmap_t, 1> _mlb_layer;
     ndarray<std::uint32_t, 1> _offsets;
+    ndarray<std::uint32_t, 1> _buffer;
 };
 
 } // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
index 9d5645d687f..d5f900dcc19 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
@@ -4,18 +4,95 @@
 #include "oneapi/dal/test/engine/fixtures.hpp"
 #include "oneapi/dal/test/engine/dataframe.hpp"
 
+#include "oneapi/dal/test/engine/common.hpp"
+#include "oneapi/dal/test/engine/fixtures.hpp"
+#include "oneapi/dal/test/engine/dataframe.hpp"
+
 namespace oneapi::dal::backend::primitives::test {
 
-TEST("frontier can be created", "[frontier]") {
+TEST("frontier basic operations", "[frontier]") {
     sycl::queue queue{ sycl::default_selector_v };
 
     const std::size_t num_items = 100;
-    REQUIRE(num_items > 0);
-    // auto f = frontier<std::uint32_t>(queue, num_items);
+    auto f = frontier<std::uint32_t>(queue, num_items);
+    auto view = f.get_device_view();
+    size_t expected_data_layer_size = (num_items + bitset<std::uint32_t>::element_bitsize - 1) /
+                                      bitset<std::uint32_t>::element_bitsize;
+    size_t expected_mlb_layer_size =
+        (expected_data_layer_size + bitset<std::uint32_t>::element_bitsize - 1) /
+        bitset<std::uint32_t>::element_bitsize;
+
+    SECTION("frontier has correct data layer size", "[frontier]") {
+        REQUIRE(f.get_data_layer_size() == expected_data_layer_size);
+
+        REQUIRE(f.get_mlb_layer_size() == expected_mlb_layer_size);
+    }
+
+    SECTION("frontier can insert elements", "[frontier]") {
+        view.insert(0);
+        view.insert(2);
+        view.insert(bitset<std::uint32_t>::element_bitsize);
+
+        auto data_layer = f.get_data_layer();
+        auto mlb_layer = f.get_mlb_layer();
+
+        std::cout << "Data layer size: " << data_layer[0] << std::endl;
+        std::cout << "MLB layer size: " << mlb_layer[0] << std::endl;
+
+        REQUIRE(data_layer[0] == static_cast<uint32_t>(5));
+        REQUIRE(data_layer[1] == static_cast<uint32_t>(1));
+        REQUIRE(mlb_layer[0] == static_cast<uint32_t>(3));
+    }
+
+    SECTION("frontier can check elements", "[frontier]") {
+        view.insert(0);
+        view.insert(2);
+        view.insert(32);
+        view.insert(64);
+
+        REQUIRE(view.check(0) == true);
+        REQUIRE(view.check(1) == false);
+        REQUIRE(view.check(2) == true);
+        REQUIRE(view.check(3) == false);
+        REQUIRE(view.check(31) == false);
+        REQUIRE(view.check(32) == true);
+        REQUIRE(view.check(33) == false);
+        REQUIRE(view.check(63) == false);
+        REQUIRE(view.check(64) == true);
+        REQUIRE(view.check(65) == false);
+    }
+
+} // TEST "frontier basic operations"
+
+TEST("frontier queue operations", "[frontier]") {
+    sycl::queue queue{ sycl::default_selector_v };
+
+    const std::size_t num_items = 100;
+    auto f = frontier<std::uint32_t>(queue, num_items);
+
+    SECTION("empty function", "[frontier]") {
+        REQUIRE(f.empty() == true);
+        auto view = f.get_device_view();
+        view.insert(0);
+        REQUIRE(f.empty() == false);
+    }
+
+    SECTION("insert function", "[frontier]") {
+        f.insert(0);
+        f.insert(2);
+        f.insert(bitset<std::uint32_t>::element_bitsize);
+
+        auto data_layer = f.get_data_layer();
+        auto mlb_layer = f.get_mlb_layer();
+
+        std::cout << "Data layer size: " << data_layer[0] << std::endl;
+        std::cout << "MLB layer size: " << mlb_layer[0] << std::endl;
 
-    // auto view = f.get_device_view();
-    // view.insert(0);
+        REQUIRE(data_layer[0] == static_cast<uint32_t>(5));
+        REQUIRE(data_layer[1] == static_cast<uint32_t>(1));
+        REQUIRE(mlb_layer[0] == static_cast<uint32_t>(3));
+    }
 
-} // TEST
+} // TEST "frontier queue operations"
 
 } // namespace oneapi::dal::backend::primitives::test
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier.hpp
deleted file mode 100644
index 3c6b3bed9bd..00000000000
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier.hpp
+++ /dev/null
@@ -1,43 +0,0 @@
-#include "oneapi/dal/backend/primitives/frontier.hpp"
-
-#include "oneapi/dal/test/engine/common.hpp"
-#include "oneapi/dal/test/engine/fixtures.hpp"
-#include "oneapi/dal/test/engine/dataframe.hpp"
-
-namespace oneapi::dal::backend::primitives::test {
-
-template <typename Param>
-class frontier_test
-        : public oneapi::dal::test::engine::float_algo_fixture<std::tuple_element_t<0, Param>> {
-public:
-    using float_t = std::tuple_element_t<0, Param>;
-
-    void generate_input(std::int64_t n = -1, std::int64_t p = -1) {
-        if (n == -1 || p == -1) {
-            this->n_ = GENERATE(7, 827, 13, 216);
-            this->p_ = GENERATE(4, 17, 41, 256);
-        }
-        else {
-            this->n_ = n;
-            this->p_ = p;
-        }
-        const auto dataframe = GENERATE_DATAFRAME(
-            oneapi::dal::test::engine::dataframe_builder{ n_, p_ }.fill_uniform(-0.5, 0.5));
-        this->data_ = dataframe.get_table(this->get_homogen_table_id());
-    }
-
-    void measure_time() {
-        // Implement the performance measurement logic here
-    }
-};
-
-TEMPLATE_LIST_TEST_M(frontier_test,
-                     "frontier test",
-                     "[frontier]",
-                     oneapi::dal::test::engine::float_types) {
-    SKIP_IF(this->not_float64_friendly());
-    this->generate_input();
-    this->measure_time();
-}
-
-} // namespace oneapi::dal::backend::primitives::test

From 10d8a3db7b6683e33752a9d76ac51d4c8ad5e3cc Mon Sep 17 00:00:00 2001
From: antonio-decaro <antonio.decaro99@outlook.it>
Date: Mon, 7 Jul 2025 13:03:06 +0000
Subject: [PATCH 03/69] feat: enhance frontier class with additional methods
 and tests for check and clear operations

---
 .../primitives/frontier/frontier_dpc.hpp      | 64 ++++++++++++++-----
 .../frontier/test/basic_frontier_ops_dpc.cpp  | 20 ++++--
 2 files changed, 65 insertions(+), 19 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
index 7826f7a82d6..8708b859b66 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -54,9 +54,10 @@ struct frontier_view {
 template <typename ElementType = std::uint32_t, sycl::usm::alloc Alloc = sycl::usm::alloc::shared>
 class frontier {
     using bitmap_t = ElementType;
+    using buffer_t = std::uint32_t;
 
 public:
-    frontier(sycl::queue& queue, std::size_t num_items) : _queue(queue) {
+    frontier(sycl::queue& queue, std::size_t num_items) : _queue(queue), _num_items(num_items) {
         auto array_size =
             (num_items + bitset<bitmap_t>::element_bitsize - 1) / bitset<bitmap_t>::element_bitsize;
         auto mlb_size = (array_size + bitset<bitmap_t>::element_bitsize - 1) /
@@ -80,11 +81,14 @@ class frontier {
         _offsets = std::move(offsets);
     }
 
-    frontier_view<bitmap_t> get_device_view() {
+    frontier_view<bitmap_t> get_device_view() const {
+        auto offsets_size_pointer = _offsets.get_mutable_data();
+        auto offsets_pointer = _offsets.get_mutable_data() + 1;
+
         return frontier_view<bitmap_t>(this->get_data_layer(),
                                        this->get_mlb_layer(),
-                                       this->get_offsets(),
-                                       this->get_offsets_size(),
+                                       offsets_pointer,
+                                       offsets_size_pointer,
                                        _data_layer.get_count());
     }
 
@@ -92,6 +96,14 @@ class frontier {
         return _data_layer.get_mutable_data();
     }
 
+    bitmap_t* get_mlb_layer() const {
+        return _mlb_layer.get_mutable_data();
+    }
+
+    std::uint32_t* get_offsets() const {
+        return _offsets.get_mutable_data() + 1;
+    }
+
     size_t get_data_layer_size() const {
         return _data_layer.get_count();
     }
@@ -100,21 +112,17 @@ class frontier {
         return _mlb_layer.get_count();
     }
 
-    bitmap_t* get_mlb_layer() const {
-        return _mlb_layer.get_mutable_data();
-    }
-
-    std::uint32_t* get_offsets() const {
-        return _offsets.get_mutable_data() + 1;
+    size_t get_offsets_size() const {
+        return _offsets.get_count() - 1;
     }
 
-    std::uint32_t* get_offsets_size() const {
-        return _offsets.get_mutable_data();
+    size_t get_num_items() const {
+        return _num_items;
     }
 
     bool empty() const {
         auto empty_buff = _buffer.slice(0, 1);
-        fill(_queue, empty_buff, bitmap_t(0)).wait();
+        fill(_queue, empty_buff, buffer_t(0)).wait();
         auto empty_buff_ptr = empty_buff.get_mutable_data();
 
         auto e = _queue.submit([&](sycl::handler& cgh) {
@@ -140,16 +148,42 @@ class frontier {
             .single_task([=]() {
                 view.insert(idx);
             })
-            .wait();
+            .wait_and_throw();
+    }
+
+    bool check(bitmap_t idx) const {
+        auto check_buff = _buffer.slice(0, 1);
+        fill(_queue, check_buff, buffer_t(0)).wait();
+        auto check_buff_ptr = check_buff.get_mutable_data();
+
+        auto e = _queue.submit([&](sycl::handler& cgh) {
+            auto view = this->get_device_view();
+
+            cgh.single_task([=]() {
+                check_buff_ptr[0] = view.check(idx) ? buffer_t(1) : buffer_t(0);
+            });
+        });
+        auto check_res = check_buff.at_device(_queue, 0, { e });
+        return check_res == buffer_t(1);
+    }
+
+    void clear() {
+        auto e = fill(_queue, _data_layer, bitmap_t(0));
+        auto e1 = fill(_queue, _mlb_layer, bitmap_t(0));
+        auto e2 = fill(_queue, _offsets, buffer_t(0));
+        e.wait_and_throw();
+        e1.wait_and_throw();
+        e2.wait_and_throw();
     }
 
 private:
     sycl::queue& _queue;
+    size_t _num_items;
 
     ndarray<bitmap_t, 1> _data_layer;
     ndarray<bitmap_t, 1> _mlb_layer;
     ndarray<std::uint32_t, 1> _offsets;
-    ndarray<std::uint32_t, 1> _buffer;
+    ndarray<buffer_t, 1> _buffer;
 };
 
 } // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
index d5f900dcc19..6439a67ad9f 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
@@ -36,9 +36,6 @@ TEST("frontier basic operations", "[frontier]") {
         auto data_layer = f.get_data_layer();
         auto mlb_layer = f.get_mlb_layer();
 
-        std::cout << "Data layer size: " << data_layer[0] << std::endl;
-        std::cout << "MLB layer size: " << mlb_layer[0] << std::endl;
-
         REQUIRE(data_layer[0] == static_cast<uint32_t>(5));
         REQUIRE(data_layer[1] == static_cast<uint32_t>(1));
         REQUIRE(mlb_layer[0] == static_cast<uint32_t>(3));
@@ -64,7 +61,7 @@ TEST("frontier basic operations", "[frontier]") {
 
 } // TEST "frontier basic operations"
 
-TEST("frontier queue operations", "[frontier]") {
+TEST("frontier queue basic operations", "[frontier]") {
     sycl::queue queue{ sycl::default_selector_v };
 
     const std::size_t num_items = 100;
@@ -93,6 +90,21 @@ TEST("frontier queue operations", "[frontier]") {
         REQUIRE(mlb_layer[0] == static_cast<uint32_t>(3));
     }
 
+    SECTION("check function", "[frontier]") {
+        f.insert(0);
+        REQUIRE(f.check(0) == true);
+        REQUIRE(f.check(1) == false);
+    }
+
+    SECTION("clear function", "[frontier]") {
+        f.insert(0);
+        f.insert(2);
+        f.insert(bitset<std::uint32_t>::element_bitsize);
+        REQUIRE(f.empty() == false);
+        f.clear();
+        REQUIRE(f.empty() == true);
+    }
+
 } // TEST "frontier queue operations"
 
 } // namespace oneapi::dal::backend::primitives::test

From 05152471999798405070fe96d34e119168cef36e Mon Sep 17 00:00:00 2001
From: antonio-decaro <antonio.decaro99@outlook.it>
Date: Tue, 8 Jul 2025 14:04:53 +0000
Subject: [PATCH 04/69] insert compunte active kernel

---
 .../dal/backend/primitives/bitset/bitset.hpp  |   5 +
 .../primitives/frontier/frontier_dpc.hpp      | 127 +++++++++++++++---
 .../frontier/test/basic_frontier_ops_dpc.cpp  |  36 +++--
 3 files changed, 141 insertions(+), 27 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
index 110bdaba70a..96d252ab674 100644
--- a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
@@ -105,6 +105,11 @@ class bitset {
         return _data;
     }
 
+    /// override operator []
+    inline element_t& operator[](std::size_t index) {
+        return _data[index];
+    }
+
 private:
     element_t* _data;
 };
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
index 8708b859b66..e18890fd6dd 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -68,7 +68,7 @@ class frontier {
             ndarray<bitmap_t, 1>::zeros(queue, { static_cast<std::int64_t>(mlb_size) }, Alloc);
         auto [offsets, e3] = ndarray<std::uint32_t, 1>::zeros(
             queue,
-            { static_cast<std::int64_t>(mlb_size + 1) },
+            { static_cast<std::int64_t>(array_size + 1) },
             sycl::usm::alloc::shared); /// First offset is to keep the size of the frontier
         _buffer = ndarray<std::uint32_t, 1>::empty(queue, { static_cast<std::int64_t>(10) }, Alloc);
 
@@ -85,39 +85,35 @@ class frontier {
         auto offsets_size_pointer = _offsets.get_mutable_data();
         auto offsets_pointer = _offsets.get_mutable_data() + 1;
 
-        return frontier_view<bitmap_t>(this->get_data_layer(),
-                                       this->get_mlb_layer(),
+        return frontier_view<bitmap_t>(this->get_data_ptr(),
+                                       this->get_mlb_ptr(),
                                        offsets_pointer,
                                        offsets_size_pointer,
                                        _data_layer.get_count());
     }
 
-    bitmap_t* get_data_layer() const {
+    inline bitmap_t* get_data_ptr() const {
         return _data_layer.get_mutable_data();
     }
 
-    bitmap_t* get_mlb_layer() const {
+    inline bitmap_t* get_mlb_ptr() const {
         return _mlb_layer.get_mutable_data();
     }
 
-    std::uint32_t* get_offsets() const {
-        return _offsets.get_mutable_data() + 1;
+    inline std::uint32_t* get_offsets_ptr() const {
+        return &_offsets.get_mutable_data()[1];
     }
 
-    size_t get_data_layer_size() const {
-        return _data_layer.get_count();
+    inline std::uint32_t* get_offsets_size_ptr() const {
+        return _offsets.get_mutable_data();
     }
 
-    size_t get_mlb_layer_size() const {
-        return _mlb_layer.get_count();
-    }
-
-    size_t get_offsets_size() const {
-        return _offsets.get_count() - 1;
+    inline size_t get_data_size() const {
+        return _data_layer.get_count();
     }
 
-    size_t get_num_items() const {
-        return _num_items;
+    inline size_t get_mlb_size() const {
+        return _mlb_layer.get_count();
     }
 
     bool empty() const {
@@ -128,7 +124,7 @@ class frontier {
         auto e = _queue.submit([&](sycl::handler& cgh) {
             const auto range = make_range_1d(_mlb_layer.get_count());
             auto sum_reduction = sycl::reduction(empty_buff_ptr, sycl::plus<>());
-            auto* f_ptr = this->get_mlb_layer();
+            auto* f_ptr = this->get_mlb_ptr();
 
             cgh.parallel_for(range, sum_reduction, [=](sycl::id<1> idx, auto& sum_v) {
                 sum_v += f_ptr[idx];
@@ -176,6 +172,101 @@ class frontier {
         e2.wait_and_throw();
     }
 
+    sycl::event compute_active_frontier() const {
+        auto bitmap = this->get_device_view();
+
+        uint32_t range = decltype(bitmap._mlb_layer)::element_bitsize;
+        size_t local_range = 1024; // Adjust as needed
+        size_t global_range =
+            _mlb_layer.get_count() + local_range - (_mlb_layer.get_count() % local_range);
+
+        bool use_local_mem =
+            device_local_mem_size(this->_queue) >= (local_range * range * sizeof(uint32_t));
+
+        auto e = this->_queue.submit([&](sycl::handler& cgh) {
+            sycl::local_accessor<uint32_t, 1> local_offsets(local_range * range, cgh);
+            sycl::local_accessor<uint32_t, 1> local_size(1, cgh);
+
+            if (use_local_mem) {
+                cgh.parallel_for(
+                    make_multiple_nd_range_1d(global_range, local_range),
+                    [=,
+                     offsets = this->get_offsets_ptr(),
+                     offsets_size = this->get_offsets_size_ptr(),
+                     data_layer = this->get_mlb_ptr(),
+                     size = this->_num_items](sycl::nd_item<1> item) {
+                        if (offsets_size[0] > 0) {
+                            return;
+                        }
+
+                        auto group = item.get_group();
+                        sycl::atomic_ref<uint32_t,
+                                         sycl::memory_order::relaxed,
+                                         sycl::memory_scope::work_group>
+                            local_size_ref{ local_size[0] };
+                        sycl::atomic_ref<uint32_t,
+                                         sycl::memory_order::relaxed,
+                                         sycl::memory_scope::device>
+                            offsets_size_ref{ offsets_size[0] };
+
+                        if (group.leader()) {
+                            local_size_ref.store(0);
+                        }
+                        sycl::group_barrier(group);
+                        for (uint32_t gid = item.get_global_linear_id(); gid < size;
+                             gid += local_range) {
+                            bitmap_t data = data_layer[gid];
+                            for (size_t i = 0; i < range; i++) {
+                                if (data & (static_cast<bitmap_t>(1) << i)) {
+                                    local_offsets[local_size_ref++] = i + gid * range;
+                                }
+                            }
+                        }
+
+                        sycl::group_barrier(group);
+
+                        size_t data_offset = 0;
+                        if (group.leader()) {
+                            data_offset = offsets_size_ref.fetch_add(local_size_ref.load());
+                        }
+                        data_offset = sycl::group_broadcast(group, data_offset, 0);
+                        for (size_t i = item.get_local_linear_id(); i < local_size_ref.load();
+                             i += item.get_local_range(0)) {
+                            offsets[data_offset + i] = local_offsets[i];
+                        }
+                    });
+            }
+            else {
+                cgh.parallel_for(make_multiple_nd_range_1d(global_range, 256),
+                                 [=,
+                                  offsets = this->get_offsets_ptr(),
+                                  offsets_size = this->get_offsets_size_ptr(),
+                                  data_layer = this->get_mlb_ptr(),
+                                  size = this->_num_items](sycl::nd_item<1> item) {
+                                     if (offsets_size[0] > 0) {
+                                         return;
+                                     }
+
+                                     sycl::atomic_ref<uint32_t,
+                                                      sycl::memory_order::relaxed,
+                                                      sycl::memory_scope::device>
+                                         offsets_size_ref{ offsets_size[0] };
+                                     auto gid = item.get_global_linear_id();
+                                     if (gid >= size)
+                                         return;
+
+                                     bitmap_t data = data_layer[gid];
+                                     for (size_t i = 0; i < range; i++) {
+                                         if (data & (static_cast<bitmap_t>(1) << i)) {
+                                             offsets[offsets_size_ref++] = i + gid * range;
+                                         }
+                                     }
+                                 });
+            }
+        });
+        return e;
+    }
+
 private:
     sycl::queue& _queue;
     size_t _num_items;
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
index 6439a67ad9f..026f6bcf728 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
@@ -23,9 +23,9 @@ TEST("frontier basic operations", "[frontier]") {
         bitset<std::uint32_t>::element_bitsize;
 
     SECTION("frontier has correct data layer size", "[frontier]") {
-        REQUIRE(f.get_data_layer_size() == expected_data_layer_size);
+        REQUIRE(f.get_data_size() == expected_data_layer_size);
 
-        REQUIRE(f.get_mlb_layer_size() == expected_mlb_layer_size);
+        REQUIRE(f.get_mlb_size() == expected_mlb_layer_size);
     }
 
     SECTION("frontier can insert elements", "[frontier]") {
@@ -33,8 +33,8 @@ TEST("frontier basic operations", "[frontier]") {
         view.insert(2);
         view.insert(bitset<std::uint32_t>::element_bitsize);
 
-        auto data_layer = f.get_data_layer();
-        auto mlb_layer = f.get_mlb_layer();
+        auto data_layer = f.get_data_ptr();
+        auto mlb_layer = f.get_mlb_ptr();
 
         REQUIRE(data_layer[0] == static_cast<uint32_t>(5));
         REQUIRE(data_layer[1] == static_cast<uint32_t>(1));
@@ -79,11 +79,8 @@ TEST("frontier queue basic operations", "[frontier]") {
         f.insert(2);
         f.insert(bitset<std::uint32_t>::element_bitsize);
 
-        auto data_layer = f.get_data_layer();
-        auto mlb_layer = f.get_mlb_layer();
-
-        std::cout << "Data layer size: " << data_layer[0] << std::endl;
-        std::cout << "MLB layer size: " << mlb_layer[0] << std::endl;
+        auto data_layer = f.get_data_ptr();
+        auto mlb_layer = f.get_mlb_ptr();
 
         REQUIRE(data_layer[0] == static_cast<uint32_t>(5));
         REQUIRE(data_layer[1] == static_cast<uint32_t>(1));
@@ -107,4 +104,25 @@ TEST("frontier queue basic operations", "[frontier]") {
 
 } // TEST "frontier queue operations"
 
+TEST("compute active frontier", "[frontier]") {
+    sycl::queue queue{ sycl::default_selector_v };
+
+    const std::size_t num_items = 100000;
+    auto f = frontier<std::uint32_t>(queue, num_items);
+    auto view = f.get_device_view();
+
+    view.insert(0);
+    view.insert(2);
+    view.insert(32);
+    view.insert(1024);
+
+    auto e = f.compute_active_frontier();
+    e.wait();
+
+    // auto offsets = f.get_offsets_ptr();
+    auto offsets_size = f.get_offsets_size_ptr();
+
+    REQUIRE(offsets_size[0] == 2);
+} // TEST "compute active frontier"
+
 } // namespace oneapi::dal::backend::primitives::test

From c4149fef01459b534665e721e860e19ba0d3b5a4 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 9 Jul 2025 14:18:46 +0200
Subject: [PATCH 05/69] add compute active frontier operation

---
 .../primitives/frontier/frontier_dpc.hpp      | 133 ++++++++++--------
 .../frontier/test/basic_frontier_ops_dpc.cpp  |  15 +-
 2 files changed, 84 insertions(+), 64 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
index e18890fd6dd..403a11267fa 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -42,6 +42,18 @@ struct frontier_view {
         return _data_layer.atomic_test(idx);
     }
 
+    inline size_t get_element_bitsize() const {
+        return bitset<bitmap_t>::element_bitsize;
+    }
+
+    inline std::uint32_t* get_offsets() const {
+        return _offsets_size;
+    }
+
+    inline std::uint32_t* get_offsets_size() const {
+        return _offsets;
+    }
+
     size_t _num_items;
 
     bitset<bitmap_t> _data_layer;
@@ -66,10 +78,8 @@ class frontier {
             ndarray<bitmap_t, 1>::zeros(queue, { static_cast<std::int64_t>(array_size) }, Alloc);
         auto [mlb_layer, e2] =
             ndarray<bitmap_t, 1>::zeros(queue, { static_cast<std::int64_t>(mlb_size) }, Alloc);
-        auto [offsets, e3] = ndarray<std::uint32_t, 1>::zeros(
-            queue,
-            { static_cast<std::int64_t>(array_size + 1) },
-            sycl::usm::alloc::shared); /// First offset is to keep the size of the frontier
+        auto [offsets, e3] = 
+            ndarray<std::uint32_t, 1>::zeros(queue, { static_cast<std::int64_t>(array_size + 1) }, Alloc); /// First offset is to keep the size of the frontier
         _buffer = ndarray<std::uint32_t, 1>::empty(queue, { static_cast<std::int64_t>(10) }, Alloc);
 
         e1.wait_and_throw();
@@ -101,7 +111,7 @@ class frontier {
     }
 
     inline std::uint32_t* get_offsets_ptr() const {
-        return &_offsets.get_mutable_data()[1];
+        return &(_offsets.get_mutable_data()[1]);
     }
 
     inline std::uint32_t* get_offsets_size_ptr() const {
@@ -175,96 +185,101 @@ class frontier {
     sycl::event compute_active_frontier() const {
         auto bitmap = this->get_device_view();
 
-        uint32_t range = decltype(bitmap._mlb_layer)::element_bitsize;
+        uint32_t element_bitsize = decltype(bitmap._mlb_layer)::element_bitsize;
         size_t local_range = 1024; // Adjust as needed
         size_t global_range =
             _mlb_layer.get_count() + local_range - (_mlb_layer.get_count() % local_range);
 
         bool use_local_mem =
-            device_local_mem_size(this->_queue) >= (local_range * range * sizeof(uint32_t));
+            device_local_mem_size(this->_queue) >= (local_range * element_bitsize * sizeof(uint32_t));
 
-        auto e = this->_queue.submit([&](sycl::handler& cgh) {
-            sycl::local_accessor<uint32_t, 1> local_offsets(local_range * range, cgh);
-            sycl::local_accessor<uint32_t, 1> local_size(1, cgh);
+        auto e0 = _queue.submit([&](sycl::handler& cgh) {
+            cgh.single_task([=, offsets_size = this->get_offsets_size_ptr(), buffer_ptr = this->_buffer.get_mutable_data(), CAF_FLAG = this->_CAF_FLAG]() {
+                buffer_ptr[CAF_FLAG] = offsets_size[0] == 0 ? 1 : 0;
+            });
+        });
 
-            if (use_local_mem) {
-                cgh.parallel_for(
-                    make_multiple_nd_range_1d(global_range, local_range),
+        auto e1 = this->_queue.submit([&](sycl::handler& cgh) {
+            cgh.depends_on(e0);
+
+            if (!use_local_mem || true) { // Force to use global memory for simplicity
+                cgh.parallel_for(make_range_1d(_mlb_layer.get_count()),
                     [=,
-                     offsets = this->get_offsets_ptr(),
-                     offsets_size = this->get_offsets_size_ptr(),
-                     data_layer = this->get_mlb_ptr(),
-                     size = this->_num_items](sycl::nd_item<1> item) {
-                        if (offsets_size[0] > 0) {
-                            return;
+                    offsets = this->get_offsets_ptr(),
+                    offsets_size = this->get_offsets_size_ptr(),
+                    data_layer = this->get_mlb_ptr(),
+                    buffer = this->_buffer.get_mutable_data(),
+                    CAF_FLAG = this->_CAF_FLAG](sycl::id<1> idx) {
+    
+                        if (!buffer[CAF_FLAG]) return;
+    
+                        sycl::atomic_ref<uint32_t,
+                                        sycl::memory_order::relaxed,
+                                        sycl::memory_scope::device>
+                            offsets_size_ref{ offsets_size[0] };
+    
+                        bitmap_t data = data_layer[idx];
+                        for (size_t i = 0; i < element_bitsize; i++) {
+                            if (data & (static_cast<bitmap_t>(1) << i)) {
+                                offsets[offsets_size_ref++] = i + idx * element_bitsize;
+                            }
                         }
+                });
+            } else {
+                sycl::local_accessor<uint32_t, 1> local_offsets(local_range * element_bitsize, cgh);
+                sycl::local_accessor<uint32_t, 1> local_size(1, cgh);
 
+                cgh.parallel_for(
+                    make_multiple_nd_range_1d(global_range, local_range),
+                    [=,
+                    offsets = this->get_offsets_ptr(),
+                    offsets_size = this->get_offsets_size_ptr(),
+                    data_layer = this->get_mlb_ptr(),
+                    size = this->_num_items,
+                    buffer = this->_buffer.get_mutable_data(),
+                    CAF_FLAG = this->_CAF_FLAG](sycl::nd_item<1> item) {
+                        if (!buffer[CAF_FLAG]) return;
+    
                         auto group = item.get_group();
                         sycl::atomic_ref<uint32_t,
-                                         sycl::memory_order::relaxed,
-                                         sycl::memory_scope::work_group>
+                                            sycl::memory_order::relaxed,
+                                            sycl::memory_scope::work_group>
                             local_size_ref{ local_size[0] };
                         sycl::atomic_ref<uint32_t,
-                                         sycl::memory_order::relaxed,
-                                         sycl::memory_scope::device>
+                                            sycl::memory_order::relaxed,
+                                            sycl::memory_scope::device>
                             offsets_size_ref{ offsets_size[0] };
-
+    
                         if (group.leader()) {
                             local_size_ref.store(0);
                         }
                         sycl::group_barrier(group);
                         for (uint32_t gid = item.get_global_linear_id(); gid < size;
-                             gid += local_range) {
+                                gid += local_range) {
                             bitmap_t data = data_layer[gid];
-                            for (size_t i = 0; i < range; i++) {
+                            for (size_t i = 0; i < element_bitsize; i++) {
                                 if (data & (static_cast<bitmap_t>(1) << i)) {
-                                    local_offsets[local_size_ref++] = i + gid * range;
+                                    local_offsets[local_size_ref++] = i + gid * element_bitsize;
                                 }
                             }
                         }
-
+    
                         sycl::group_barrier(group);
-
+    
                         size_t data_offset = 0;
                         if (group.leader()) {
                             data_offset = offsets_size_ref.fetch_add(local_size_ref.load());
                         }
                         data_offset = sycl::group_broadcast(group, data_offset, 0);
                         for (size_t i = item.get_local_linear_id(); i < local_size_ref.load();
-                             i += item.get_local_range(0)) {
+                                i += item.get_local_range(0)) {
                             offsets[data_offset + i] = local_offsets[i];
                         }
                     });
             }
-            else {
-                cgh.parallel_for(make_multiple_nd_range_1d(global_range, 256),
-                                 [=,
-                                  offsets = this->get_offsets_ptr(),
-                                  offsets_size = this->get_offsets_size_ptr(),
-                                  data_layer = this->get_mlb_ptr(),
-                                  size = this->_num_items](sycl::nd_item<1> item) {
-                                     if (offsets_size[0] > 0) {
-                                         return;
-                                     }
-
-                                     sycl::atomic_ref<uint32_t,
-                                                      sycl::memory_order::relaxed,
-                                                      sycl::memory_scope::device>
-                                         offsets_size_ref{ offsets_size[0] };
-                                     auto gid = item.get_global_linear_id();
-                                     if (gid >= size)
-                                         return;
-
-                                     bitmap_t data = data_layer[gid];
-                                     for (size_t i = 0; i < range; i++) {
-                                         if (data & (static_cast<bitmap_t>(1) << i)) {
-                                             offsets[offsets_size_ref++] = i + gid * range;
-                                         }
-                                     }
-                                 });
-            }
+
         });
-        return e;
+        return e1;
     }
 
 private:
@@ -275,6 +290,8 @@ class frontier {
     ndarray<bitmap_t, 1> _mlb_layer;
     ndarray<std::uint32_t, 1> _offsets;
     ndarray<buffer_t, 1> _buffer;
+    const size_t _TMP_VAR = 0;
+    const size_t _CAF_FLAG = 0; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
 };
 
 } // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
index 026f6bcf728..97c99e8b41a 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
@@ -11,7 +11,7 @@
 namespace oneapi::dal::backend::primitives::test {
 
 TEST("frontier basic operations", "[frontier]") {
-    sycl::queue queue{ sycl::default_selector_v };
+    sycl::queue queue{ sycl::cpu_selector_v };
 
     const std::size_t num_items = 100;
     auto f = frontier<std::uint32_t>(queue, num_items);
@@ -62,7 +62,7 @@ TEST("frontier basic operations", "[frontier]") {
 } // TEST "frontier basic operations"
 
 TEST("frontier queue basic operations", "[frontier]") {
-    sycl::queue queue{ sycl::default_selector_v };
+    sycl::queue queue{ sycl::gpu_selector_v };
 
     const std::size_t num_items = 100;
     auto f = frontier<std::uint32_t>(queue, num_items);
@@ -105,7 +105,7 @@ TEST("frontier queue basic operations", "[frontier]") {
 } // TEST "frontier queue operations"
 
 TEST("compute active frontier", "[frontier]") {
-    sycl::queue queue{ sycl::default_selector_v };
+    sycl::queue queue{ sycl::gpu_selector_v };
 
     const std::size_t num_items = 100000;
     auto f = frontier<std::uint32_t>(queue, num_items);
@@ -114,15 +114,18 @@ TEST("compute active frontier", "[frontier]") {
     view.insert(0);
     view.insert(2);
     view.insert(32);
-    view.insert(1024);
+    view.insert(33);
+    view.insert(64);
+    view.insert(65);
+    view.insert(95);
 
     auto e = f.compute_active_frontier();
     e.wait();
 
-    // auto offsets = f.get_offsets_ptr();
     auto offsets_size = f.get_offsets_size_ptr();
 
-    REQUIRE(offsets_size[0] == 2);
+    REQUIRE(offsets_size[0] == 3);
+    f.clear();
 } // TEST "compute active frontier"
 
 } // namespace oneapi::dal::backend::primitives::test

From 7a12f2c420ea202f9e7fe5b1c1150a377b24708d Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 16 Jul 2025 14:48:53 +0200
Subject: [PATCH 06/69] bug fix

---
 .../dal/backend/primitives/bitset/bitset.hpp  |   4 +-
 .../primitives/frontier/advance_dpc.hpp       | 242 ++++++++++++++++++
 .../primitives/frontier/frontier_dpc.hpp      |  12 +-
 .../dal/backend/primitives/frontier/graph.hpp |   0
 .../frontier/test/basic_frontier_ops_dpc.cpp  |  74 ++++--
 5 files changed, 305 insertions(+), 27 deletions(-)
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/graph.hpp

diff --git a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
index 96d252ab674..847d1021cbc 100644
--- a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
@@ -14,14 +14,14 @@ class bitset {
     bitset(element_t* data) : _data(data) {}
 
     /// Sets the bit at the specified index to 1.
-    inline void set(std::uint32_t index) {
+    inline void set(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
         _data[element_index] |= (element_t(1) << bit_index);
     }
 
     /// Clears the bit at the specified index to 0.
-    inline void clear(std::uint32_t index) {
+    inline void clear(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
         _data[element_index] &= ~(element_t(1) << bit_index);
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
new file mode 100644
index 00000000000..da78687dcb0
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
@@ -0,0 +1,242 @@
+#pragma once
+
+#include "oneapi/dal/backend/primitives/frontier.hpp"
+
+
+namespace oneapi::dal::backend::primitives {
+
+struct ContextState {
+  size_t group_offset;
+  const uint16_t coarsening_factor;
+  const uint32_t offsets_size;
+  const sycl::nd_item<1> item;
+};
+
+template<typename InFrontierDevT, typename OutFrontierDevT>
+struct Context {
+  size_t limit;
+  InFrontierDevT in_dev_frontier;
+  OutFrontierDevT out_dev_frontier;
+
+  Context(size_t limit, InFrontierDevT in_dev_frontier, OutFrontierDevT out_dev_frontier)
+      : limit(limit), in_dev_frontier(in_dev_frontier), out_dev_frontier(out_dev_frontier) {}
+
+  inline ContextState init(sycl::nd_item<1>& item) const {
+    return {
+        item.get_group_linear_id(),
+        static_cast<uint16_t>(item.get_local_range(0) / in_dev_frontier.get_element_bitsize()),
+        in_dev_frontier.get_offsets_size()[0],
+        item,
+    };
+  }
+
+  inline bool need_to_process(ContextState& state) const { return (state.group_offset * state.coarsening_factor < state.offsets_size); }
+
+  inline void complete_iteration(ContextState& state) const { state.group_offset += state.item.get_group_range(0); }
+
+  inline size_t get_assigned_element(const ContextState& state) const {
+    const uint16_t bitmap_range = in_dev_frontier.getBitmapRange();
+    const uint32_t acutal_id_offset = (state.group_offset * state.coarsening_factor) + (state.item.get_local_linear_id() / bitmap_range);
+    const int* bitmap_offsets = in_dev_frontier.get_offsets();
+    // const size_t acutal_id_offset = (item.get_group_linear_id() * coarsening_factor) + (item.get_local_linear_id() / bitmap_range);
+    const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * bitmap_range) + (state.item.get_local_linear_id() % bitmap_range);
+    return assigned_vertex;
+  }
+
+  inline bool check(const ContextState& state, size_t vertex) const {
+    return vertex < limit && in_dev_frontier.check(vertex);
+    
+  }
+
+  inline void insert(const ContextState& state, size_t vertex) const {
+    out_dev_frontier.insert(vertex);
+  }
+};
+
+template<typename T,
+         typename ContextT,
+         graph::detail::DeviceGraphConcept GraphDevT,
+         typename LambdaT>
+struct BitmapKernel {
+  void operator()(sycl::nd_item<1> item) const {
+    // 0. retrieve global and local ids
+    const size_t gid = item.get_global_linear_id();
+    const size_t lid = item.get_local_linear_id();
+    const auto wgroup = item.get_group();
+    const auto wgroup_id = item.get_group_linear_id();
+    const size_t wgroup_size = wgroup.get_local_range(0);
+    const auto sgroup = item.get_sub_group();
+    const auto sgroup_id = sgroup.get_group_id();
+    const size_t sgroup_size = sgroup.get_local_range()[0];
+    const size_t llid = sgroup.get_local_linear_id();
+
+    auto state = context.init(item);
+
+
+    while (context.need_to_process(state)) {
+      const auto assigned_vertex = context.get_assigned_element(state);
+
+      // 1. load number of edges in local memory
+      if (sgroup.leader()) { subgroup_reduce_tail[sgroup_id] = 0; }
+      if (wgroup.leader()) { workgroup_reduce_tail[0] = 0; }
+
+      sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group> sg_tail{subgroup_reduce_tail[sgroup_id]};
+      sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group> wg_tail{workgroup_reduce_tail[0]};
+
+      const uint32_t offset = sgroup_id * sgroup_size;
+      if (context.check(state, assigned_vertex)) {
+        uint32_t n_edges = graph_dev.getDegree(assigned_vertex); // GRAPH degree of the vertex
+        if (n_edges >= wgroup_size * wgroup_size) { // assign to the workgroup
+          uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
+          n_edges_wg[loc] = n_edges;
+          workgroup_reduce[loc] = assigned_vertex;
+          workgroup_ids[loc] = lid;
+        } else if (n_edges >= sgroup_size) { // assign to the subgroup
+          uint32_t loc = sg_tail.fetch_add(static_cast<uint32_t>(1));
+          n_edges_sg[offset + loc] = n_edges;
+          subgroup_reduce[offset + loc] = assigned_vertex;
+          subgroup_ids[offset + loc] = lid;
+        }
+        visited[lid] = false;
+      } else {
+        visited[lid] = true;
+      }
+
+      sycl::group_barrier(wgroup);
+      for (size_t i = 0; i < wg_tail.load(); i++) {
+        auto vertex = workgroup_reduce[i];
+        size_t n_edges = n_edges_wg[i];
+        auto start = graph_dev.begin(vertex); // GRAPH edge iterator
+
+        for (auto j = lid; j < n_edges; j += wgroup_size) {
+          auto n = start + j;
+          auto edge = n.getIndex(); // GRAPH edge index
+          auto weight = graph_dev.getEdgeWeight(edge); // GRAPH edge weight
+          auto neighbor = *n;
+          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
+        }
+
+        if (wgroup.leader()) { visited[workgroup_ids[i]] = true; }
+      }
+
+      sycl::group_barrier(sgroup);
+
+      for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) { // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
+        size_t vertex_id = offset + i;
+        auto vertex = subgroup_reduce[vertex_id];
+        size_t n_edges = n_edges_sg[vertex_id];
+
+        auto start = graph_dev.begin(vertex); // GRAPH edge iterator
+
+        for (auto j = llid; j < n_edges; j += sgroup_size) {
+          auto n = start + j;
+          auto edge = n.getIndex(); // GRAPH edge index
+          auto weight = graph_dev.getEdgeWeight(edge); // GRAPH edge weight
+          auto neighbor = *n;
+          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
+        }
+
+        if (sgroup.leader()) { visited[subgroup_ids[vertex_id]] = true; }
+      }
+      sycl::group_barrier(sgroup);
+
+      if (!visited[lid]) {
+        auto vertex = assigned_vertex;
+        auto start = graph_dev.begin(vertex); // GRAPH edge iterator
+        auto end = graph_dev.end(vertex); // GRAPH edge iterator
+
+        for (auto n = start; n != end; ++n) {
+          auto edge = n.getIndex(); // GRAPH edge index
+          auto weight = graph_dev.getEdgeWeight(edge); // GRAPH edge weight
+          auto neighbor = *n;
+          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
+        }
+      }
+      context.complete_iteration(state);
+    }
+  }
+
+  const ContextT context;
+  const GraphDevT graph_dev;
+  const sycl::local_accessor<uint32_t, 1> n_edges_wg;
+  const sycl::local_accessor<uint32_t, 1> n_edges_sg;
+  const sycl::local_accessor<bool, 1> visited;
+  const sycl::local_accessor<T, 1> subgroup_reduce;
+  const sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail;
+  const sycl::local_accessor<uint32_t, 1> subgroup_ids;
+  const sycl::local_accessor<T, 1> workgroup_reduce;
+  const sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail;
+  const sycl::local_accessor<uint32_t, 1> workgroup_ids;
+  const LambdaT functor;
+};
+
+template<typename T,
+         graph::detail::GraphConcept GraphT,
+         typename InFrontierT,
+         typename OutFrontierT,
+         typename LambdaT>
+sygraph::Event launchBitmapKernel(GraphT& graph, const InFrontierT& in, const OutFrontierT& out, LambdaT&& functor, size_t expected_size) {
+  sycl::queue& q = graph.getQueue();
+
+  size_t num_nodes = graph.getVertexCount();
+
+  using element_t = std::conditional_t<InFW == sygraph::frontier::frontier_view::vertex, typename GraphT::vertex_t, typename GraphT::edge_t>;
+
+  auto in_dev_frontier = in.get_device_view();
+  auto out_dev_frontier = out.get_device_view();
+  auto graph_dev = graph.getDeviceGraph(); // GRAPH device view
+
+  size_t coarsening_factor = types::detail::COMPUTE_UNIT_SIZE / 16; // sygraph::detail::device::getSubgroupSize(q);
+
+  sycl::event to_wait;
+  sycl::range<1> local_range;
+  size_t global_size;
+  size_t bitmap_range = in.get_element_bitsize();
+  to_wait = in.compute_active_frontier();
+  local_range = {bitmap_range * coarsening_factor};
+  if (expected_size > 0) {
+    global_size = {expected_size + (local_range[0] - (expected_size % local_range[0]))};
+  } else {
+    global_size = {local_range[0] * (sygraph::detail::device::getMaxComputeUints(q) * 8)};
+  }
+
+  sycl::range<1> global_range{global_size > local_range[0] ? global_size + (local_range[0] - (global_size % local_range[0])) : local_range[0]};
+
+  Context<InFW, OutFW, decltype(in_dev_frontier), decltype(out_dev_frontier)> context{num_nodes, in_dev_frontier, out_dev_frontier};
+  using bitmap_kernel_t = BitmapKernel<InFW, OutFW, element_t, decltype(context), decltype(graph_dev), LambdaT>;
+
+  const uint32_t max_num_subgroups = sygraph::detail::device::getMaxNumSubgroups(q);
+
+  auto e = q.submit([&](sycl::handler& cgh) {
+    cgh.depends_on(to_wait);
+    sycl::local_accessor<uint32_t, 1> n_edges_wg{local_range, cgh};
+    sycl::local_accessor<uint32_t, 1> n_edges_sg{local_range, cgh};
+    sycl::local_accessor<bool, 1> visited{local_range, cgh};
+    sycl::local_accessor<element_t, 1> subgroup_reduce{local_range, cgh};
+    sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail{max_num_subgroups, cgh};
+    sycl::local_accessor<uint32_t, 1> subgroup_ids{local_range, cgh};
+    sycl::local_accessor<element_t, 1> workgroup_reduce{local_range, cgh};
+    sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail{1, cgh};
+    sycl::local_accessor<uint32_t, 1> workgroup_ids{local_range, cgh};
+    sycl::local_accessor<element_t, 1> individual_reduce{local_range, cgh};
+    sycl::local_accessor<uint32_t, 1> individual_reduce_tail{1, cgh};
+
+
+    cgh.parallel_for<workgroup_mapped_advance_kernel<InFW, OutFW>>(sycl::nd_range<1>{global_range, local_range},
+                                                                   bitmap_kernel_t{context,
+                                                                                   graph_dev,
+                                                                                   n_edges_wg,
+                                                                                   n_edges_sg,
+                                                                                   visited,
+                                                                                   subgroup_reduce,
+                                                                                   subgroup_reduce_tail,
+                                                                                   subgroup_ids,
+                                                                                   workgroup_reduce,
+                                                                                   workgroup_reduce_tail,
+                                                                                   workgroup_ids,
+                                                                                   std::forward<LambdaT>(functor)});
+  });
+  return {e};
+}
+
+} // namespace oneapi::dal::backend::primitives
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
index 403a11267fa..41f608e06f9 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -63,6 +63,8 @@ struct frontier_view {
     std::uint32_t* _offsets_size;
 };
 
+#ifdef ONEDAL_DATA_PARALLEL
+
 template <typename ElementType = std::uint32_t, sycl::usm::alloc Alloc = sycl::usm::alloc::shared>
 class frontier {
     using bitmap_t = ElementType;
@@ -127,11 +129,12 @@ class frontier {
     }
 
     bool empty() const {
-        auto empty_buff = _buffer.slice(0, 1);
-        fill(_queue, empty_buff, buffer_t(0)).wait();
-        auto empty_buff_ptr = empty_buff.get_mutable_data();
+        ndview<std::uint32_t, 1> empty_buff = _buffer.slice(0, 1);
+        auto copy_e = fill(_queue, empty_buff, buffer_t(0));
+        auto* const empty_buff_ptr = empty_buff.get_mutable_data();
 
         auto e = _queue.submit([&](sycl::handler& cgh) {
+            cgh.depends_on(copy_e);
             const auto range = make_range_1d(_mlb_layer.get_count());
             auto sum_reduction = sycl::reduction(empty_buff_ptr, sycl::plus<>());
             auto* f_ptr = this->get_mlb_ptr();
@@ -140,7 +143,6 @@ class frontier {
                 sum_v += f_ptr[idx];
             });
         });
-        e.wait_and_throw();
         auto empty_sum = empty_buff.at_device(_queue, 0, { e });
         return empty_sum == 0;
     }
@@ -294,4 +296,6 @@ class frontier {
     const size_t _CAF_FLAG = 0; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
 };
 
+#endif
+
 } // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
index 97c99e8b41a..fa05bd1f9e7 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
@@ -10,8 +10,26 @@
 
 namespace oneapi::dal::backend::primitives::test {
 
+void print_device_name(sycl::queue& queue) {
+    const auto device = queue.get_device();
+    const auto device_name = device.get_info<sycl::info::device::name>();
+    std::cout << "Running on device: " << device_name << std::endl;
+}
+
+template<typename T>
+void print_frontier(const T* data, size_t num_items) {
+    size_t element_bitsize = sizeof(T) * 8;
+    for (size_t i = 0; i < num_items; ++i) {
+        size_t offset = num_items / element_bitsize;
+        size_t bit = i % element_bitsize;
+        std::cout << ((data[offset] & (static_cast<T>(1) << bit)) ? "1" : "0");
+    }       
+}
+
 TEST("frontier basic operations", "[frontier]") {
-    sycl::queue queue{ sycl::cpu_selector_v };
+    DECLARE_TEST_POLICY(policy);
+    auto& queue = policy.get_queue();
+    print_device_name(queue);
 
     const std::size_t num_items = 100;
     auto f = frontier<std::uint32_t>(queue, num_items);
@@ -62,15 +80,20 @@ TEST("frontier basic operations", "[frontier]") {
 } // TEST "frontier basic operations"
 
 TEST("frontier queue basic operations", "[frontier]") {
-    sycl::queue queue{ sycl::gpu_selector_v };
+    DECLARE_TEST_POLICY(policy);
+    auto& queue = policy.get_queue();
+    print_device_name(queue);
 
     const std::size_t num_items = 100;
-    auto f = frontier<std::uint32_t>(queue, num_items);
+    auto f = frontier<std::uint32_t, sycl::usm::alloc::device>(queue, num_items);
 
     SECTION("empty function", "[frontier]") {
         REQUIRE(f.empty() == true);
-        auto view = f.get_device_view();
-        view.insert(0);
+        queue.single_task([=, view = f.get_device_view()]() {
+            view.insert(0);
+        }).wait_and_throw();
+        std::cout << (f.check(0) ? "Frontier is not empty" : "Frontier is empty") << std::endl;
+        std::vector<std::uint32_t> data_layer_cpy(f.get_data_size());
         REQUIRE(f.empty() == false);
     }
 
@@ -79,12 +102,19 @@ TEST("frontier queue basic operations", "[frontier]") {
         f.insert(2);
         f.insert(bitset<std::uint32_t>::element_bitsize);
 
-        auto data_layer = f.get_data_ptr();
-        auto mlb_layer = f.get_mlb_ptr();
-
-        REQUIRE(data_layer[0] == static_cast<uint32_t>(5));
-        REQUIRE(data_layer[1] == static_cast<uint32_t>(1));
-        REQUIRE(mlb_layer[0] == static_cast<uint32_t>(3));
+        auto* data_layer = f.get_data_ptr();
+        auto* mlb_layer = f.get_mlb_ptr();
+
+        bool* check = sycl::malloc_device<bool>(1, queue);
+        queue.single_task([=, view = f.get_device_view()]() {
+            check[0] = data_layer[0] == static_cast<uint32_t>(5);
+            check[0] &= data_layer[1] == static_cast<uint32_t>(1);
+            check[0] &= mlb_layer[0] == static_cast<uint32_t>(3);
+        }).wait_and_throw();
+        bool tmp_check;
+        queue.copy(check, &tmp_check, 1).wait_and_throw();
+        REQUIRE(tmp_check == true);
+        sycl::free(check, queue);
     }
 
     SECTION("check function", "[frontier]") {
@@ -105,19 +135,21 @@ TEST("frontier queue basic operations", "[frontier]") {
 } // TEST "frontier queue operations"
 
 TEST("compute active frontier", "[frontier]") {
-    sycl::queue queue{ sycl::gpu_selector_v };
+    DECLARE_TEST_POLICY(policy);
+    auto& queue = policy.get_queue();
 
     const std::size_t num_items = 100000;
-    auto f = frontier<std::uint32_t>(queue, num_items);
-    auto view = f.get_device_view();
+    auto f = frontier<std::uint32_t, sycl::usm::alloc::host>(queue, num_items);
 
-    view.insert(0);
-    view.insert(2);
-    view.insert(32);
-    view.insert(33);
-    view.insert(64);
-    view.insert(65);
-    view.insert(95);
+    queue.single_task([=, view = f.get_device_view()]() {
+        view.insert(0);
+        view.insert(2);
+        view.insert(32);
+        view.insert(33);
+        view.insert(64);
+        view.insert(65);
+        view.insert(95);
+    }).wait_and_throw();
 
     auto e = f.compute_active_frontier();
     e.wait();

From 74459af83b4d4224028f670832dd54debf0d4404 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Thu, 17 Jul 2025 01:56:28 +0200
Subject: [PATCH 07/69] refactor: rename clear and gas methods to unset and
 atomic_unset for consistency; update related functionality; fixed bug for
 SIGSEGV

---
 .../dal/backend/primitives/bitset/bitset.hpp  |  38 +---
 .../primitives/frontier/frontier_dpc.hpp      | 120 ++++++-------
 .../frontier/test/basic_frontier_ops_dpc.cpp  | 162 ++++--------------
 3 files changed, 92 insertions(+), 228 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
index 847d1021cbc..63d728c5cc0 100644
--- a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
@@ -21,7 +21,7 @@ class bitset {
     }
 
     /// Clears the bit at the specified index to 0.
-    inline void clear(std::uint32_t index) const {
+    inline void unset(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
         _data[element_index] &= ~(element_t(1) << bit_index);
@@ -34,36 +34,26 @@ class bitset {
         return (_data[element_index] & (element_t(1) << bit_index)) != 0;
     }
 
-    inline bool gas(std::uint32_t index) const {
-        element_t element_index = index / element_bitsize;
-        element_t bit_index = index % element_bitsize;
-        bool set = (_data[element_index] & (element_t(1) << bit_index)) != 0;
-        if (!set) {
-            _data[element_index] &= ~(element_t(1) << bit_index); // Clear
-        }
-        return set;
-    }
-
     /// Sets the bit at the specified index using atomic operations.
     template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
               sycl::memory_scope mem_scope = sycl::memory_scope::device>
     inline void atomic_set(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
-        sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
+        sycl::atomic_ref<element_t, mem_order, mem_scope>
             atomic_element(_data[element_index]);
-        atomic_element.fetch_or(element_t(1) << bit_index);
+        atomic_element.store(atomic_element.load() | (element_t(1) << bit_index));
     }
 
     /// Clears the bit at the specified index using atomic operations.
     template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
               sycl::memory_scope mem_scope = sycl::memory_scope::device>
-    inline void atomic_clear(std::uint32_t index) {
+    inline void atomic_unset(std::uint32_t index) {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
-        sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
+        sycl::atomic_ref<element_t, mem_order, mem_scope>
             atomic_element(_data[element_index]);
-        atomic_element.fetch_and(~(element_t(1) << bit_index));
+        atomic_element.store(atomic_element.load() & ~(element_t(1) << bit_index));
     }
 
     /// Checks if the bit at the specified index is set using atomic operations.
@@ -72,25 +62,11 @@ class bitset {
     inline bool atomic_test(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
-        sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
+        sycl::atomic_ref<element_t, mem_order, mem_scope>
             atomic_element(_data[element_index]);
         return (atomic_element.load() & (element_t(1) << bit_index)) != 0;
     }
 
-    template <sycl::memory_order mem_order = sycl::memory_order::relaxed,
-              sycl::memory_scope mem_scope = sycl::memory_scope::device>
-    inline bool atomic_gas(std::uint32_t index) const {
-        element_t element_index = index / element_bitsize;
-        element_t bit_index = index % element_bitsize;
-        sycl::atomic_ref<element_t, mem_order, mem_scope, sycl::access::address_space::local_space>
-            atomic_element(_data[element_index]);
-        bool set = (atomic_element.load() & (element_t(1) << bit_index)) != 0;
-        if (!set) {
-            atomic_element.fetch_and(~(element_t(1) << bit_index)); // Clear
-        }
-        return set;
-    }
-
     /// Returns the pointer to the underlying data.
     inline element_t* get_data() {
         return _data;
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
index 41f608e06f9..ce2747c4c39 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -20,8 +20,8 @@ struct frontier_view {
                   std::uint32_t* offsets_size,
                   size_t num_items)
             : _num_items(num_items),
-              _data_layer(data_layer),
-              _mlb_layer(mlb_layer),
+              _data_layer(bitset<bitmap_t>{data_layer}),
+              _mlb_layer(bitset<bitmap_t>{mlb_layer}),
               _offsets(offsets),
               _offsets_size(offsets_size) {}
 
@@ -31,7 +31,7 @@ struct frontier_view {
         }
         if (!_mlb_layer.test(idx / divide_factor)) {
             _mlb_layer.atomic_set(idx / divide_factor);
-        };
+        }
     }
 
     inline void remove(std::uint32_t idx) const {
@@ -65,67 +65,60 @@ struct frontier_view {
 
 #ifdef ONEDAL_DATA_PARALLEL
 
-template <typename ElementType = std::uint32_t, sycl::usm::alloc Alloc = sycl::usm::alloc::shared>
+template <typename ElementType = std::uint32_t>
 class frontier {
     using bitmap_t = ElementType;
     using buffer_t = std::uint32_t;
 
 public:
-    frontier(sycl::queue& queue, std::size_t num_items) : _queue(queue), _num_items(num_items) {
-        auto array_size =
+    frontier(sycl::queue& queue, std::size_t num_items, sycl::usm::alloc alloc = sycl::usm::alloc::shared) : _queue(queue), _num_items(num_items) {
+        std::int64_t array_size =
             (num_items + bitset<bitmap_t>::element_bitsize - 1) / bitset<bitmap_t>::element_bitsize;
-        auto mlb_size = (array_size + bitset<bitmap_t>::element_bitsize - 1) /
+        std::int64_t mlb_size = (array_size + bitset<bitmap_t>::element_bitsize - 1) /
                         bitset<bitmap_t>::element_bitsize;
-        auto [data_layer, e1] =
-            ndarray<bitmap_t, 1>::zeros(queue, { static_cast<std::int64_t>(array_size) }, Alloc);
-        auto [mlb_layer, e2] =
-            ndarray<bitmap_t, 1>::zeros(queue, { static_cast<std::int64_t>(mlb_size) }, Alloc);
-        auto [offsets, e3] = 
-            ndarray<std::uint32_t, 1>::zeros(queue, { static_cast<std::int64_t>(array_size + 1) }, Alloc); /// First offset is to keep the size of the frontier
-        _buffer = ndarray<std::uint32_t, 1>::empty(queue, { static_cast<std::int64_t>(10) }, Alloc);
+        _data_layer =
+            ndarray<bitmap_t, 1>::empty(_queue, { array_size }, alloc);
+        _mlb_layer =
+            ndarray<bitmap_t, 1>::empty(_queue, { mlb_size }, alloc);
+        _offsets =
+            ndarray<std::uint32_t, 1>::empty(_queue, { array_size + 1 }, alloc); /// First offset is to keep the size of the frontier
+        _buffer = ndarray<std::uint32_t, 1>::empty(_queue, { 10 }, alloc);
+
+        sycl::event e1, e2, e3;
+        e1 = _data_layer.fill(_queue, bitmap_t(0));
+        e2 = _mlb_layer.fill(_queue, bitmap_t(0));
+        e3 = _offsets.fill(_queue, buffer_t(0));
 
         e1.wait_and_throw();
         e2.wait_and_throw();
         e3.wait_and_throw();
-
-        _data_layer = std::move(data_layer);
-        _mlb_layer = std::move(mlb_layer);
-        _offsets = std::move(offsets);
     }
 
-    frontier_view<bitmap_t> get_device_view() const {
+    const frontier_view<bitmap_t> get_device_view() const {
         auto offsets_size_pointer = _offsets.get_mutable_data();
         auto offsets_pointer = _offsets.get_mutable_data() + 1;
 
-        return frontier_view<bitmap_t>(this->get_data_ptr(),
-                                       this->get_mlb_ptr(),
+        return frontier_view<bitmap_t>(_data_layer.get_mutable_data(),
+                                       _mlb_layer.get_mutable_data(),
                                        offsets_pointer,
                                        offsets_size_pointer,
                                        _data_layer.get_count());
     }
 
-    inline bitmap_t* get_data_ptr() const {
-        return _data_layer.get_mutable_data();
-    }
-
-    inline bitmap_t* get_mlb_ptr() const {
-        return _mlb_layer.get_mutable_data();
+    inline ndview<bitmap_t, 1> get_data() const {
+        return _data_layer;
     }
 
-    inline std::uint32_t* get_offsets_ptr() const {
-        return &(_offsets.get_mutable_data()[1]);
+    inline ndview<bitmap_t, 1> get_mlb() const {
+        return _mlb_layer;
     }
 
-    inline std::uint32_t* get_offsets_size_ptr() const {
-        return _offsets.get_mutable_data();
+    inline ndview<std::uint32_t, 1> get_offsets() const {
+        return _offsets.slice(1, _offsets.get_count());
     }
 
-    inline size_t get_data_size() const {
-        return _data_layer.get_count();
-    }
-
-    inline size_t get_mlb_size() const {
-        return _mlb_layer.get_count();
+    inline ndview<std::uint32_t, 1> get_offsets_size() const {
+        return _offsets.slice(0, 1);
     }
 
     bool empty() const {
@@ -137,7 +130,7 @@ class frontier {
             cgh.depends_on(copy_e);
             const auto range = make_range_1d(_mlb_layer.get_count());
             auto sum_reduction = sycl::reduction(empty_buff_ptr, sycl::plus<>());
-            auto* f_ptr = this->get_mlb_ptr();
+            auto* const f_ptr = _mlb_layer.get_mutable_data();
 
             cgh.parallel_for(range, sum_reduction, [=](sycl::id<1> idx, auto& sum_v) {
                 sum_v += f_ptr[idx];
@@ -148,31 +141,19 @@ class frontier {
     }
 
     void insert(bitmap_t idx) {
-        if (idx >= _data_layer.get_count() * bitset<bitmap_t>::element_bitsize) {
-            throw dal::domain_error("Index is out of range");
-        }
         auto view = this->get_device_view();
-        _queue
-            .single_task([=]() {
-                view.insert(idx);
-            })
-            .wait_and_throw();
+        _queue.submit(
+            [&](sycl::handler& cgh) {
+                cgh.single_task([=]() {
+                    view.insert(idx);
+                });
+            }
+        ).wait_and_throw();
     }
 
     bool check(bitmap_t idx) const {
-        auto check_buff = _buffer.slice(0, 1);
-        fill(_queue, check_buff, buffer_t(0)).wait();
-        auto check_buff_ptr = check_buff.get_mutable_data();
-
-        auto e = _queue.submit([&](sycl::handler& cgh) {
-            auto view = this->get_device_view();
-
-            cgh.single_task([=]() {
-                check_buff_ptr[0] = view.check(idx) ? buffer_t(1) : buffer_t(0);
-            });
-        });
-        auto check_res = check_buff.at_device(_queue, 0, { e });
-        return check_res == buffer_t(1);
+        bitmap_t tmp_data = _data_layer.at_device(_queue, idx / bitset<bitmap_t>::element_bitsize);
+        return (tmp_data & (static_cast<bitmap_t>(1) << (idx % bitset<bitmap_t>::element_bitsize))) != 0;
     }
 
     void clear() {
@@ -187,16 +168,19 @@ class frontier {
     sycl::event compute_active_frontier() const {
         auto bitmap = this->get_device_view();
 
+        auto offsets_size_pointer = _offsets.get_mutable_data();
+        auto offsets_pointer = _offsets.get_mutable_data() + 1;
+
         uint32_t element_bitsize = decltype(bitmap._mlb_layer)::element_bitsize;
         size_t local_range = 1024; // Adjust as needed
         size_t global_range =
             _mlb_layer.get_count() + local_range - (_mlb_layer.get_count() % local_range);
 
         bool use_local_mem =
-            device_local_mem_size(this->_queue) >= (local_range * element_bitsize * sizeof(uint32_t));
+            device_local_mem_size(this->_queue) >= static_cast<std::int64_t>(local_range * element_bitsize * sizeof(uint32_t));
 
         auto e0 = _queue.submit([&](sycl::handler& cgh) {
-            cgh.single_task([=, offsets_size = this->get_offsets_size_ptr(), buffer_ptr = this->_buffer.get_mutable_data(), CAF_FLAG = this->_CAF_FLAG]() {
+            cgh.single_task([=, offsets_size = this->get_offsets_size().get_mutable_data(), buffer_ptr = this->_buffer.get_mutable_data(), CAF_FLAG = this->_CAF_FLAG]() {
                 buffer_ptr[CAF_FLAG] = offsets_size[0] == 0 ? 1 : 0;
             });
         });
@@ -207,9 +191,9 @@ class frontier {
             if (!use_local_mem || true) { // Force to use global memory for simplicity
                 cgh.parallel_for(make_range_1d(_mlb_layer.get_count()),
                     [=,
-                    offsets = this->get_offsets_ptr(),
-                    offsets_size = this->get_offsets_size_ptr(),
-                    data_layer = this->get_mlb_ptr(),
+                    offsets = offsets_pointer,
+                    offsets_size = offsets_size_pointer,
+                    data_layer = this->_mlb_layer.get_mutable_data(),
                     buffer = this->_buffer.get_mutable_data(),
                     CAF_FLAG = this->_CAF_FLAG](sycl::id<1> idx) {
     
@@ -234,9 +218,9 @@ class frontier {
                 cgh.parallel_for(
                     make_multiple_nd_range_1d(global_range, local_range),
                     [=,
-                    offsets = this->get_offsets_ptr(),
-                    offsets_size = this->get_offsets_size_ptr(),
-                    data_layer = this->get_mlb_ptr(),
+                    offsets = offsets_pointer,
+                    offsets_size = offsets_size_pointer,
+                    data_layer = this->_mlb_layer.get_mutable_data(),
                     size = this->_num_items,
                     buffer = this->_buffer.get_mutable_data(),
                     CAF_FLAG = this->_CAF_FLAG](sycl::nd_item<1> item) {
@@ -293,7 +277,7 @@ class frontier {
     ndarray<std::uint32_t, 1> _offsets;
     ndarray<buffer_t, 1> _buffer;
     const size_t _TMP_VAR = 0;
-    const size_t _CAF_FLAG = 0; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
+    const size_t _CAF_FLAG = 1; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
 };
 
 #endif
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
index fa05bd1f9e7..93bb2737204 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
@@ -17,67 +17,14 @@ void print_device_name(sycl::queue& queue) {
 }
 
 template<typename T>
-void print_frontier(const T* data, size_t num_items) {
+void print_frontier(const T* data, size_t count, size_t num_items) {
     size_t element_bitsize = sizeof(T) * 8;
-    for (size_t i = 0; i < num_items; ++i) {
-        size_t offset = num_items / element_bitsize;
-        size_t bit = i % element_bitsize;
-        std::cout << ((data[offset] & (static_cast<T>(1) << bit)) ? "1" : "0");
-    }       
-}
-
-TEST("frontier basic operations", "[frontier]") {
-    DECLARE_TEST_POLICY(policy);
-    auto& queue = policy.get_queue();
-    print_device_name(queue);
-
-    const std::size_t num_items = 100;
-    auto f = frontier<std::uint32_t>(queue, num_items);
-    auto view = f.get_device_view();
-    size_t expected_data_layer_size = (num_items + bitset<std::uint32_t>::element_bitsize - 1) /
-                                      bitset<std::uint32_t>::element_bitsize;
-    size_t expected_mlb_layer_size =
-        (expected_data_layer_size + bitset<std::uint32_t>::element_bitsize - 1) /
-        bitset<std::uint32_t>::element_bitsize;
-
-    SECTION("frontier has correct data layer size", "[frontier]") {
-        REQUIRE(f.get_data_size() == expected_data_layer_size);
-
-        REQUIRE(f.get_mlb_size() == expected_mlb_layer_size);
+    for (size_t i = 0; i < count; ++i) {
+        for (size_t j = 0; j < element_bitsize; ++j) {
+            std::cout << ((data[i] & (static_cast<T>(1) << j)) ? "1" : "0");
+        }
     }
-
-    SECTION("frontier can insert elements", "[frontier]") {
-        view.insert(0);
-        view.insert(2);
-        view.insert(bitset<std::uint32_t>::element_bitsize);
-
-        auto data_layer = f.get_data_ptr();
-        auto mlb_layer = f.get_mlb_ptr();
-
-        REQUIRE(data_layer[0] == static_cast<uint32_t>(5));
-        REQUIRE(data_layer[1] == static_cast<uint32_t>(1));
-        REQUIRE(mlb_layer[0] == static_cast<uint32_t>(3));
-    }
-
-    SECTION("frontier can check elements", "[frontier]") {
-        view.insert(0);
-        view.insert(2);
-        view.insert(32);
-        view.insert(64);
-
-        REQUIRE(view.check(0) == true);
-        REQUIRE(view.check(1) == false);
-        REQUIRE(view.check(2) == true);
-        REQUIRE(view.check(3) == false);
-        REQUIRE(view.check(31) == false);
-        REQUIRE(view.check(32) == true);
-        REQUIRE(view.check(33) == false);
-        REQUIRE(view.check(63) == false);
-        REQUIRE(view.check(64) == true);
-        REQUIRE(view.check(65) == false);
-    }
-
-} // TEST "frontier basic operations"
+}
 
 TEST("frontier queue basic operations", "[frontier]") {
     DECLARE_TEST_POLICY(policy);
@@ -85,79 +32,36 @@ TEST("frontier queue basic operations", "[frontier]") {
     print_device_name(queue);
 
     const std::size_t num_items = 100;
-    auto f = frontier<std::uint32_t, sycl::usm::alloc::device>(queue, num_items);
-
-    SECTION("empty function", "[frontier]") {
-        REQUIRE(f.empty() == true);
-        queue.single_task([=, view = f.get_device_view()]() {
-            view.insert(0);
-        }).wait_and_throw();
-        std::cout << (f.check(0) ? "Frontier is not empty" : "Frontier is empty") << std::endl;
-        std::vector<std::uint32_t> data_layer_cpy(f.get_data_size());
-        REQUIRE(f.empty() == false);
-    }
-
-    SECTION("insert function", "[frontier]") {
-        f.insert(0);
-        f.insert(2);
-        f.insert(bitset<std::uint32_t>::element_bitsize);
-
-        auto* data_layer = f.get_data_ptr();
-        auto* mlb_layer = f.get_mlb_ptr();
-
-        bool* check = sycl::malloc_device<bool>(1, queue);
-        queue.single_task([=, view = f.get_device_view()]() {
-            check[0] = data_layer[0] == static_cast<uint32_t>(5);
-            check[0] &= data_layer[1] == static_cast<uint32_t>(1);
-            check[0] &= mlb_layer[0] == static_cast<uint32_t>(3);
-        }).wait_and_throw();
-        bool tmp_check;
-        queue.copy(check, &tmp_check, 1).wait_and_throw();
-        REQUIRE(tmp_check == true);
-        sycl::free(check, queue);
-    }
-
-    SECTION("check function", "[frontier]") {
-        f.insert(0);
-        REQUIRE(f.check(0) == true);
-        REQUIRE(f.check(1) == false);
+    auto f = frontier<std::uint32_t>(queue, num_items, sycl::usm::alloc::shared);
+
+    REQUIRE(f.empty() == true);
+    f.insert(0);
+    f.insert(2);
+    f.insert(32);
+    f.insert(128);
+
+    REQUIRE(f.empty() == false);
+
+    REQUIRE(f.get_data().at_device(queue, 0) == 5);
+    REQUIRE(f.get_data().at_device(queue, 1) == 1);
+    REQUIRE(f.get_mlb().at_device(queue, 0) == 19);
+
+    REQUIRE(f.check(0) == true);
+    REQUIRE(f.check(1) == false);
+    REQUIRE(f.check(2) == true);
+    REQUIRE(f.check(3) == false);
+    REQUIRE(f.check(bitset<std::uint32_t>::element_bitsize) == true);
+    REQUIRE(f.check(bitset<std::uint32_t>::element_bitsize + 1) == false);
+    
+    auto e = f.compute_active_frontier();
+    REQUIRE(f.get_offsets_size().at_device(queue, 0, {e}) == 3);
+    for (int i = 0; i < 3; i++) {
+        std::cout << "Active frontier item " << i << ": " << f.get_offsets().at_device(queue, i) << std::endl;
     }
 
-    SECTION("clear function", "[frontier]") {
-        f.insert(0);
-        f.insert(2);
-        f.insert(bitset<std::uint32_t>::element_bitsize);
-        REQUIRE(f.empty() == false);
-        f.clear();
-        REQUIRE(f.empty() == true);
-    }
+    f.clear();
+    REQUIRE(f.empty() == true);
 
 } // TEST "frontier queue operations"
 
-TEST("compute active frontier", "[frontier]") {
-    DECLARE_TEST_POLICY(policy);
-    auto& queue = policy.get_queue();
-
-    const std::size_t num_items = 100000;
-    auto f = frontier<std::uint32_t, sycl::usm::alloc::host>(queue, num_items);
-
-    queue.single_task([=, view = f.get_device_view()]() {
-        view.insert(0);
-        view.insert(2);
-        view.insert(32);
-        view.insert(33);
-        view.insert(64);
-        view.insert(65);
-        view.insert(95);
-    }).wait_and_throw();
-
-    auto e = f.compute_active_frontier();
-    e.wait();
-
-    auto offsets_size = f.get_offsets_size_ptr();
-
-    REQUIRE(offsets_size[0] == 3);
-    f.clear();
-} // TEST "compute active frontier"
-
 } // namespace oneapi::dal::backend::primitives::test

From b14112805e8aa8f27df40d88a88d76663880ea02 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Thu, 17 Jul 2025 19:50:09 +0200
Subject: [PATCH 08/69] feat: add advance operation tests for frontier class;
 include device name printing and frontier checks

---
 .../dal/backend/primitives/bitset/bitset.hpp  |   2 +
 .../dal/backend/primitives/frontier.hpp       |   4 +-
 .../primitives/frontier/advance_dpc.hpp       |  85 +++++-----
 .../primitives/frontier/frontier_dpc.hpp      |   4 +-
 .../dal/backend/primitives/frontier/graph.hpp | 158 ++++++++++++++++++
 .../frontier/test/advance_frontier_dpc.cpp    |  82 +++++++++
 6 files changed, 291 insertions(+), 44 deletions(-)
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp

diff --git a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
index 63d728c5cc0..a821c04f00a 100644
--- a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
@@ -1,3 +1,5 @@
+#pragma once
+
 #include "oneapi/dal/backend/memory.hpp"
 
 namespace oneapi::dal::backend::primitives {
diff --git a/cpp/oneapi/dal/backend/primitives/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier.hpp
index 0ce734a968e..9e35cff3f12 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier.hpp
@@ -1 +1,3 @@
-#include "oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp"
\ No newline at end of file
+#include "oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp"
+#include "oneapi/dal/backend/primitives/frontier/advance_dpc.hpp"
+#include "oneapi/dal/backend/primitives/frontier/graph.hpp"
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
index da78687dcb0..31eb9bdb909 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
@@ -1,6 +1,8 @@
 #pragma once
 
-#include "oneapi/dal/backend/primitives/frontier.hpp"
+#include "oneapi/dal/backend/primitives/ndarray.hpp"
+#include "oneapi/dal/backend/primitives/frontier/graph.hpp"
+#include "oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp"
 
 
 namespace oneapi::dal::backend::primitives {
@@ -35,9 +37,9 @@ struct Context {
   inline void complete_iteration(ContextState& state) const { state.group_offset += state.item.get_group_range(0); }
 
   inline size_t get_assigned_element(const ContextState& state) const {
-    const uint16_t bitmap_range = in_dev_frontier.getBitmapRange();
+    const uint16_t bitmap_range = in_dev_frontier.get_element_bitsize();
     const uint32_t acutal_id_offset = (state.group_offset * state.coarsening_factor) + (state.item.get_local_linear_id() / bitmap_range);
-    const int* bitmap_offsets = in_dev_frontier.get_offsets();
+    const auto* bitmap_offsets = in_dev_frontier.get_offsets();
     // const size_t acutal_id_offset = (item.get_group_linear_id() * coarsening_factor) + (item.get_local_linear_id() / bitmap_range);
     const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * bitmap_range) + (state.item.get_local_linear_id() % bitmap_range);
     return assigned_vertex;
@@ -55,15 +57,15 @@ struct Context {
 
 template<typename T,
          typename ContextT,
-         graph::detail::DeviceGraphConcept GraphDevT,
+         typename GraphDevT,
          typename LambdaT>
 struct BitmapKernel {
   void operator()(sycl::nd_item<1> item) const {
     // 0. retrieve global and local ids
-    const size_t gid = item.get_global_linear_id();
+    // const size_t gid = item.get_global_linear_id();
     const size_t lid = item.get_local_linear_id();
     const auto wgroup = item.get_group();
-    const auto wgroup_id = item.get_group_linear_id();
+    // const auto wgroup_id = item.get_group_linear_id();
     const size_t wgroup_size = wgroup.get_local_range(0);
     const auto sgroup = item.get_sub_group();
     const auto sgroup_id = sgroup.get_group_id();
@@ -85,7 +87,7 @@ struct BitmapKernel {
 
       const uint32_t offset = sgroup_id * sgroup_size;
       if (context.check(state, assigned_vertex)) {
-        uint32_t n_edges = graph_dev.getDegree(assigned_vertex); // GRAPH degree of the vertex
+        uint32_t n_edges = graph_dev.get_degree(assigned_vertex); // GRAPH degree of the vertex
         if (n_edges >= wgroup_size * wgroup_size) { // assign to the workgroup
           uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
           n_edges_wg[loc] = n_edges;
@@ -110,8 +112,8 @@ struct BitmapKernel {
 
         for (auto j = lid; j < n_edges; j += wgroup_size) {
           auto n = start + j;
-          auto edge = n.getIndex(); // GRAPH edge index
-          auto weight = graph_dev.getEdgeWeight(edge); // GRAPH edge weight
+          auto edge = n.get_index(); // GRAPH edge index
+          auto weight = graph_dev.get_weight(edge); // GRAPH edge weight
           auto neighbor = *n;
           if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
         }
@@ -130,8 +132,8 @@ struct BitmapKernel {
 
         for (auto j = llid; j < n_edges; j += sgroup_size) {
           auto n = start + j;
-          auto edge = n.getIndex(); // GRAPH edge index
-          auto weight = graph_dev.getEdgeWeight(edge); // GRAPH edge weight
+          auto edge = n.get_index(); // GRAPH edge index
+          auto weight = graph_dev.get_weight(edge); // GRAPH edge weight
           auto neighbor = *n;
           if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
         }
@@ -146,8 +148,8 @@ struct BitmapKernel {
         auto end = graph_dev.end(vertex); // GRAPH edge iterator
 
         for (auto n = start; n != end; ++n) {
-          auto edge = n.getIndex(); // GRAPH edge index
-          auto weight = graph_dev.getEdgeWeight(edge); // GRAPH edge weight
+          auto edge = n.get_index(); // GRAPH edge index
+          auto weight = graph_dev.get_weight(edge); // GRAPH edge weight
           auto neighbor = *n;
           if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
         }
@@ -170,42 +172,43 @@ struct BitmapKernel {
   const LambdaT functor;
 };
 
-template<typename T,
-         graph::detail::GraphConcept GraphT,
-         typename InFrontierT,
-         typename OutFrontierT,
+template<typename FrontierSizeT,
+         typename GraphT,
          typename LambdaT>
-sygraph::Event launchBitmapKernel(GraphT& graph, const InFrontierT& in, const OutFrontierT& out, LambdaT&& functor, size_t expected_size) {
-  sycl::queue& q = graph.getQueue();
+sycl::event advance(const GraphT& graph, frontier<FrontierSizeT>& in, frontier<FrontierSizeT>& out, LambdaT&& functor, size_t expected_size = 0) {
+  sycl::queue& q = graph.get_queue();
 
-  size_t num_nodes = graph.getVertexCount();
+  size_t num_nodes = graph.get_vertex_count();
 
-  using element_t = std::conditional_t<InFW == sygraph::frontier::frontier_view::vertex, typename GraphT::vertex_t, typename GraphT::edge_t>;
+  using element_t = FrontierSizeT;
+  // using element_t = std::conditional_t<InFW == sygraph::frontier::frontier_view::vertex, typename GraphT::vertex_t, typename GraphT::edge_t>;
 
   auto in_dev_frontier = in.get_device_view();
   auto out_dev_frontier = out.get_device_view();
-  auto graph_dev = graph.getDeviceGraph(); // GRAPH device view
+  auto graph_dev = graph.get_device_view(); // GRAPH device view
 
-  size_t coarsening_factor = types::detail::COMPUTE_UNIT_SIZE / 16; // sygraph::detail::device::getSubgroupSize(q);
+  size_t coarsening_factor = 256 /*CU size*/ / 16 /*Subgroup Size*/;
 
   sycl::event to_wait;
   sycl::range<1> local_range;
   size_t global_size;
-  size_t bitmap_range = in.get_element_bitsize();
+  size_t bitmap_range = in_dev_frontier.get_element_bitsize();
   to_wait = in.compute_active_frontier();
   local_range = {bitmap_range * coarsening_factor};
   if (expected_size > 0) {
     global_size = {expected_size + (local_range[0] - (expected_size % local_range[0]))};
   } else {
-    global_size = {local_range[0] * (sygraph::detail::device::getMaxComputeUints(q) * 8)};
+    global_size = {local_range[0] * 128};
+    // global_size = {local_range[0] * (sygraph::detail::device::getMaxComputeUints(q) * 8)};
   }
 
   sycl::range<1> global_range{global_size > local_range[0] ? global_size + (local_range[0] - (global_size % local_range[0])) : local_range[0]};
 
-  Context<InFW, OutFW, decltype(in_dev_frontier), decltype(out_dev_frontier)> context{num_nodes, in_dev_frontier, out_dev_frontier};
-  using bitmap_kernel_t = BitmapKernel<InFW, OutFW, element_t, decltype(context), decltype(graph_dev), LambdaT>;
+  Context<decltype(in_dev_frontier), decltype(out_dev_frontier)> context{num_nodes, in_dev_frontier, out_dev_frontier};
+  using bitmap_kernel_t = BitmapKernel<element_t, decltype(context), decltype(graph_dev), LambdaT>;
 
-  const uint32_t max_num_subgroups = sygraph::detail::device::getMaxNumSubgroups(q);
+  const uint32_t max_num_subgroups = 32;
+  // const uint32_t max_num_subgroups = sygraph::detail::device::getMaxNumSubgroups(q);
 
   auto e = q.submit([&](sycl::handler& cgh) {
     cgh.depends_on(to_wait);
@@ -222,19 +225,19 @@ sygraph::Event launchBitmapKernel(GraphT& graph, const InFrontierT& in, const Ou
     sycl::local_accessor<uint32_t, 1> individual_reduce_tail{1, cgh};
 
 
-    cgh.parallel_for<workgroup_mapped_advance_kernel<InFW, OutFW>>(sycl::nd_range<1>{global_range, local_range},
-                                                                   bitmap_kernel_t{context,
-                                                                                   graph_dev,
-                                                                                   n_edges_wg,
-                                                                                   n_edges_sg,
-                                                                                   visited,
-                                                                                   subgroup_reduce,
-                                                                                   subgroup_reduce_tail,
-                                                                                   subgroup_ids,
-                                                                                   workgroup_reduce,
-                                                                                   workgroup_reduce_tail,
-                                                                                   workgroup_ids,
-                                                                                   std::forward<LambdaT>(functor)});
+    cgh.parallel_for(sycl::nd_range<1>{global_range, local_range},
+      bitmap_kernel_t{context,
+                      graph_dev,
+                      n_edges_wg,
+                      n_edges_sg,
+                      visited,
+                      subgroup_reduce,
+                      subgroup_reduce_tail,
+                      subgroup_ids,
+                      workgroup_reduce,
+                      workgroup_reduce_tail,
+                      workgroup_ids,
+                      std::forward<LambdaT>(functor)});
   });
   return {e};
 }
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
index ce2747c4c39..05c7c310967 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -47,11 +47,11 @@ struct frontier_view {
     }
 
     inline std::uint32_t* get_offsets() const {
-        return _offsets_size;
+        return _offsets;
     }
 
     inline std::uint32_t* get_offsets_size() const {
-        return _offsets;
+        return _offsets_size;
     }
 
     size_t _num_items;
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index e69de29bb2d..825a119dbc5 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -0,0 +1,158 @@
+#pragma once
+
+#include "oneapi/dal/common.hpp"
+#include "oneapi/dal/graph/detail/common.hpp"
+#include "oneapi/dal/graph/detail/container.hpp"
+#include "oneapi/dal/backend/primitives/bitset.hpp"
+#include "oneapi/dal/backend/primitives/ndarray.hpp"
+
+namespace oneapi::dal::backend::primitives {
+
+template<typename VertexT = std::uint32_t, typename EdgeT = std::uint32_t, typename WeightT = std::uint32_t>
+class csr_graph_view {
+  using vertex_t = VertexT;
+  using edge_t = EdgeT;
+  using weight_t = WeightT;
+
+  struct neighbor_iterator_t {
+    neighbor_iterator_t(const vertex_t* start_ptr, vertex_t* ptr)
+      : _ptr(ptr), _start_ptr(start_ptr) {}
+    
+    SYCL_EXTERNAL bool operator==(const neighbor_iterator_t& other) const {
+      return _ptr == other._ptr;
+    }
+
+    SYCL_EXTERNAL bool operator!=(const neighbor_iterator_t& other) const {
+      return _ptr != other._ptr;
+    }
+
+    SYCL_EXTERNAL neighbor_iterator_t& operator++() {
+      ++_ptr;
+      return *this;
+    }
+
+    SYCL_EXTERNAL neighbor_iterator_t operator+(int n) const {
+      neighbor_iterator_t tmp = *this;
+      tmp._ptr += n;
+      return tmp;
+    }
+
+    SYCL_EXTERNAL vertex_t operator*() const {
+      return *_ptr;
+    }
+
+    SYCL_EXTERNAL edge_t get_index() const {
+      return static_cast<edge_t>(_ptr - _start_ptr);
+    }
+
+    vertex_t* _ptr;
+    const vertex_t* _start_ptr;
+  };
+
+public:
+  csr_graph_view(std::size_t num_nodes,
+                 vertex_t* row_ptr,
+                 edge_t* col_indices,
+                 weight_t* weights)
+      : _num_nodes(num_nodes),
+        _row_ptr(row_ptr),
+        _col_indices(col_indices),
+        _weights(weights) {
+    ONEDAL_ASSERT(_row_ptr != nullptr, "Row pointer must not be null");
+    ONEDAL_ASSERT(_col_indices != nullptr, "Column indices must not be null");
+    ONEDAL_ASSERT(_weights != nullptr, "Weights must not be null");
+  }
+
+  SYCL_EXTERNAL inline std::uint32_t get_degree(const vertex_t vertex) const {
+    ONEDAL_ASSERT(vertex < _num_nodes, "Vertex index out of bounds");
+    return static_cast<std::uint32_t>(_row_ptr[vertex + 1] - _row_ptr[vertex]);
+  }
+
+  SYCL_EXTERNAL inline weight_t get_weight(const edge_t edge) const {
+    return _weights[edge];
+  }
+
+  SYCL_EXTERNAL inline neighbor_iterator_t begin(vertex_t vertex) const {
+    ONEDAL_ASSERT(vertex < _num_nodes, "Vertex index out of bounds");
+    return neighbor_iterator_t(_col_indices, _col_indices + _row_ptr[vertex]);
+  }
+
+  SYCL_EXTERNAL inline neighbor_iterator_t end(vertex_t vertex) const {
+    ONEDAL_ASSERT(vertex < _num_nodes, "Vertex index out of bounds");
+    return neighbor_iterator_t(_col_indices, _col_indices + _row_ptr[vertex + 1]);
+  }
+
+private:
+  std::size_t _num_nodes;
+  vertex_t* _row_ptr;
+  edge_t* _col_indices;
+  weight_t* _weights;
+};
+
+template<typename VertexT = std::uint32_t, typename EdgeT = std::uint32_t, typename WeightT = std::uint32_t>
+class csr_graph {
+  using vertex_t = VertexT;
+  using edge_t = EdgeT;
+  using weight_t = WeightT;
+  using graph_view_t = csr_graph_view<vertex_t, edge_t, weight_t>;
+
+public:
+  csr_graph(sycl::queue& queue,
+            std::vector<VertexT> row_ptr,
+            std::vector<EdgeT> col_indices,
+            std::vector<WeightT> weights = {},
+            sycl::usm::alloc alloc = sycl::usm::alloc::shared) 
+            : _queue(queue), _num_nodes(row_ptr.size() - 1) {
+
+    std::int64_t row_ptr_size = static_cast<std::int64_t>(row_ptr.size());
+    std::int64_t col_indices_size = static_cast<std::int64_t>(col_indices.size());
+    std::int64_t weights_size = static_cast<std::int64_t>(weights.size());
+
+    _row_ptr = ndarray<vertex_t, 1>::empty(_queue, {row_ptr_size}, alloc);
+    _col_indices = ndarray<edge_t, 1>::empty(_queue, {col_indices_size}, alloc);
+    _weights = ndarray<weight_t, 1>::empty(_queue, {weights_size}, alloc);
+
+    auto e1 = dal::backend::copy_host2usm(_queue,
+                              _row_ptr.get_mutable_data(),
+                              row_ptr.data(),
+                              row_ptr.size());
+
+    auto e2 = dal::backend::copy_host2usm(_queue,
+                              _col_indices.get_mutable_data(),
+                              col_indices.data(),
+                              col_indices.size());
+
+    auto e3 = dal::backend::copy_host2usm(_queue,
+                              _weights.get_mutable_data(),
+                              weights.data(),
+                              weights.size());
+
+    e1.wait_and_throw();
+    e2.wait_and_throw();
+    e3.wait_and_throw();
+  }
+
+  graph_view_t get_device_view() const {
+    return { _num_nodes, 
+             _row_ptr.get_mutable_data(), 
+             _col_indices.get_mutable_data(), 
+             _weights.get_mutable_data() };
+  }
+
+  sycl::queue& get_queue() const {
+    return _queue;
+  }
+
+  std::size_t get_vertex_count() const {
+    return _num_nodes;
+  }
+
+private:
+  sycl::queue& _queue;
+  std::size_t _num_nodes;
+  ndarray<vertex_t, 1> _row_ptr;
+  ndarray<edge_t, 1> _col_indices;
+  ndarray<weight_t, 1> _weights;
+};
+
+} // namespace oneapi::dal::backend::primitives
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp
new file mode 100644
index 00000000000..0dc930e28a0
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp
@@ -0,0 +1,82 @@
+#include "oneapi/dal/backend/primitives/frontier.hpp"
+
+#include "oneapi/dal/test/engine/common.hpp"
+#include "oneapi/dal/test/engine/fixtures.hpp"
+#include "oneapi/dal/test/engine/dataframe.hpp"
+
+#include "oneapi/dal/test/engine/common.hpp"
+#include "oneapi/dal/test/engine/fixtures.hpp"
+#include "oneapi/dal/test/engine/dataframe.hpp"
+
+namespace oneapi::dal::backend::primitives::test {
+
+void print_device_name(sycl::queue& queue) {
+    const auto device = queue.get_device();
+    const auto device_name = device.get_info<sycl::info::device::name>();
+    std::cout << "Running on device: " << device_name << std::endl;
+}
+
+template<typename T>
+void print_frontier(const T* data, size_t count, size_t num_items) {
+    size_t element_bitsize = sizeof(T) * 8;
+    for (size_t i = 0; i < count; ++i) {
+        for (size_t j = 0; j < element_bitsize; ++j) {
+            std::cout << ((data[i] & (static_cast<T>(1) << j)) ? "1" : "0");
+        }
+    }
+}
+
+TEST("test advance operation", "[advance]") {
+    DECLARE_TEST_POLICY(policy);
+    auto& queue = policy.get_queue();
+    print_device_name(queue);
+
+    std::vector<std::uint32_t> row_ptr = {0, 2, 4, 6};
+    std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 0, 1};
+    std::vector<std::uint32_t> weights = {1, 1, 1, 1, 1, 1};
+
+    auto graph = csr_graph(queue, row_ptr, col_indices, weights);
+    auto first_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+    auto second_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+    auto third_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+
+    first_frontier.insert(0);
+
+    REQUIRE(first_frontier.check(0) == true);
+    REQUIRE(first_frontier.check(1) == false);
+    REQUIRE(first_frontier.check(2) == false);
+    
+    std::cout << "First Frontier: ";
+    for (size_t i = 0; i < graph.get_vertex_count(); ++i) {
+        std::cout << "Vertex " << i << ": " << (first_frontier.check(i) ? "in frontier" : "not in frontier") << std::endl;
+    }
+    
+    advance(graph, first_frontier, second_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
+        return true; // Always advance
+    }).wait_and_throw();
+
+    REQUIRE(second_frontier.check(0) == false);
+    REQUIRE(second_frontier.check(1) == true);
+    REQUIRE(second_frontier.check(2) == true);
+    
+    std::cout << "Second Frontier: ";
+    for (size_t i = 0; i < graph.get_vertex_count(); ++i) {
+        std::cout << "Vertex " << i << ": " << (second_frontier.check(i) ? "in frontier" : "not in frontier") << std::endl;
+    }
+
+    advance(graph, second_frontier, third_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
+        return true; // Always advance
+    }).wait_and_throw();
+
+    std::cout << "Third Frontier: ";
+    for (size_t i = 0; i < graph.get_vertex_count(); ++i) {
+        std::cout << "Vertex " << i << ": " << (third_frontier.check(i) ? "in frontier" : "not in frontier") << std::endl;
+    }
+
+    REQUIRE(third_frontier.check(0) == true);
+    REQUIRE(third_frontier.check(1) == true);
+    REQUIRE(third_frontier.check(2) == true);
+
+} // TEST "test advance operation"
+
+} // namespace oneapi::dal::backend::primitives::test

From 40eea0b3f1a2afa225919deb8653b582c51af305 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 23 Jul 2025 17:31:52 +0200
Subject: [PATCH 09/69] fixed advance operator

---
 cpp/oneapi/dal/backend/common.hpp             |   5 +
 .../dal/backend/primitives/bitset/bitset.hpp  |   4 +-
 .../primitives/frontier/advance_dpc.hpp       | 204 ++++++++----------
 .../primitives/frontier/frontier_dpc.hpp      |   3 +-
 .../frontier/test/advance_frontier_dpc.cpp    |  91 ++++----
 5 files changed, 152 insertions(+), 155 deletions(-)

diff --git a/cpp/oneapi/dal/backend/common.hpp b/cpp/oneapi/dal/backend/common.hpp
index 8298d49867f..7821809a343 100644
--- a/cpp/oneapi/dal/backend/common.hpp
+++ b/cpp/oneapi/dal/backend/common.hpp
@@ -564,6 +564,11 @@ inline std::int64_t device_max_sg_size(const sycl::queue& q) {
     return dal::detail::integral_cast<std::int64_t>(*result_iter);
 }
 
+inline std::int64_t device_max_sg_count(const sycl::queue& q) {
+    const auto res = q.get_device().template get_info<sycl::info::device::max_num_sub_groups>();
+    return dal::detail::integral_cast<std::int64_t>(res);
+}
+
 inline std::int64_t propose_wg_size(const sycl::queue& q) {
     // TODO: a temporary solution that limits work item count used on the device.
     // Needs to change to more smart logic in the future.
diff --git a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
index a821c04f00a..a6479a2864e 100644
--- a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
@@ -44,7 +44,7 @@ class bitset {
         element_t bit_index = index % element_bitsize;
         sycl::atomic_ref<element_t, mem_order, mem_scope>
             atomic_element(_data[element_index]);
-        atomic_element.store(atomic_element.load() | (element_t(1) << bit_index));
+        atomic_element |= (element_t(1) << bit_index);
     }
 
     /// Clears the bit at the specified index using atomic operations.
@@ -55,7 +55,7 @@ class bitset {
         element_t bit_index = index % element_bitsize;
         sycl::atomic_ref<element_t, mem_order, mem_scope>
             atomic_element(_data[element_index]);
-        atomic_element.store(atomic_element.load() & ~(element_t(1) << bit_index));
+        atomic_element &= ~(element_t(1) << bit_index);
     }
 
     /// Checks if the bit at the specified index is set using atomic operations.
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
index 31eb9bdb909..b0530a26373 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
@@ -26,31 +26,26 @@ struct Context {
   inline ContextState init(sycl::nd_item<1>& item) const {
     return {
         item.get_group_linear_id(),
-        static_cast<uint16_t>(item.get_local_range(0) / in_dev_frontier.get_element_bitsize()),
-        in_dev_frontier.get_offsets_size()[0],
+        static_cast<uint16_t>(item.get_local_range(0) / in_dev_frontier.getBitmapRange()),
+        in_dev_frontier.getOffsetsSize()[0],
         item,
     };
   }
 
-  inline bool need_to_process(ContextState& state) const { return (state.group_offset * state.coarsening_factor < state.offsets_size); }
-
-  inline void complete_iteration(ContextState& state) const { state.group_offset += state.item.get_group_range(0); }
-
-  inline size_t get_assigned_element(const ContextState& state) const {
-    const uint16_t bitmap_range = in_dev_frontier.get_element_bitsize();
-    const uint32_t acutal_id_offset = (state.group_offset * state.coarsening_factor) + (state.item.get_local_linear_id() / bitmap_range);
+  inline size_t get_assigned_element(sycl::nd_item<1> item) const {
+    const uint16_t element_bitsize = in_dev_frontier.get_element_bitsize();
     const auto* bitmap_offsets = in_dev_frontier.get_offsets();
-    // const size_t acutal_id_offset = (item.get_group_linear_id() * coarsening_factor) + (item.get_local_linear_id() / bitmap_range);
-    const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * bitmap_range) + (state.item.get_local_linear_id() % bitmap_range);
+    const size_t coarsening_factor = item.get_local_range(0) / element_bitsize;
+    const uint32_t acutal_id_offset = (item.get_group_linear_id() * coarsening_factor) + (item.get_local_linear_id() / element_bitsize);
+    const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * element_bitsize) + (item.get_local_linear_id() % element_bitsize);
     return assigned_vertex;
   }
 
-  inline bool check(const ContextState& state, size_t vertex) const {
-    return vertex < limit && in_dev_frontier.check(vertex);
-    
+  inline bool check(sycl::nd_item<1> item, size_t vertex) const {
+    return vertex < limit && in_dev_frontier.check(vertex); 
   }
 
-  inline void insert(const ContextState& state, size_t vertex) const {
+  inline void insert(size_t vertex) const {
     out_dev_frontier.insert(vertex);
   }
 };
@@ -62,99 +57,91 @@ template<typename T,
 struct BitmapKernel {
   void operator()(sycl::nd_item<1> item) const {
     // 0. retrieve global and local ids
-    // const size_t gid = item.get_global_linear_id();
     const size_t lid = item.get_local_linear_id();
     const auto wgroup = item.get_group();
-    // const auto wgroup_id = item.get_group_linear_id();
     const size_t wgroup_size = wgroup.get_local_range(0);
     const auto sgroup = item.get_sub_group();
     const auto sgroup_id = sgroup.get_group_id();
     const size_t sgroup_size = sgroup.get_local_range()[0];
     const size_t llid = sgroup.get_local_linear_id();
 
-    auto state = context.init(item);
-
-
-    while (context.need_to_process(state)) {
-      const auto assigned_vertex = context.get_assigned_element(state);
-
-      // 1. load number of edges in local memory
-      if (sgroup.leader()) { subgroup_reduce_tail[sgroup_id] = 0; }
-      if (wgroup.leader()) { workgroup_reduce_tail[0] = 0; }
-
-      sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group> sg_tail{subgroup_reduce_tail[sgroup_id]};
-      sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group> wg_tail{workgroup_reduce_tail[0]};
-
-      const uint32_t offset = sgroup_id * sgroup_size;
-      if (context.check(state, assigned_vertex)) {
-        uint32_t n_edges = graph_dev.get_degree(assigned_vertex); // GRAPH degree of the vertex
-        if (n_edges >= wgroup_size * wgroup_size) { // assign to the workgroup
-          uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
-          n_edges_wg[loc] = n_edges;
-          workgroup_reduce[loc] = assigned_vertex;
-          workgroup_ids[loc] = lid;
-        } else if (n_edges >= sgroup_size) { // assign to the subgroup
-          uint32_t loc = sg_tail.fetch_add(static_cast<uint32_t>(1));
-          n_edges_sg[offset + loc] = n_edges;
-          subgroup_reduce[offset + loc] = assigned_vertex;
-          subgroup_ids[offset + loc] = lid;
-        }
-        visited[lid] = false;
-      } else {
-        visited[lid] = true;
+    const auto assigned_vertex = context.get_assigned_element(item);
+
+    // 1. load number of edges in local memory
+    if (sgroup.leader()) { subgroup_reduce_tail[sgroup_id] = 0; }
+    if (wgroup.leader()) { workgroup_reduce_tail[0] = 0; }
+
+    sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group> sg_tail{subgroup_reduce_tail[sgroup_id]};
+    sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group> wg_tail{workgroup_reduce_tail[0]};
+
+    const uint32_t offset = sgroup_id * sgroup_size;
+    if (context.check(item, assigned_vertex)) {
+      uint32_t n_edges = graph_dev.get_degree(assigned_vertex); 
+      if (n_edges >= wgroup_size * wgroup_size) { // assign to the workgroup
+        uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
+        n_edges_wg[loc] = n_edges;
+        workgroup_reduce[loc] = assigned_vertex;
+        workgroup_ids[loc] = lid;
+      } else if (n_edges >= sgroup_size) { // assign to the subgroup
+        uint32_t loc = sg_tail.fetch_add(static_cast<uint32_t>(1));
+        n_edges_sg[offset + loc] = n_edges;
+        subgroup_reduce[offset + loc] = assigned_vertex;
+        subgroup_ids[offset + loc] = lid;
       }
+      visited[lid] = false;
+    } else {
+      visited[lid] = true;
+    }
 
-      sycl::group_barrier(wgroup);
-      for (size_t i = 0; i < wg_tail.load(); i++) {
-        auto vertex = workgroup_reduce[i];
-        size_t n_edges = n_edges_wg[i];
-        auto start = graph_dev.begin(vertex); // GRAPH edge iterator
-
-        for (auto j = lid; j < n_edges; j += wgroup_size) {
-          auto n = start + j;
-          auto edge = n.get_index(); // GRAPH edge index
-          auto weight = graph_dev.get_weight(edge); // GRAPH edge weight
-          auto neighbor = *n;
-          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
-        }
-
-        if (wgroup.leader()) { visited[workgroup_ids[i]] = true; }
+    sycl::group_barrier(wgroup);
+    for (size_t i = 0; i < wg_tail.load(); i++) {
+      auto vertex = workgroup_reduce[i];
+      size_t n_edges = n_edges_wg[i];
+      auto start = graph_dev.begin(vertex); 
+
+      for (auto j = lid; j < n_edges; j += wgroup_size) {
+        auto n = start + j;
+        auto edge = n.get_index(); 
+        auto weight = graph_dev.get_weight(edge); 
+        auto neighbor = *n;
+        if (functor(vertex, neighbor, edge, weight)) { context.insert(neighbor); }
       }
 
-      sycl::group_barrier(sgroup);
+      if (wgroup.leader()) { visited[workgroup_ids[i]] = true; }
+    }
 
-      for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) { // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
-        size_t vertex_id = offset + i;
-        auto vertex = subgroup_reduce[vertex_id];
-        size_t n_edges = n_edges_sg[vertex_id];
+    sycl::group_barrier(sgroup);
 
-        auto start = graph_dev.begin(vertex); // GRAPH edge iterator
+    for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) { // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
+      size_t vertex_id = offset + i;
+      auto vertex = subgroup_reduce[vertex_id];
+      size_t n_edges = n_edges_sg[vertex_id];
 
-        for (auto j = llid; j < n_edges; j += sgroup_size) {
-          auto n = start + j;
-          auto edge = n.get_index(); // GRAPH edge index
-          auto weight = graph_dev.get_weight(edge); // GRAPH edge weight
-          auto neighbor = *n;
-          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
-        }
+      auto start = graph_dev.begin(vertex); 
 
-        if (sgroup.leader()) { visited[subgroup_ids[vertex_id]] = true; }
+      for (auto j = llid; j < n_edges; j += sgroup_size) {
+        auto n = start + j;
+        auto edge = n.get_index();
+        auto weight = graph_dev.get_weight(edge); 
+        auto neighbor = *n;
+        if (functor(vertex, neighbor, edge, weight)) { context.insert(neighbor); }
       }
-      sycl::group_barrier(sgroup);
-
-      if (!visited[lid]) {
-        auto vertex = assigned_vertex;
-        auto start = graph_dev.begin(vertex); // GRAPH edge iterator
-        auto end = graph_dev.end(vertex); // GRAPH edge iterator
-
-        for (auto n = start; n != end; ++n) {
-          auto edge = n.get_index(); // GRAPH edge index
-          auto weight = graph_dev.get_weight(edge); // GRAPH edge weight
-          auto neighbor = *n;
-          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
-        }
+
+      if (sgroup.leader()) { visited[subgroup_ids[vertex_id]] = true; }
+    }
+    sycl::group_barrier(sgroup);
+
+    if (!visited[lid]) {
+      auto vertex = assigned_vertex;
+      auto start = graph_dev.begin(vertex); 
+      auto end = graph_dev.end(vertex); 
+
+      for (auto n = start; n != end; ++n) {
+        auto edge = n.get_index(); 
+        auto weight = graph_dev.get_weight(edge); 
+        auto neighbor = *n;
+        if (functor(vertex, neighbor, edge, weight)) { context.insert(neighbor); }
       }
-      context.complete_iteration(state);
     }
   }
 
@@ -176,39 +163,30 @@ template<typename FrontierSizeT,
          typename GraphT,
          typename LambdaT>
 sycl::event advance(const GraphT& graph, frontier<FrontierSizeT>& in, frontier<FrontierSizeT>& out, LambdaT&& functor, size_t expected_size = 0) {
+  using element_t = FrontierSizeT;
+  
   sycl::queue& q = graph.get_queue();
 
   size_t num_nodes = graph.get_vertex_count();
 
-  using element_t = FrontierSizeT;
-  // using element_t = std::conditional_t<InFW == sygraph::frontier::frontier_view::vertex, typename GraphT::vertex_t, typename GraphT::edge_t>;
-
   auto in_dev_frontier = in.get_device_view();
   auto out_dev_frontier = out.get_device_view();
-  auto graph_dev = graph.get_device_view(); // GRAPH device view
-
-  size_t coarsening_factor = 256 /*CU size*/ / 16 /*Subgroup Size*/;
-
-  sycl::event to_wait;
-  sycl::range<1> local_range;
-  size_t global_size;
-  size_t bitmap_range = in_dev_frontier.get_element_bitsize();
-  to_wait = in.compute_active_frontier();
-  local_range = {bitmap_range * coarsening_factor};
-  if (expected_size > 0) {
-    global_size = {expected_size + (local_range[0] - (expected_size % local_range[0]))};
-  } else {
-    global_size = {local_range[0] * 128};
-    // global_size = {local_range[0] * (sygraph::detail::device::getMaxComputeUints(q) * 8)};
-  }
-
-  sycl::range<1> global_range{global_size > local_range[0] ? global_size + (local_range[0] - (global_size % local_range[0])) : local_range[0]};
+  auto graph_dev = graph.get_device_view();
+
+  size_t coarsening_factor = 1; // it should be Compute Unit Size / num subgroups
+  
+  size_t element_bitsize = in_dev_frontier.get_element_bitsize();
+  sycl::event to_wait = in.compute_active_frontier();
+  size_t offset_size = in.get_offsets_size().at_device(q, 0, {to_wait});
+  sycl::range<1> local_range = {element_bitsize * coarsening_factor};
+  size_t global_size = offset_size * element_bitsize;
+  
+  sycl::range<1> global_range{(global_size % local_range[0] == 0) ? global_size : global_size + (local_range[0] - global_size % local_range[0])};
 
   Context<decltype(in_dev_frontier), decltype(out_dev_frontier)> context{num_nodes, in_dev_frontier, out_dev_frontier};
   using bitmap_kernel_t = BitmapKernel<element_t, decltype(context), decltype(graph_dev), LambdaT>;
 
-  const uint32_t max_num_subgroups = 32;
-  // const uint32_t max_num_subgroups = sygraph::detail::device::getMaxNumSubgroups(q);
+  const uint32_t max_num_subgroups = device_max_sg_count(q);
 
   auto e = q.submit([&](sycl::handler& cgh) {
     cgh.depends_on(to_wait);
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
index 05c7c310967..0d9a599bf74 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -1,6 +1,7 @@
 #pragma once
 
 #include "oneapi/dal/common.hpp"
+#include "oneapi/dal/backend/common.hpp"
 #include "oneapi/dal/graph/detail/common.hpp"
 #include "oneapi/dal/graph/detail/container.hpp"
 #include "oneapi/dal/backend/primitives/bitset.hpp"
@@ -172,7 +173,7 @@ class frontier {
         auto offsets_pointer = _offsets.get_mutable_data() + 1;
 
         uint32_t element_bitsize = decltype(bitmap._mlb_layer)::element_bitsize;
-        size_t local_range = 1024; // Adjust as needed
+        size_t local_range = propose_wg_size(this->_queue); 
         size_t global_range =
             _mlb_layer.get_count() + local_range - (_mlb_layer.get_count() % local_range);
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp
index 0dc930e28a0..750ff18b4e7 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp
@@ -26,56 +26,69 @@ void print_frontier(const T* data, size_t count, size_t num_items) {
     }
 }
 
+std::vector<uint32_t> compute_next_frontier(std::vector<uint32_t>& row_ptr,
+                                       std::vector<uint32_t>& col_indices,
+                                       std::vector<uint32_t>& frontier) {
+    std::vector<uint32_t> next_frontier;
+
+    for (auto node : frontier) {
+        auto start = row_ptr[node];
+        auto end = row_ptr[node + 1];
+
+        for (size_t i = start; i < end; ++i) {
+            auto neighbor = col_indices[i];
+            next_frontier.push_back(neighbor);
+        }
+    }
+    // Remove duplicates
+    std::sort(next_frontier.begin(), next_frontier.end());
+    next_frontier.erase(std::unique(next_frontier.begin(), next_frontier.end()), next_frontier.end());
+    return next_frontier;
+}
+
+template<typename T>
+void compare_frontiers(T& device_frontier, std::vector<uint32_t>& host_frontier, size_t num_nodes) {
+    for (size_t i = 0; i < num_nodes; ++i) {
+        bool tmpd = device_frontier.check(i);
+        bool tmph = std::find(host_frontier.begin(), host_frontier.end(), i) != host_frontier.end();
+        if (tmpd != tmph) {
+            std::cout << "Mismatch at vertex " << i << ": device = " << tmpd << ", host = " << tmph << std::endl;
+
+        }
+        REQUIRE(tmpd == tmph);
+    }
+}
+
 TEST("test advance operation", "[advance]") {
     DECLARE_TEST_POLICY(policy);
     auto& queue = policy.get_queue();
     print_device_name(queue);
 
-    std::vector<std::uint32_t> row_ptr = {0, 2, 4, 6};
-    std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 0, 1};
-    std::vector<std::uint32_t> weights = {1, 1, 1, 1, 1, 1};
-
-    auto graph = csr_graph(queue, row_ptr, col_indices, weights);
-    auto first_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
-    auto second_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
-    auto third_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
-
-    first_frontier.insert(0);
+    // std::vector<std::uint32_t> row_ptr = {0, 2, 4, 6};
+    // std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 0, 1};
+    // std::vector<std::uint32_t> weights = {1, 1, 1, 1, 1, 1};
+    std::vector<std::uint32_t> row_ptr = {0, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225, 229, 233, 237, 241, 245, 249, 253, 257, 261, 265, 269, 273, 277, 281, 285, 289, 293, 297, 301, 305, 309, 313, 317, 321, 325, 329, 333, 337, 341, 345, 349, 353, 357, 361, 365, 369, 373, 377, 381, 385, 389, 393, 397, 401, 405, 409, 413, 417, 421, 425, 429, 433, 437, 441, 445, 449, 453, 457, 461, 465, 469, 473, 477, 481, 485, 489, 493, 497, 501, 504, 506};
+    std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 3, 0, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 6, 3, 4, 6, 7, 4, 5, 7, 8, 5, 6, 8, 9, 6, 7, 9, 10, 7, 8, 10, 11, 8, 9, 11, 12, 9, 10, 12, 13, 10, 11, 13, 14, 11, 12, 14, 15, 12, 13, 15, 16, 13, 14, 16, 17, 14, 15, 17, 18, 15, 16, 18, 19, 16, 17, 19, 20, 17, 18, 20, 21, 18, 19, 21, 22, 19, 20, 22, 23, 20, 21, 23, 24, 21, 22, 24, 25, 22, 23, 25, 26, 23, 24, 26, 27, 24, 25, 27, 28, 25, 26, 28, 29, 26, 27, 29, 30, 27, 28, 30, 31, 28, 29, 31, 32, 29, 30, 32, 33, 30, 31, 33, 34, 31, 32, 34, 35, 32, 33, 35, 36, 33, 34, 36, 37, 34, 35, 37, 38, 35, 36, 38, 39, 36, 37, 39, 40, 37, 38, 40, 41, 38, 39, 41, 42, 39, 40, 42, 43, 40, 41, 43, 44, 41, 42, 44, 45, 42, 43, 45, 46, 43, 44, 46, 47, 44, 45, 47, 48, 45, 46, 48, 49, 46, 47, 49, 50, 47, 48, 50, 51, 48, 49, 51, 52, 49, 50, 52, 53, 50, 51, 53, 54, 51, 52, 54, 55, 52, 53, 55, 56, 53, 54, 56, 57, 54, 55, 57, 58, 55, 56, 58, 59, 56, 57, 59, 60, 57, 58, 60, 61, 58, 59, 61, 62, 59, 60, 62, 63, 60, 61, 63, 64, 61, 62, 64, 65, 62, 63, 65, 66, 63, 64, 66, 67, 64, 65, 67, 68, 65, 66, 68, 69, 66, 67, 69, 70, 67, 68, 70, 71, 68, 69, 71, 72, 69, 70, 72, 73, 70, 71, 73, 74, 71, 72, 74, 75, 72, 73, 75, 76, 73, 74, 76, 77, 74, 75, 77, 78, 75, 76, 78, 79, 76, 77, 79, 80, 77, 78, 80, 81, 78, 79, 81, 82, 79, 80, 82, 83, 80, 81, 83, 84, 81, 82, 84, 85, 82, 83, 85, 86, 83, 84, 86, 87, 84, 85, 87, 88, 85, 86, 88, 89, 86, 87, 89, 90, 87, 88, 90, 91, 88, 89, 91, 92, 89, 90, 92, 93, 90, 91, 93, 94, 91, 92, 94, 95, 92, 93, 95, 96, 93, 94, 96, 97, 94, 95, 97, 98, 95, 96, 98, 99, 96, 97, 99, 100, 97, 98, 100, 101, 98, 99, 101, 102, 99, 100, 102, 103, 100, 101, 103, 104, 101, 102, 104, 105, 102, 103, 105, 106, 103, 104, 106, 107, 104, 105, 107, 108, 105, 106, 108, 109, 106, 107, 109, 110, 107, 108, 110, 111, 108, 109, 111, 112, 109, 110, 112, 113, 110, 111, 113, 114, 111, 112, 114, 115, 112, 113, 115, 116, 113, 114, 116, 117, 114, 115, 117, 118, 115, 116, 118, 119, 116, 117, 119, 120, 117, 118, 120, 121, 118, 119, 121, 122, 119, 120, 122, 123, 120, 121, 123, 124, 121, 122, 124, 125, 122, 123, 125, 126, 123, 124, 126, 127, 124, 125, 127, 125, 126};
+    std::vector<std::uint32_t> weights(col_indices.size(), 1);
+    size_t num_nodes = row_ptr.size() - 1;
 
-    REQUIRE(first_frontier.check(0) == true);
-    REQUIRE(first_frontier.check(1) == false);
-    REQUIRE(first_frontier.check(2) == false);
-    
-    std::cout << "First Frontier: ";
-    for (size_t i = 0; i < graph.get_vertex_count(); ++i) {
-        std::cout << "Vertex " << i << ": " << (first_frontier.check(i) ? "in frontier" : "not in frontier") << std::endl;
-    }
     
-    advance(graph, first_frontier, second_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
-        return true; // Always advance
-    }).wait_and_throw();
-
-    REQUIRE(second_frontier.check(0) == false);
-    REQUIRE(second_frontier.check(1) == true);
-    REQUIRE(second_frontier.check(2) == true);
+    auto graph = csr_graph(queue, row_ptr, col_indices, weights);
+    auto in_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+    auto out_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
     
-    std::cout << "Second Frontier: ";
-    for (size_t i = 0; i < graph.get_vertex_count(); ++i) {
-        std::cout << "Vertex " << i << ": " << (second_frontier.check(i) ? "in frontier" : "not in frontier") << std::endl;
-    }
+    in_frontier.insert(3);
+    in_frontier.insert(4);
+    in_frontier.insert(52);
+    in_frontier.insert(100);
+    std::vector<std::uint32_t> host_frontier = {3, 4, 52, 100};
 
-    advance(graph, second_frontier, third_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
+    advance(graph, in_frontier, out_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
         return true; // Always advance
     }).wait_and_throw();
-
-    std::cout << "Third Frontier: ";
-    for (size_t i = 0; i < graph.get_vertex_count(); ++i) {
-        std::cout << "Vertex " << i << ": " << (third_frontier.check(i) ? "in frontier" : "not in frontier") << std::endl;
-    }
-
-    REQUIRE(third_frontier.check(0) == true);
-    REQUIRE(third_frontier.check(1) == true);
-    REQUIRE(third_frontier.check(2) == true);
+    
+    auto tmp_frontier = compute_next_frontier(row_ptr, col_indices, host_frontier);
+    compare_frontiers(out_frontier, tmp_frontier, num_nodes);
 
 } // TEST "test advance operation"
 

From 80835a60f16c13662ce22c3d4375bcb5b60f1761 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 23 Jul 2025 17:48:35 +0200
Subject: [PATCH 10/69] implemented async advance

---
 .../primitives/frontier/advance_dpc.hpp       | 201 +++++++++++-------
 1 file changed, 120 insertions(+), 81 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
index b0530a26373..d590288a24e 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
@@ -7,6 +7,9 @@
 
 namespace oneapi::dal::backend::primitives {
 
+/// ContextState holds the state of the current processing group in the kernel
+/// It includes the group offset, coarsening factor, offsets size, and the SYCL
+/// nd_item for the current work item.
 struct ContextState {
   size_t group_offset;
   const uint16_t coarsening_factor;
@@ -14,6 +17,12 @@ struct ContextState {
   const sycl::nd_item<1> item;
 };
 
+/// Context is a template class that provides an interface for the kernel to
+/// interact with the frontier data structure. It holds the limit of the graph,
+/// the input frontier, and the output frontier. It provides methods to initialize
+/// the context state, check if there are more elements to process, get the
+/// assigned element, check if a vertex is in the frontier, and insert a vertex
+/// into the output frontier.
 template<typename InFrontierDevT, typename OutFrontierDevT>
 struct Context {
   size_t limit;
@@ -26,37 +35,47 @@ struct Context {
   inline ContextState init(sycl::nd_item<1>& item) const {
     return {
         item.get_group_linear_id(),
-        static_cast<uint16_t>(item.get_local_range(0) / in_dev_frontier.getBitmapRange()),
-        in_dev_frontier.getOffsetsSize()[0],
+        static_cast<uint16_t>(item.get_local_range(0) / in_dev_frontier.get_element_bitsize()),
+        in_dev_frontier.get_offsets_size()[0],
         item,
     };
   }
 
-  inline size_t get_assigned_element(sycl::nd_item<1> item) const {
+  /// This method checks if there are more elements to process in the current group.
+  inline bool need_to_process(ContextState& state) const { return (state.group_offset * state.coarsening_factor < state.offsets_size); }
+
+  /// This method completes the current iteration by updating the group offset.
+  inline void complete_iteration(ContextState& state) const { state.group_offset += state.item.get_group_range(0); }
+
+  /// This method retrieves the assigned element for the current work item.
+  inline size_t get_assigned_element(const ContextState& state) const {
     const uint16_t element_bitsize = in_dev_frontier.get_element_bitsize();
-    const auto* bitmap_offsets = in_dev_frontier.get_offsets();
-    const size_t coarsening_factor = item.get_local_range(0) / element_bitsize;
-    const uint32_t acutal_id_offset = (item.get_group_linear_id() * coarsening_factor) + (item.get_local_linear_id() / element_bitsize);
-    const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * element_bitsize) + (item.get_local_linear_id() % element_bitsize);
+    const uint32_t acutal_id_offset = (state.group_offset * state.coarsening_factor) + (state.item.get_local_linear_id() / element_bitsize);
+    const uint32_t* bitmap_offsets = in_dev_frontier.get_offsets();
+    // const size_t acutal_id_offset = (item.get_group_linear_id() * coarsening_factor) + (item.get_local_linear_id() / bitmap_range);
+    const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * element_bitsize) + (state.item.get_local_linear_id() % element_bitsize);
     return assigned_vertex;
   }
 
-  inline bool check(sycl::nd_item<1> item, size_t vertex) const {
-    return vertex < limit && in_dev_frontier.check(vertex); 
+  /// This method checks if a vertex is in the input frontier.
+  inline bool check(const ContextState& state, size_t vertex) const {
+    return vertex < limit && in_dev_frontier.check(vertex);
   }
 
-  inline void insert(size_t vertex) const {
+  /// This method inserts a vertex into the output frontier.
+  inline void insert(const ContextState& state, size_t vertex) const {
     out_dev_frontier.insert(vertex);
   }
 };
 
+/// BitmapKernel is a template struct that defines the kernel to be executed on the device.
+/// It processes the input frontier and advances it based on the provided functor.
 template<typename T,
          typename ContextT,
          typename GraphDevT,
          typename LambdaT>
 struct BitmapKernel {
   void operator()(sycl::nd_item<1> item) const {
-    // 0. retrieve global and local ids
     const size_t lid = item.get_local_linear_id();
     const auto wgroup = item.get_group();
     const size_t wgroup_size = wgroup.get_local_range(0);
@@ -65,83 +84,92 @@ struct BitmapKernel {
     const size_t sgroup_size = sgroup.get_local_range()[0];
     const size_t llid = sgroup.get_local_linear_id();
 
-    const auto assigned_vertex = context.get_assigned_element(item);
-
-    // 1. load number of edges in local memory
-    if (sgroup.leader()) { subgroup_reduce_tail[sgroup_id] = 0; }
-    if (wgroup.leader()) { workgroup_reduce_tail[0] = 0; }
-
-    sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group> sg_tail{subgroup_reduce_tail[sgroup_id]};
-    sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group> wg_tail{workgroup_reduce_tail[0]};
-
-    const uint32_t offset = sgroup_id * sgroup_size;
-    if (context.check(item, assigned_vertex)) {
-      uint32_t n_edges = graph_dev.get_degree(assigned_vertex); 
-      if (n_edges >= wgroup_size * wgroup_size) { // assign to the workgroup
-        uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
-        n_edges_wg[loc] = n_edges;
-        workgroup_reduce[loc] = assigned_vertex;
-        workgroup_ids[loc] = lid;
-      } else if (n_edges >= sgroup_size) { // assign to the subgroup
-        uint32_t loc = sg_tail.fetch_add(static_cast<uint32_t>(1));
-        n_edges_sg[offset + loc] = n_edges;
-        subgroup_reduce[offset + loc] = assigned_vertex;
-        subgroup_ids[offset + loc] = lid;
+    auto state = context.init(item);
+
+    while (context.need_to_process(state)) {
+      const auto assigned_vertex = context.get_assigned_element(state);
+
+      if (sgroup.leader()) { subgroup_reduce_tail[sgroup_id] = 0; }
+      if (wgroup.leader()) { workgroup_reduce_tail[0] = 0; }
+
+      sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group> sg_tail{subgroup_reduce_tail[sgroup_id]};
+      sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group> wg_tail{workgroup_reduce_tail[0]};
+
+      // 1. distribute the workload based on the number of edges to the workgroup, subgroup or workitem
+      const uint32_t offset = sgroup_id * sgroup_size;
+      if (context.check(state, assigned_vertex)) {
+        uint32_t n_edges = graph_dev.get_degree(assigned_vertex); 
+        if (n_edges >= wgroup_size * wgroup_size) { // if the number of edges is large enough, we can assign the vertex to the workgroup
+          uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
+          n_edges_wg[loc] = n_edges;
+          workgroup_reduce[loc] = assigned_vertex;
+          workgroup_ids[loc] = lid;
+        } else if (n_edges >= sgroup_size) { // assign to the subgroup
+          uint32_t loc = sg_tail.fetch_add(static_cast<uint32_t>(1));
+          n_edges_sg[offset + loc] = n_edges;
+          subgroup_reduce[offset + loc] = assigned_vertex;
+          subgroup_ids[offset + loc] = lid;
+        }
+        visited[lid] = false;
+      } else {
+        visited[lid] = true;
       }
-      visited[lid] = false;
-    } else {
-      visited[lid] = true;
-    }
 
-    sycl::group_barrier(wgroup);
-    for (size_t i = 0; i < wg_tail.load(); i++) {
-      auto vertex = workgroup_reduce[i];
-      size_t n_edges = n_edges_wg[i];
-      auto start = graph_dev.begin(vertex); 
-
-      for (auto j = lid; j < n_edges; j += wgroup_size) {
-        auto n = start + j;
-        auto edge = n.get_index(); 
-        auto weight = graph_dev.get_weight(edge); 
-        auto neighbor = *n;
-        if (functor(vertex, neighbor, edge, weight)) { context.insert(neighbor); }
+      sycl::group_barrier(wgroup);
+
+      // 2. process the the edge of one vertex at a time using the workgroup
+      for (size_t i = 0; i < wg_tail.load(); i++) {
+        auto vertex = workgroup_reduce[i];
+        size_t n_edges = n_edges_wg[i];
+        auto start = graph_dev.begin(vertex); 
+
+        for (auto j = lid; j < n_edges; j += wgroup_size) {
+          auto n = start + j;
+          auto edge = n.get_index(); 
+          auto weight = graph_dev.get_weight(edge); 
+          auto neighbor = *n;
+          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
+        }
+
+        if (wgroup.leader()) { visited[workgroup_ids[i]] = true; }
       }
 
-      if (wgroup.leader()) { visited[workgroup_ids[i]] = true; }
-    }
+      sycl::group_barrier(sgroup);
 
-    sycl::group_barrier(sgroup);
+      // 3. process the edges of one vertex at a time using the subgroup
+      for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) { // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
+        size_t vertex_id = offset + i;
+        auto vertex = subgroup_reduce[vertex_id];
+        size_t n_edges = n_edges_sg[vertex_id];
 
-    for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) { // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
-      size_t vertex_id = offset + i;
-      auto vertex = subgroup_reduce[vertex_id];
-      size_t n_edges = n_edges_sg[vertex_id];
+        auto start = graph_dev.begin(vertex); 
 
-      auto start = graph_dev.begin(vertex); 
+        for (auto j = llid; j < n_edges; j += sgroup_size) {
+          auto n = start + j;
+          auto edge = n.get_index();
+          auto weight = graph_dev.get_weight(edge); 
+          auto neighbor = *n;
+          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
+        }
 
-      for (auto j = llid; j < n_edges; j += sgroup_size) {
-        auto n = start + j;
-        auto edge = n.get_index();
-        auto weight = graph_dev.get_weight(edge); 
-        auto neighbor = *n;
-        if (functor(vertex, neighbor, edge, weight)) { context.insert(neighbor); }
+        if (sgroup.leader()) { visited[subgroup_ids[vertex_id]] = true; }
       }
-
-      if (sgroup.leader()) { visited[subgroup_ids[vertex_id]] = true; }
-    }
-    sycl::group_barrier(sgroup);
-
-    if (!visited[lid]) {
-      auto vertex = assigned_vertex;
-      auto start = graph_dev.begin(vertex); 
-      auto end = graph_dev.end(vertex); 
-
-      for (auto n = start; n != end; ++n) {
-        auto edge = n.get_index(); 
-        auto weight = graph_dev.get_weight(edge); 
-        auto neighbor = *n;
-        if (functor(vertex, neighbor, edge, weight)) { context.insert(neighbor); }
+      sycl::group_barrier(sgroup);
+
+      // 4. process the edges of the vertices that were not assigned to the workgroup or subgroup
+      if (!visited[lid]) {
+        auto vertex = assigned_vertex;
+        auto start = graph_dev.begin(vertex); 
+        auto end = graph_dev.end(vertex); 
+
+        for (auto n = start; n != end; ++n) {
+          auto edge = n.get_index(); 
+          auto weight = graph_dev.get_weight(edge); 
+          auto neighbor = *n;
+          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
+        }
       }
+      context.complete_iteration(state); // complete the current iteration
     }
   }
 
@@ -159,6 +187,11 @@ struct BitmapKernel {
   const LambdaT functor;
 };
 
+/// advance is a function that launches the BitmapKernel on the device to advance the frontier.
+/// It takes the graph, input frontier, output frontier, and the functor.
+/// The expected_size parameter is used to specify the expected size of the input frontier, in order
+/// to optimize the kernel launch parameters. If expected_size is zero, a default size is used.
+/// It returns a sycl::event that can be used to synchronize the execution.
 template<typename FrontierSizeT,
          typename GraphT,
          typename LambdaT>
@@ -176,10 +209,16 @@ sycl::event advance(const GraphT& graph, frontier<FrontierSizeT>& in, frontier<F
   size_t coarsening_factor = 1; // it should be Compute Unit Size / num subgroups
   
   size_t element_bitsize = in_dev_frontier.get_element_bitsize();
-  sycl::event to_wait = in.compute_active_frontier();
-  size_t offset_size = in.get_offsets_size().at_device(q, 0, {to_wait});
   sycl::range<1> local_range = {element_bitsize * coarsening_factor};
-  size_t global_size = offset_size * element_bitsize;
+  size_t global_size;
+
+  if (expected_size > 0) {
+      global_size = expected_size * element_bitsize;
+    } else {
+      global_size = 1024; // This parameter should be tuned according to the device capabilities
+    }
+
+  sycl::event to_wait = in.compute_active_frontier();
   
   sycl::range<1> global_range{(global_size % local_range[0] == 0) ? global_size : global_size + (local_range[0] - global_size % local_range[0])};
 

From 944d754db653244d18222ad19ebe9546246c2788 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 23 Jul 2025 18:28:03 +0200
Subject: [PATCH 11/69] add documentation for frontier

---
 cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
index 0d9a599bf74..bd94141a91c 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
@@ -9,6 +9,7 @@
 
 namespace oneapi::dal::backend::primitives {
 
+/// @brief A view of a frontier that provides an interface for the kernel to interact with the frontier data structure.
 template <typename ElementType = std::uint32_t>
 struct frontier_view {
     using bitmap_t = ElementType;
@@ -66,6 +67,7 @@ struct frontier_view {
 
 #ifdef ONEDAL_DATA_PARALLEL
 
+/// @brief The Two-Layer bitmap frontier class
 template <typename ElementType = std::uint32_t>
 class frontier {
     using bitmap_t = ElementType;
@@ -166,6 +168,10 @@ class frontier {
         e2.wait_and_throw();
     }
 
+    /// @brief Computes the active frontier by filling the offsets array with the indices of the active vertices.
+    /// It returns a sycl::event that can be used to synchronize the execution.
+    /// The offsets array is filled with the indices of the active vertices in the first layer of the frontier.
+    /// This is used by the primitives to understand which vertices are active in the frontier.
     sycl::event compute_active_frontier() const {
         auto bitmap = this->get_device_view();
 

From 8cbd1feace9077c1da140d130e0ac809a788da74 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Fri, 25 Jul 2025 16:07:42 +0200
Subject: [PATCH 12/69] Refactor frontier implementation and add tests

- Removed the existing frontier_dpc.hpp file to streamline the codebase.
- Introduced new test files for advance operation, BFS, and basic frontier operations.
- Implemented comprehensive tests to validate the functionality of the frontier data structure.
- Enhanced the frontier class with additional methods for better performance and usability.
- Ensured compatibility with SYCL and improved device memory management.
---
 cpp/oneapi/dal/backend/primitives/BUILD       |   2 +
 .../dal/backend/primitives/frontier.hpp       |   2 +-
 .../dal/backend/primitives/frontier/BUILD     |  14 +-
 .../primitives/frontier/advance_dpc.hpp       |   2 +-
 .../backend/primitives/frontier/frontier.hpp  | 145 +++++++++
 .../primitives/frontier/frontier_dpc.cpp      | 194 ++++++++++++
 .../primitives/frontier/frontier_dpc.hpp      | 292 ------------------
 ...vance_frontier_dpc.cpp => advance_dpc.cpp} |  14 +-
 .../primitives/frontier/test/bfs_dpc.cpp      |  90 ++++++
 ..._frontier_ops_dpc.cpp => frontier_dpc.cpp} |  10 +-
 10 files changed, 453 insertions(+), 312 deletions(-)
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
 delete mode 100644 cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
 rename cpp/oneapi/dal/backend/primitives/frontier/test/{advance_frontier_dpc.cpp => advance_dpc.cpp} (90%)
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
 rename cpp/oneapi/dal/backend/primitives/frontier/test/{basic_frontier_ops_dpc.cpp => frontier_dpc.cpp} (87%)

diff --git a/cpp/oneapi/dal/backend/primitives/BUILD b/cpp/oneapi/dal/backend/primitives/BUILD
index c7241ade6af..2fc9e2cb5ca 100644
--- a/cpp/oneapi/dal/backend/primitives/BUILD
+++ b/cpp/oneapi/dal/backend/primitives/BUILD
@@ -37,6 +37,7 @@ dal_collect_modules(
         "lapack",
         "optimizers",
         "objective_function",
+        "frontier",
         "placement",
         "reduction",
         "regression",
@@ -88,6 +89,7 @@ dal_collect_test_suites(
         "lapack",
         "optimizers",
         "objective_function",
+        "frontier",
         "placement",
         "reduction",
         "regression",
diff --git a/cpp/oneapi/dal/backend/primitives/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier.hpp
index 9e35cff3f12..245ef5b7f91 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier.hpp
@@ -1,3 +1,3 @@
-#include "oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp"
+#include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 #include "oneapi/dal/backend/primitives/frontier/advance_dpc.hpp"
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/BUILD b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
index 394618090e5..1a224d76188 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/BUILD
+++ b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
@@ -6,7 +6,13 @@ load("@onedal//dev/bazel:dal.bzl",
 
 dal_module (
     name = "frontier",
-    auto = True
+    auto = True,
+    dal_deps = [
+        "@onedal//cpp/oneapi/dal/backend/primitives:common",
+        "@onedal//cpp/oneapi/dal/backend/primitives:blas",
+        "@onedal//cpp/oneapi/dal/backend/primitives/optimizers",
+        "@onedal//cpp/oneapi/dal/backend/primitives:sparse_blas",
+    ],
 )
 
 dal_test_suite (
@@ -14,16 +20,10 @@ dal_test_suite (
     framework = "catch2",
     compile_as = [ "dpc++" ],
     private = True,
-    # hdrs = glob([
-    #     "test/*.hpp",
-    # ]),
     srcs = glob([
         "test/*_dpc.cpp",
-    ], exclude=[
-        "test/*perf*.cpp",
     ]),
     dal_deps = [
         ":frontier",
-        "@onedal//cpp/oneapi/dal/backend/primitives:rng",
     ],
 )
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
index d590288a24e..ef91511d661 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
@@ -2,7 +2,7 @@
 
 #include "oneapi/dal/backend/primitives/ndarray.hpp"
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"
-#include "oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp"
+#include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 
 
 namespace oneapi::dal::backend::primitives {
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
new file mode 100644
index 00000000000..5de56bc2fde
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -0,0 +1,145 @@
+#pragma once
+
+#include "oneapi/dal/common.hpp"
+#include "oneapi/dal/backend/common.hpp"
+#include "oneapi/dal/graph/detail/common.hpp"
+#include "oneapi/dal/graph/detail/container.hpp"
+#include "oneapi/dal/backend/primitives/bitset.hpp"
+#include "oneapi/dal/backend/primitives/ndarray.hpp"
+
+namespace oneapi::dal::backend::primitives {
+
+/// @brief A view of a frontier that provides an interface for the kernel to interact with the frontier data structure.
+template <typename ElementType>
+class frontier_view {
+public:
+    using bitmap_t = ElementType;
+    static constexpr std::size_t divide_factor = bitset<bitmap_t>::element_bitsize;
+
+    frontier_view() = default;
+    frontier_view(bitmap_t* data_layer,
+                  bitmap_t* mlb_layer,
+                  std::uint32_t* offsets,
+                  std::uint32_t* offsets_size,
+                  size_t num_items)
+            : _num_items(num_items),
+              _data_layer(bitset<bitmap_t>{data_layer}),
+              _mlb_layer(bitset<bitmap_t>{mlb_layer}),
+              _offsets(offsets),
+              _offsets_size(offsets_size) {}
+
+    inline void insert(std::uint32_t idx) const {
+        if (!_data_layer.test(idx)) {
+            _data_layer.atomic_set(idx);
+        }
+        if (!_mlb_layer.test(idx / divide_factor)) {
+            _mlb_layer.atomic_set(idx / divide_factor);
+        }
+    }
+
+    inline void remove(std::uint32_t idx) const {
+        throw dal::domain_error("Frontier does not support remove operation");
+    }
+
+    inline bool check(std::uint32_t idx) const {
+        return _data_layer.atomic_test(idx);
+    }
+
+    inline size_t get_element_bitsize() const {
+        return bitset<bitmap_t>::element_bitsize;
+    }
+
+    inline std::uint32_t* get_offsets() const {
+        return _offsets;
+    }
+
+    inline std::uint32_t* get_offsets_size() const {
+        return _offsets_size;
+    }
+
+private:
+    size_t _num_items;
+
+    bitset<bitmap_t> _data_layer;
+    bitset<bitmap_t> _mlb_layer;
+
+    std::uint32_t* _offsets;
+    std::uint32_t* _offsets_size;
+};
+
+/// @brief The Two-Layer bitmap frontier class
+template <typename ElementType>
+class frontier {
+    using buffer_t = std::uint32_t;
+
+public:
+    frontier(sycl::queue& queue, std::size_t num_items, sycl::usm::alloc alloc = sycl::usm::alloc::shared);
+
+    const frontier_view<ElementType> get_device_view() const {
+        auto offsets_size_pointer = _offsets.get_mutable_data();
+        auto offsets_pointer = _offsets.get_mutable_data() + 1;
+
+        return { _data_layer.get_mutable_data(),
+                _mlb_layer.get_mutable_data(),
+                offsets_pointer,
+                offsets_size_pointer,
+                static_cast<std::size_t>(_data_layer.get_count()) };
+    }
+
+    inline ndview<ElementType, 1> get_data() const {
+        return _data_layer;
+    }
+
+    inline ndview<ElementType, 1> get_mlb() const {
+        return _mlb_layer;
+    }
+
+    inline ndview<std::uint32_t, 1> get_offsets() const {
+        return _offsets.slice(1, _offsets.get_count());
+    }
+
+    inline ndview<std::uint32_t, 1> get_offsets_size() const {
+        return _offsets.slice(0, 1);
+    }
+
+    bool empty();
+
+    void insert(ElementType idx);
+
+    bool check(ElementType idx);
+
+    void clear();
+
+    /// @brief Computes the active frontier by filling the offsets array with the indices of the active vertices.
+    /// It returns a sycl::event that can be used to synchronize the execution.
+    /// The offsets array is filled with the indices of the active vertices in the first layer of the frontier.
+    /// This is used by the primitives to understand which vertices are active in the frontier.
+    sycl::event compute_active_frontier();
+
+    static void swap(frontier<ElementType>& f1, frontier<ElementType>& f2) {
+        using std::swap;
+        swap(f1._data_layer, f2._data_layer);
+        swap(f1._mlb_layer, f2._mlb_layer);
+        swap(f1._offsets, f2._offsets);
+        swap(f1._queue, f2._queue);
+        swap(f1._num_items, f2._num_items);
+    }
+
+private:
+    sycl::queue& _queue;
+    size_t _num_items;
+
+    ndarray<ElementType, 1> _data_layer;
+    ndarray<ElementType, 1> _mlb_layer;
+    ndarray<std::uint32_t, 1> _offsets;
+    ndarray<buffer_t, 1> _buffer;
+    const size_t _TMP_VAR = 0;
+    const size_t _CAF_FLAG = 1; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
+};
+
+template <typename ElementType>
+void swap_frontiers(frontier<ElementType>& f1, frontier<ElementType>& f2) {
+    frontier<ElementType>::swap(f1, f2);
+}
+
+} // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
new file mode 100644
index 00000000000..bbda488a7f9
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -0,0 +1,194 @@
+
+#include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
+#include "oneapi/dal/backend/common.hpp"
+#include "oneapi/dal/backend/primitives/ndarray.hpp"
+#include "oneapi/dal/graph/detail/common.hpp"
+
+namespace oneapi::dal::backend::primitives {
+
+#ifdef ONEDAL_DATA_PARALLEL
+    
+template <typename ElementType>
+frontier<ElementType>::frontier(sycl::queue& queue, std::size_t num_items, sycl::usm::alloc alloc) : _queue(queue), _num_items(num_items) {
+    std::int64_t array_size =
+        (num_items + bitset<ElementType>::element_bitsize - 1) / bitset<ElementType>::element_bitsize;
+    std::int64_t mlb_size = (array_size + bitset<ElementType>::element_bitsize - 1) /
+                    bitset<ElementType>::element_bitsize;
+    _data_layer =
+        ndarray<ElementType, 1>::empty(_queue, { array_size }, alloc);
+    _mlb_layer =
+        ndarray<ElementType, 1>::empty(_queue, { mlb_size }, alloc);
+    _offsets =
+        ndarray<std::uint32_t, 1>::empty(_queue, { array_size + 1 }, alloc); /// First offset is to keep the size of the frontier
+    _buffer = ndarray<std::uint32_t, 1>::empty(_queue, { 10 }, alloc);
+
+    sycl::event e1, e2, e3;
+    e1 = _data_layer.fill(_queue, ElementType(0));
+    e2 = _mlb_layer.fill(_queue, ElementType(0));
+    e3 = _offsets.fill(_queue, std::uint32_t(0));
+
+    e1.wait_and_throw();
+    e2.wait_and_throw();
+    e3.wait_and_throw();
+}
+
+template <typename ElementType>
+bool frontier<ElementType>::empty() {
+    ndview<std::uint32_t, 1> empty_buff = _buffer.slice(0, 1);
+    auto copy_e = fill(_queue, empty_buff, buffer_t(0));
+    auto* const empty_buff_ptr = empty_buff.get_mutable_data();
+
+    auto e = _queue.submit([&](sycl::handler& cgh) {
+        cgh.depends_on(copy_e);
+        const auto range = make_range_1d(_mlb_layer.get_count());
+        auto sum_reduction = sycl::reduction(empty_buff_ptr, sycl::plus<>());
+        auto* const f_ptr = _mlb_layer.get_mutable_data();
+
+        cgh.parallel_for(range, sum_reduction, [=](sycl::id<1> idx, auto& sum_v) {
+            sum_v += f_ptr[idx];
+        });
+    });
+    auto empty_sum = empty_buff.at_device(_queue, 0, { e });
+    return empty_sum == 0;
+}
+
+template <typename ElementType>
+inline void frontier<ElementType>::insert(ElementType idx) {
+    auto view = this->get_device_view();
+    _queue.submit([&](sycl::handler& cgh) {
+        cgh.single_task([=]() {
+            view.insert(idx);
+        });
+    }).wait_and_throw();
+}
+
+template <typename ElementType>
+inline bool frontier<ElementType>::check(ElementType idx) {
+    ElementType tmp_data = _data_layer.at_device(_queue, idx / bitset<ElementType>::element_bitsize);
+    return (tmp_data & (static_cast<ElementType>(1) << (idx % bitset<ElementType>::element_bitsize))) != 0;
+}
+
+template <typename ElementType>
+inline void frontier<ElementType>::clear() {
+    auto e = _data_layer.fill(_queue, ElementType(0));
+    auto e1 = _mlb_layer.fill(_queue, ElementType(0));
+    auto e2 = _offsets.fill(_queue, ElementType(0));
+    e.wait_and_throw();
+    e1.wait_and_throw();
+    e2.wait_and_throw();
+}
+
+template <typename ElementType>
+inline sycl::event frontier<ElementType>::compute_active_frontier() {
+    auto bitmap = this->get_device_view();
+
+    auto offsets_size_pointer = _offsets.get_mutable_data();
+    auto offsets_pointer = _offsets.get_mutable_data() + 1;
+
+    uint32_t element_bitsize = bitmap.get_element_bitsize();
+    size_t local_range = propose_wg_size(this->_queue); 
+    size_t global_range =
+        _mlb_layer.get_count() + local_range - (_mlb_layer.get_count() % local_range);
+
+    bool use_local_mem =
+        device_local_mem_size(this->_queue) >= static_cast<std::int64_t>(local_range * element_bitsize * sizeof(uint32_t));
+
+    auto e0 = _queue.submit([&](sycl::handler& cgh) {
+        cgh.single_task([=, offsets_size = this->get_offsets_size().get_mutable_data(), buffer_ptr = this->_buffer.get_mutable_data(), CAF_FLAG = this->_CAF_FLAG]() {
+            buffer_ptr[CAF_FLAG] = offsets_size[0] == 0 ? 1 : 0;
+        });
+    });
+
+    auto e1 = this->_queue.submit([&](sycl::handler& cgh) {
+        cgh.depends_on(e0);
+
+        if (!use_local_mem || true) { // Force to use global memory for simplicity
+            cgh.parallel_for(make_range_1d(_mlb_layer.get_count()),
+                [=,
+                offsets = offsets_pointer,
+                offsets_size = offsets_size_pointer,
+                data_layer = this->_mlb_layer.get_mutable_data(),
+                buffer = this->_buffer.get_mutable_data(),
+                CAF_FLAG = this->_CAF_FLAG](sycl::id<1> idx) {
+
+                    if (!buffer[CAF_FLAG]) return;
+
+                    sycl::atomic_ref<uint32_t,
+                                    sycl::memory_order::relaxed,
+                                    sycl::memory_scope::device>
+                        offsets_size_ref{ offsets_size[0] };
+
+                    ElementType data = data_layer[idx];
+                    for (size_t i = 0; i < element_bitsize; i++) {
+                        if (data & (static_cast<ElementType>(1) << i)) {
+                            offsets[offsets_size_ref++] = i + idx * element_bitsize;
+                        }
+                    }
+            });
+        } else {
+            sycl::local_accessor<uint32_t, 1> local_offsets(local_range * element_bitsize, cgh);
+            sycl::local_accessor<uint32_t, 1> local_size(1, cgh);
+
+            cgh.parallel_for(
+                make_multiple_nd_range_1d(global_range, local_range),
+                [=,
+                offsets = offsets_pointer,
+                offsets_size = offsets_size_pointer,
+                data_layer = this->_mlb_layer.get_mutable_data(),
+                size = this->_num_items,
+                buffer = this->_buffer.get_mutable_data(),
+                CAF_FLAG = this->_CAF_FLAG](sycl::nd_item<1> item) {
+                    if (!buffer[CAF_FLAG]) return;
+
+                    auto group = item.get_group();
+                    sycl::atomic_ref<uint32_t,
+                                        sycl::memory_order::relaxed,
+                                        sycl::memory_scope::work_group>
+                        local_size_ref{ local_size[0] };
+                    sycl::atomic_ref<uint32_t,
+                                        sycl::memory_order::relaxed,
+                                        sycl::memory_scope::device>
+                        offsets_size_ref{ offsets_size[0] };
+
+                    if (group.leader()) {
+                        local_size_ref.store(0);
+                    }
+                    sycl::group_barrier(group);
+                    for (uint32_t gid = item.get_global_linear_id(); gid < size;
+                            gid += local_range) {
+                        ElementType data = data_layer[gid];
+                        for (size_t i = 0; i < element_bitsize; i++) {
+                            if (data & (static_cast<ElementType>(1) << i)) {
+                                local_offsets[local_size_ref++] = i + gid * element_bitsize;
+                            }
+                        }
+                    }
+
+                    sycl::group_barrier(group);
+
+                    size_t data_offset = 0;
+                    if (group.leader()) {
+                        data_offset = offsets_size_ref.fetch_add(local_size_ref.load());
+                    }
+                    data_offset = sycl::group_broadcast(group, data_offset, 0);
+                    for (size_t i = item.get_local_linear_id(); i < local_size_ref.load();
+                            i += item.get_local_range(0)) {
+                        offsets[data_offset + i] = local_offsets[i];
+                    }
+                });
+        }
+
+    });
+    return e1;
+
+}
+
+#define INSTANTIATE(F) \
+    template class frontier<F>;
+    
+INSTANTIATE(std::uint64_t)
+INSTANTIATE(std::uint32_t)
+
+#endif
+
+} // namespace oneapi::dal::backend::primitives
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
deleted file mode 100644
index bd94141a91c..00000000000
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.hpp
+++ /dev/null
@@ -1,292 +0,0 @@
-#pragma once
-
-#include "oneapi/dal/common.hpp"
-#include "oneapi/dal/backend/common.hpp"
-#include "oneapi/dal/graph/detail/common.hpp"
-#include "oneapi/dal/graph/detail/container.hpp"
-#include "oneapi/dal/backend/primitives/bitset.hpp"
-#include "oneapi/dal/backend/primitives/ndarray.hpp"
-
-namespace oneapi::dal::backend::primitives {
-
-/// @brief A view of a frontier that provides an interface for the kernel to interact with the frontier data structure.
-template <typename ElementType = std::uint32_t>
-struct frontier_view {
-    using bitmap_t = ElementType;
-    static constexpr std::size_t divide_factor = bitset<bitmap_t>::element_bitsize;
-
-    frontier_view() = default;
-    frontier_view(bitmap_t* data_layer,
-                  bitmap_t* mlb_layer,
-                  std::uint32_t* offsets,
-                  std::uint32_t* offsets_size,
-                  size_t num_items)
-            : _num_items(num_items),
-              _data_layer(bitset<bitmap_t>{data_layer}),
-              _mlb_layer(bitset<bitmap_t>{mlb_layer}),
-              _offsets(offsets),
-              _offsets_size(offsets_size) {}
-
-    inline void insert(std::uint32_t idx) const {
-        if (!_data_layer.test(idx)) {
-            _data_layer.atomic_set(idx);
-        }
-        if (!_mlb_layer.test(idx / divide_factor)) {
-            _mlb_layer.atomic_set(idx / divide_factor);
-        }
-    }
-
-    inline void remove(std::uint32_t idx) const {
-        throw dal::domain_error("Frontier does not support remove operation");
-    }
-
-    inline bool check(std::uint32_t idx) const {
-        return _data_layer.atomic_test(idx);
-    }
-
-    inline size_t get_element_bitsize() const {
-        return bitset<bitmap_t>::element_bitsize;
-    }
-
-    inline std::uint32_t* get_offsets() const {
-        return _offsets;
-    }
-
-    inline std::uint32_t* get_offsets_size() const {
-        return _offsets_size;
-    }
-
-    size_t _num_items;
-
-    bitset<bitmap_t> _data_layer;
-    bitset<bitmap_t> _mlb_layer;
-
-    std::uint32_t* _offsets;
-    std::uint32_t* _offsets_size;
-};
-
-#ifdef ONEDAL_DATA_PARALLEL
-
-/// @brief The Two-Layer bitmap frontier class
-template <typename ElementType = std::uint32_t>
-class frontier {
-    using bitmap_t = ElementType;
-    using buffer_t = std::uint32_t;
-
-public:
-    frontier(sycl::queue& queue, std::size_t num_items, sycl::usm::alloc alloc = sycl::usm::alloc::shared) : _queue(queue), _num_items(num_items) {
-        std::int64_t array_size =
-            (num_items + bitset<bitmap_t>::element_bitsize - 1) / bitset<bitmap_t>::element_bitsize;
-        std::int64_t mlb_size = (array_size + bitset<bitmap_t>::element_bitsize - 1) /
-                        bitset<bitmap_t>::element_bitsize;
-        _data_layer =
-            ndarray<bitmap_t, 1>::empty(_queue, { array_size }, alloc);
-        _mlb_layer =
-            ndarray<bitmap_t, 1>::empty(_queue, { mlb_size }, alloc);
-        _offsets =
-            ndarray<std::uint32_t, 1>::empty(_queue, { array_size + 1 }, alloc); /// First offset is to keep the size of the frontier
-        _buffer = ndarray<std::uint32_t, 1>::empty(_queue, { 10 }, alloc);
-
-        sycl::event e1, e2, e3;
-        e1 = _data_layer.fill(_queue, bitmap_t(0));
-        e2 = _mlb_layer.fill(_queue, bitmap_t(0));
-        e3 = _offsets.fill(_queue, buffer_t(0));
-
-        e1.wait_and_throw();
-        e2.wait_and_throw();
-        e3.wait_and_throw();
-    }
-
-    const frontier_view<bitmap_t> get_device_view() const {
-        auto offsets_size_pointer = _offsets.get_mutable_data();
-        auto offsets_pointer = _offsets.get_mutable_data() + 1;
-
-        return frontier_view<bitmap_t>(_data_layer.get_mutable_data(),
-                                       _mlb_layer.get_mutable_data(),
-                                       offsets_pointer,
-                                       offsets_size_pointer,
-                                       _data_layer.get_count());
-    }
-
-    inline ndview<bitmap_t, 1> get_data() const {
-        return _data_layer;
-    }
-
-    inline ndview<bitmap_t, 1> get_mlb() const {
-        return _mlb_layer;
-    }
-
-    inline ndview<std::uint32_t, 1> get_offsets() const {
-        return _offsets.slice(1, _offsets.get_count());
-    }
-
-    inline ndview<std::uint32_t, 1> get_offsets_size() const {
-        return _offsets.slice(0, 1);
-    }
-
-    bool empty() const {
-        ndview<std::uint32_t, 1> empty_buff = _buffer.slice(0, 1);
-        auto copy_e = fill(_queue, empty_buff, buffer_t(0));
-        auto* const empty_buff_ptr = empty_buff.get_mutable_data();
-
-        auto e = _queue.submit([&](sycl::handler& cgh) {
-            cgh.depends_on(copy_e);
-            const auto range = make_range_1d(_mlb_layer.get_count());
-            auto sum_reduction = sycl::reduction(empty_buff_ptr, sycl::plus<>());
-            auto* const f_ptr = _mlb_layer.get_mutable_data();
-
-            cgh.parallel_for(range, sum_reduction, [=](sycl::id<1> idx, auto& sum_v) {
-                sum_v += f_ptr[idx];
-            });
-        });
-        auto empty_sum = empty_buff.at_device(_queue, 0, { e });
-        return empty_sum == 0;
-    }
-
-    void insert(bitmap_t idx) {
-        auto view = this->get_device_view();
-        _queue.submit(
-            [&](sycl::handler& cgh) {
-                cgh.single_task([=]() {
-                    view.insert(idx);
-                });
-            }
-        ).wait_and_throw();
-    }
-
-    bool check(bitmap_t idx) const {
-        bitmap_t tmp_data = _data_layer.at_device(_queue, idx / bitset<bitmap_t>::element_bitsize);
-        return (tmp_data & (static_cast<bitmap_t>(1) << (idx % bitset<bitmap_t>::element_bitsize))) != 0;
-    }
-
-    void clear() {
-        auto e = fill(_queue, _data_layer, bitmap_t(0));
-        auto e1 = fill(_queue, _mlb_layer, bitmap_t(0));
-        auto e2 = fill(_queue, _offsets, buffer_t(0));
-        e.wait_and_throw();
-        e1.wait_and_throw();
-        e2.wait_and_throw();
-    }
-
-    /// @brief Computes the active frontier by filling the offsets array with the indices of the active vertices.
-    /// It returns a sycl::event that can be used to synchronize the execution.
-    /// The offsets array is filled with the indices of the active vertices in the first layer of the frontier.
-    /// This is used by the primitives to understand which vertices are active in the frontier.
-    sycl::event compute_active_frontier() const {
-        auto bitmap = this->get_device_view();
-
-        auto offsets_size_pointer = _offsets.get_mutable_data();
-        auto offsets_pointer = _offsets.get_mutable_data() + 1;
-
-        uint32_t element_bitsize = decltype(bitmap._mlb_layer)::element_bitsize;
-        size_t local_range = propose_wg_size(this->_queue); 
-        size_t global_range =
-            _mlb_layer.get_count() + local_range - (_mlb_layer.get_count() % local_range);
-
-        bool use_local_mem =
-            device_local_mem_size(this->_queue) >= static_cast<std::int64_t>(local_range * element_bitsize * sizeof(uint32_t));
-
-        auto e0 = _queue.submit([&](sycl::handler& cgh) {
-            cgh.single_task([=, offsets_size = this->get_offsets_size().get_mutable_data(), buffer_ptr = this->_buffer.get_mutable_data(), CAF_FLAG = this->_CAF_FLAG]() {
-                buffer_ptr[CAF_FLAG] = offsets_size[0] == 0 ? 1 : 0;
-            });
-        });
-
-        auto e1 = this->_queue.submit([&](sycl::handler& cgh) {
-            cgh.depends_on(e0);
-
-            if (!use_local_mem || true) { // Force to use global memory for simplicity
-                cgh.parallel_for(make_range_1d(_mlb_layer.get_count()),
-                    [=,
-                    offsets = offsets_pointer,
-                    offsets_size = offsets_size_pointer,
-                    data_layer = this->_mlb_layer.get_mutable_data(),
-                    buffer = this->_buffer.get_mutable_data(),
-                    CAF_FLAG = this->_CAF_FLAG](sycl::id<1> idx) {
-    
-                        if (!buffer[CAF_FLAG]) return;
-    
-                        sycl::atomic_ref<uint32_t,
-                                        sycl::memory_order::relaxed,
-                                        sycl::memory_scope::device>
-                            offsets_size_ref{ offsets_size[0] };
-    
-                        bitmap_t data = data_layer[idx];
-                        for (size_t i = 0; i < element_bitsize; i++) {
-                            if (data & (static_cast<bitmap_t>(1) << i)) {
-                                offsets[offsets_size_ref++] = i + idx * element_bitsize;
-                            }
-                        }
-                });
-            } else {
-                sycl::local_accessor<uint32_t, 1> local_offsets(local_range * element_bitsize, cgh);
-                sycl::local_accessor<uint32_t, 1> local_size(1, cgh);
-
-                cgh.parallel_for(
-                    make_multiple_nd_range_1d(global_range, local_range),
-                    [=,
-                    offsets = offsets_pointer,
-                    offsets_size = offsets_size_pointer,
-                    data_layer = this->_mlb_layer.get_mutable_data(),
-                    size = this->_num_items,
-                    buffer = this->_buffer.get_mutable_data(),
-                    CAF_FLAG = this->_CAF_FLAG](sycl::nd_item<1> item) {
-                        if (!buffer[CAF_FLAG]) return;
-    
-                        auto group = item.get_group();
-                        sycl::atomic_ref<uint32_t,
-                                            sycl::memory_order::relaxed,
-                                            sycl::memory_scope::work_group>
-                            local_size_ref{ local_size[0] };
-                        sycl::atomic_ref<uint32_t,
-                                            sycl::memory_order::relaxed,
-                                            sycl::memory_scope::device>
-                            offsets_size_ref{ offsets_size[0] };
-    
-                        if (group.leader()) {
-                            local_size_ref.store(0);
-                        }
-                        sycl::group_barrier(group);
-                        for (uint32_t gid = item.get_global_linear_id(); gid < size;
-                                gid += local_range) {
-                            bitmap_t data = data_layer[gid];
-                            for (size_t i = 0; i < element_bitsize; i++) {
-                                if (data & (static_cast<bitmap_t>(1) << i)) {
-                                    local_offsets[local_size_ref++] = i + gid * element_bitsize;
-                                }
-                            }
-                        }
-    
-                        sycl::group_barrier(group);
-    
-                        size_t data_offset = 0;
-                        if (group.leader()) {
-                            data_offset = offsets_size_ref.fetch_add(local_size_ref.load());
-                        }
-                        data_offset = sycl::group_broadcast(group, data_offset, 0);
-                        for (size_t i = item.get_local_linear_id(); i < local_size_ref.load();
-                                i += item.get_local_range(0)) {
-                            offsets[data_offset + i] = local_offsets[i];
-                        }
-                    });
-            }
-
-        });
-        return e1;
-    }
-
-private:
-    sycl::queue& _queue;
-    size_t _num_items;
-
-    ndarray<bitmap_t, 1> _data_layer;
-    ndarray<bitmap_t, 1> _mlb_layer;
-    ndarray<std::uint32_t, 1> _offsets;
-    ndarray<buffer_t, 1> _buffer;
-    const size_t _TMP_VAR = 0;
-    const size_t _CAF_FLAG = 1; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
-};
-
-#endif
-
-} // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
similarity index 90%
rename from cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp
rename to cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index 750ff18b4e7..0008d0196a6 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -1,4 +1,6 @@
-#include "oneapi/dal/backend/primitives/frontier.hpp"
+#include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
+#include "oneapi/dal/backend/primitives/frontier/advance_dpc.hpp"
+#include "oneapi/dal/backend/primitives/frontier/graph.hpp"
 
 #include "oneapi/dal/test/engine/common.hpp"
 #include "oneapi/dal/test/engine/fixtures.hpp"
@@ -10,6 +12,8 @@
 
 namespace oneapi::dal::backend::primitives::test {
 
+namespace pr = dal::backend::primitives;
+
 void print_device_name(sycl::queue& queue) {
     const auto device = queue.get_device();
     const auto device_name = device.get_info<sycl::info::device::name>();
@@ -73,9 +77,9 @@ TEST("test advance operation", "[advance]") {
     size_t num_nodes = row_ptr.size() - 1;
 
     
-    auto graph = csr_graph(queue, row_ptr, col_indices, weights);
-    auto in_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
-    auto out_frontier = frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+    auto graph = pr::csr_graph(queue, row_ptr, col_indices, weights);
+    auto in_frontier = pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+    auto out_frontier = pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
     
     in_frontier.insert(3);
     in_frontier.insert(4);
@@ -83,7 +87,7 @@ TEST("test advance operation", "[advance]") {
     in_frontier.insert(100);
     std::vector<std::uint32_t> host_frontier = {3, 4, 52, 100};
 
-    advance(graph, in_frontier, out_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
+    pr::advance(graph, in_frontier, out_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
         return true; // Always advance
     }).wait_and_throw();
     
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
new file mode 100644
index 00000000000..6ab2f007cfe
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -0,0 +1,90 @@
+#include "oneapi/dal/backend/primitives/frontier.hpp"
+
+#include "oneapi/dal/test/engine/common.hpp"
+#include "oneapi/dal/test/engine/fixtures.hpp"
+#include "oneapi/dal/test/engine/dataframe.hpp"
+#include <queue>
+
+namespace oneapi::dal::backend::primitives::test {
+
+namespace pr = dal::backend::primitives;
+
+void print_device_name(sycl::queue& queue) {
+    const auto device = queue.get_device();
+    const auto device_name = device.get_info<sycl::info::device::name>();
+    std::cout << "Running on device: " << device_name << std::endl;
+}
+
+template<typename T>
+std::vector<std::uint32_t> host_bfs(std::vector<T>& row_offsets, std::vector<T>& col_indices, T src) {
+    std::vector<std::uint32_t> distances(row_offsets.size() - 1, std::numeric_limits<std::uint32_t>::max());
+    std::queue<T> q;
+    q.push(src);
+    distances[src] = 0;
+
+    while (!q.empty()) {
+        T node = q.front();
+        q.pop();
+
+        for (size_t i = row_offsets[node]; i < row_offsets[node + 1]; ++i) {
+            auto neighbor = col_indices[i];
+            if (distances[neighbor] == std::numeric_limits<std::uint32_t>::max()) {
+                distances[neighbor] = distances[node] + 1;
+                q.push(neighbor);
+            }
+        }
+    }
+    return distances;
+}
+
+TEST("test advance operation", "[advance]") {
+    DECLARE_TEST_POLICY(policy);
+    auto& queue = policy.get_queue();
+    print_device_name(queue);
+
+    std::vector<std::uint32_t> row_ptr = {0, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225, 229, 233, 237, 241, 245, 249, 253, 257, 261, 265, 269, 273, 277, 281, 285, 289, 293, 297, 301, 305, 309, 313, 317, 321, 325, 329, 333, 337, 341, 345, 349, 353, 357, 361, 365, 369, 373, 377, 381, 385, 389, 393, 397, 401, 405, 409, 413, 417, 421, 425, 429, 433, 437, 441, 445, 449, 453, 457, 461, 465, 469, 473, 477, 481, 485, 489, 493, 497, 501, 504, 506};
+    std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 3, 0, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 6, 3, 4, 6, 7, 4, 5, 7, 8, 5, 6, 8, 9, 6, 7, 9, 10, 7, 8, 10, 11, 8, 9, 11, 12, 9, 10, 12, 13, 10, 11, 13, 14, 11, 12, 14, 15, 12, 13, 15, 16, 13, 14, 16, 17, 14, 15, 17, 18, 15, 16, 18, 19, 16, 17, 19, 20, 17, 18, 20, 21, 18, 19, 21, 22, 19, 20, 22, 23, 20, 21, 23, 24, 21, 22, 24, 25, 22, 23, 25, 26, 23, 24, 26, 27, 24, 25, 27, 28, 25, 26, 28, 29, 26, 27, 29, 30, 27, 28, 30, 31, 28, 29, 31, 32, 29, 30, 32, 33, 30, 31, 33, 34, 31, 32, 34, 35, 32, 33, 35, 36, 33, 34, 36, 37, 34, 35, 37, 38, 35, 36, 38, 39, 36, 37, 39, 40, 37, 38, 40, 41, 38, 39, 41, 42, 39, 40, 42, 43, 40, 41, 43, 44, 41, 42, 44, 45, 42, 43, 45, 46, 43, 44, 46, 47, 44, 45, 47, 48, 45, 46, 48, 49, 46, 47, 49, 50, 47, 48, 50, 51, 48, 49, 51, 52, 49, 50, 52, 53, 50, 51, 53, 54, 51, 52, 54, 55, 52, 53, 55, 56, 53, 54, 56, 57, 54, 55, 57, 58, 55, 56, 58, 59, 56, 57, 59, 60, 57, 58, 60, 61, 58, 59, 61, 62, 59, 60, 62, 63, 60, 61, 63, 64, 61, 62, 64, 65, 62, 63, 65, 66, 63, 64, 66, 67, 64, 65, 67, 68, 65, 66, 68, 69, 66, 67, 69, 70, 67, 68, 70, 71, 68, 69, 71, 72, 69, 70, 72, 73, 70, 71, 73, 74, 71, 72, 74, 75, 72, 73, 75, 76, 73, 74, 76, 77, 74, 75, 77, 78, 75, 76, 78, 79, 76, 77, 79, 80, 77, 78, 80, 81, 78, 79, 81, 82, 79, 80, 82, 83, 80, 81, 83, 84, 81, 82, 84, 85, 82, 83, 85, 86, 83, 84, 86, 87, 84, 85, 87, 88, 85, 86, 88, 89, 86, 87, 89, 90, 87, 88, 90, 91, 88, 89, 91, 92, 89, 90, 92, 93, 90, 91, 93, 94, 91, 92, 94, 95, 92, 93, 95, 96, 93, 94, 96, 97, 94, 95, 97, 98, 95, 96, 98, 99, 96, 97, 99, 100, 97, 98, 100, 101, 98, 99, 101, 102, 99, 100, 102, 103, 100, 101, 103, 104, 101, 102, 104, 105, 102, 103, 105, 106, 103, 104, 106, 107, 104, 105, 107, 108, 105, 106, 108, 109, 106, 107, 109, 110, 107, 108, 110, 111, 108, 109, 111, 112, 109, 110, 112, 113, 110, 111, 113, 114, 111, 112, 114, 115, 112, 113, 115, 116, 113, 114, 116, 117, 114, 115, 117, 118, 115, 116, 118, 119, 116, 117, 119, 120, 117, 118, 120, 121, 118, 119, 121, 122, 119, 120, 122, 123, 120, 121, 123, 124, 121, 122, 124, 125, 122, 123, 125, 126, 123, 124, 126, 127, 124, 125, 127, 125, 126};
+    std::vector<std::uint32_t> weights(col_indices.size(), 1);
+    
+    auto graph = pr::csr_graph(queue, row_ptr, col_indices, weights);
+    size_t num_nodes = row_ptr.size() - 1;
+    auto in_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
+    auto out_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
+    pr::ndarray<std::uint32_t, 1> distance = pr::ndarray<std::uint32_t, 1>::empty(queue, {static_cast<std::int64_t>(num_nodes)}, sycl::usm::alloc::device);
+    auto distance_ptr = distance.get_mutable_data();
+
+    const std::uint32_t src = 0;
+
+    queue.submit([&](sycl::handler& cgh) {
+        cgh.parallel_for(sycl::range<1>(num_nodes), [=](sycl::id<1> idx) {
+            distance_ptr[idx] = idx[0] == src ? 0 : num_nodes + 1;
+        });
+    }).wait_and_throw();
+    
+    in_frontier.insert(src);
+    size_t iter = 0;
+
+    /// Start BFS
+    while (!in_frontier.empty()) {
+        pr::advance(graph, in_frontier, out_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
+            bool visited = distance_ptr[neighbor] < num_nodes + 1;
+            if (!visited) {
+                distance_ptr[neighbor] = iter + 1;
+            }
+            return !visited;
+        }).wait_and_throw();
+        iter++;
+        pr::swap_frontiers(in_frontier, out_frontier);
+        out_frontier.clear();
+    }
+    /// End BFS
+
+    auto expected_distances = host_bfs(row_ptr, col_indices, src);
+    auto actual_distances = distance.to_host(queue).get_data();
+    for (size_t i = 0; i < num_nodes; ++i) {
+        REQUIRE(actual_distances[i] == expected_distances[i]);
+    }
+
+} // TEST "test advance operation"
+
+} // namespace oneapi::dal::backend::primitives::test
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
similarity index 87%
rename from cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
rename to cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
index 93bb2737204..6117bf61ee2 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/basic_frontier_ops_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
@@ -1,8 +1,4 @@
-#include "oneapi/dal/backend/primitives/frontier.hpp"
-
-#include "oneapi/dal/test/engine/common.hpp"
-#include "oneapi/dal/test/engine/fixtures.hpp"
-#include "oneapi/dal/test/engine/dataframe.hpp"
+#include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 
 #include "oneapi/dal/test/engine/common.hpp"
 #include "oneapi/dal/test/engine/fixtures.hpp"
@@ -10,6 +6,8 @@
 
 namespace oneapi::dal::backend::primitives::test {
 
+namespace pr = dal::backend::primitives;
+
 void print_device_name(sycl::queue& queue) {
     const auto device = queue.get_device();
     const auto device_name = device.get_info<sycl::info::device::name>();
@@ -32,7 +30,7 @@ TEST("frontier queue basic operations", "[frontier]") {
     print_device_name(queue);
 
     const std::size_t num_items = 100;
-    auto f = frontier<std::uint32_t>(queue, num_items, sycl::usm::alloc::shared);
+    auto f = pr::frontier<std::uint32_t>(queue, num_items, sycl::usm::alloc::shared);
 
     REQUIRE(f.empty() == true);
     f.insert(0);

From 27a71b032754e5785676b2358d816437151f2bc0 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Mon, 28 Jul 2025 17:11:58 +0200
Subject: [PATCH 13/69] add performance tests for bfs

---
 .../dal/backend/primitives/frontier/BUILD     | 15 ++++++
 .../test/{bfs_dpc.cpp => bfs_perf_dpc.cpp}    | 52 ++++++++++++++++++-
 2 files changed, 65 insertions(+), 2 deletions(-)
 rename cpp/oneapi/dal/backend/primitives/frontier/test/{bfs_dpc.cpp => bfs_perf_dpc.cpp} (77%)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/BUILD b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
index 1a224d76188..ef392864d39 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/BUILD
+++ b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
@@ -22,6 +22,21 @@ dal_test_suite (
     private = True,
     srcs = glob([
         "test/*_dpc.cpp",
+    ], exclude=[
+        "test/*perf*.cpp",
+    ]),
+    dal_deps = [
+        ":frontier",
+    ],
+)
+
+dal_test_suite(
+    name = "perf_tests",
+    framework = "catch2",
+    compile_as = [ "dpc++" ],
+    private = True,
+    srcs = glob([
+        "test/*perf_dpc.cpp",
     ]),
     dal_deps = [
         ":frontier",
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
similarity index 77%
rename from cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
rename to cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
index 6ab2f007cfe..579861e2841 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
@@ -4,11 +4,51 @@
 #include "oneapi/dal/test/engine/fixtures.hpp"
 #include "oneapi/dal/test/engine/dataframe.hpp"
 #include <queue>
+#include <vector>
+#include <map>
+#include <chrono>
 
 namespace oneapi::dal::backend::primitives::test {
 
 namespace pr = dal::backend::primitives;
 
+class PerformanceTester {
+public:
+    void add(const std::string& name, const sycl::event& event) {
+        if (timings_.find(name) == timings_.end()) {
+            timings_[name] = std::vector<sycl::event>();
+        }
+        timings_[name].push_back(event);
+    }
+
+    void set_start() {
+        start_time_ = std::chrono::high_resolution_clock::now();
+    }
+
+    void set_end() {
+        auto end_time = std::chrono::high_resolution_clock::now();
+        auto duration = std::chrono::duration_cast<std::chrono::milliseconds>(end_time - start_time_).count();
+        std::cout << "Total execution time: " << duration << " ms" << std::endl;
+    }
+
+    void print() const {
+        for (const auto& [name, events] : timings_) {
+            std::cout << "Performance for " << name << ": ";
+            for (const auto& event : events) {
+                auto duration = event.get_profiling_info<sycl::info::event_profiling::command_end>() -
+                                event.get_profiling_info<sycl::info::event_profiling::command_start>();
+                std::cout << duration / 1e6 << " ms ";
+            }
+            std::cout << std::endl;
+        }
+    }
+
+private:
+    // define start time
+    std::chrono::high_resolution_clock::time_point start_time_;
+    std::map<std::string, std::vector<sycl::event>> timings_;
+};
+
 void print_device_name(sycl::queue& queue) {
     const auto device = queue.get_device();
     const auto device_name = device.get_info<sycl::info::device::name>();
@@ -42,6 +82,8 @@ TEST("test advance operation", "[advance]") {
     auto& queue = policy.get_queue();
     print_device_name(queue);
 
+    PerformanceTester perf_tester;
+
     std::vector<std::uint32_t> row_ptr = {0, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225, 229, 233, 237, 241, 245, 249, 253, 257, 261, 265, 269, 273, 277, 281, 285, 289, 293, 297, 301, 305, 309, 313, 317, 321, 325, 329, 333, 337, 341, 345, 349, 353, 357, 361, 365, 369, 373, 377, 381, 385, 389, 393, 397, 401, 405, 409, 413, 417, 421, 425, 429, 433, 437, 441, 445, 449, 453, 457, 461, 465, 469, 473, 477, 481, 485, 489, 493, 497, 501, 504, 506};
     std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 3, 0, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 6, 3, 4, 6, 7, 4, 5, 7, 8, 5, 6, 8, 9, 6, 7, 9, 10, 7, 8, 10, 11, 8, 9, 11, 12, 9, 10, 12, 13, 10, 11, 13, 14, 11, 12, 14, 15, 12, 13, 15, 16, 13, 14, 16, 17, 14, 15, 17, 18, 15, 16, 18, 19, 16, 17, 19, 20, 17, 18, 20, 21, 18, 19, 21, 22, 19, 20, 22, 23, 20, 21, 23, 24, 21, 22, 24, 25, 22, 23, 25, 26, 23, 24, 26, 27, 24, 25, 27, 28, 25, 26, 28, 29, 26, 27, 29, 30, 27, 28, 30, 31, 28, 29, 31, 32, 29, 30, 32, 33, 30, 31, 33, 34, 31, 32, 34, 35, 32, 33, 35, 36, 33, 34, 36, 37, 34, 35, 37, 38, 35, 36, 38, 39, 36, 37, 39, 40, 37, 38, 40, 41, 38, 39, 41, 42, 39, 40, 42, 43, 40, 41, 43, 44, 41, 42, 44, 45, 42, 43, 45, 46, 43, 44, 46, 47, 44, 45, 47, 48, 45, 46, 48, 49, 46, 47, 49, 50, 47, 48, 50, 51, 48, 49, 51, 52, 49, 50, 52, 53, 50, 51, 53, 54, 51, 52, 54, 55, 52, 53, 55, 56, 53, 54, 56, 57, 54, 55, 57, 58, 55, 56, 58, 59, 56, 57, 59, 60, 57, 58, 60, 61, 58, 59, 61, 62, 59, 60, 62, 63, 60, 61, 63, 64, 61, 62, 64, 65, 62, 63, 65, 66, 63, 64, 66, 67, 64, 65, 67, 68, 65, 66, 68, 69, 66, 67, 69, 70, 67, 68, 70, 71, 68, 69, 71, 72, 69, 70, 72, 73, 70, 71, 73, 74, 71, 72, 74, 75, 72, 73, 75, 76, 73, 74, 76, 77, 74, 75, 77, 78, 75, 76, 78, 79, 76, 77, 79, 80, 77, 78, 80, 81, 78, 79, 81, 82, 79, 80, 82, 83, 80, 81, 83, 84, 81, 82, 84, 85, 82, 83, 85, 86, 83, 84, 86, 87, 84, 85, 87, 88, 85, 86, 88, 89, 86, 87, 89, 90, 87, 88, 90, 91, 88, 89, 91, 92, 89, 90, 92, 93, 90, 91, 93, 94, 91, 92, 94, 95, 92, 93, 95, 96, 93, 94, 96, 97, 94, 95, 97, 98, 95, 96, 98, 99, 96, 97, 99, 100, 97, 98, 100, 101, 98, 99, 101, 102, 99, 100, 102, 103, 100, 101, 103, 104, 101, 102, 104, 105, 102, 103, 105, 106, 103, 104, 106, 107, 104, 105, 107, 108, 105, 106, 108, 109, 106, 107, 109, 110, 107, 108, 110, 111, 108, 109, 111, 112, 109, 110, 112, 113, 110, 111, 113, 114, 111, 112, 114, 115, 112, 113, 115, 116, 113, 114, 116, 117, 114, 115, 117, 118, 115, 116, 118, 119, 116, 117, 119, 120, 117, 118, 120, 121, 118, 119, 121, 122, 119, 120, 122, 123, 120, 121, 123, 124, 121, 122, 124, 125, 122, 123, 125, 126, 123, 124, 126, 127, 124, 125, 127, 125, 126};
     std::vector<std::uint32_t> weights(col_indices.size(), 1);
@@ -65,20 +107,26 @@ TEST("test advance operation", "[advance]") {
     size_t iter = 0;
 
     /// Start BFS
+    perf_tester.set_start();
     while (!in_frontier.empty()) {
-        pr::advance(graph, in_frontier, out_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
+        auto e = pr::advance(graph, in_frontier, out_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
             bool visited = distance_ptr[neighbor] < num_nodes + 1;
             if (!visited) {
                 distance_ptr[neighbor] = iter + 1;
             }
             return !visited;
-        }).wait_and_throw();
+        });
+        perf_tester.add("advance", e);
+        e.wait_and_throw();
         iter++;
         pr::swap_frontiers(in_frontier, out_frontier);
         out_frontier.clear();
     }
+    perf_tester.set_end();
     /// End BFS
 
+    // perf_tester.print();
+
     auto expected_distances = host_bfs(row_ptr, col_indices, src);
     auto actual_distances = distance.to_host(queue).get_data();
     for (size_t i = 0; i < num_nodes; ++i) {

From 9dcba2e83d1b872bf8f7a65c5e1013afbc41903f Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 27 Aug 2025 16:21:39 +0200
Subject: [PATCH 14/69] Refactor advance function to remove expected_size
 parameter and optimize global size calculation

---
 .../primitives/frontier/advance_dpc.hpp       | 40 +++++++++----------
 .../primitives/frontier/frontier_dpc.cpp      | 21 +++++-----
 2 files changed, 29 insertions(+), 32 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
index ef91511d661..38551a07279 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
@@ -195,7 +195,7 @@ struct BitmapKernel {
 template<typename FrontierSizeT,
          typename GraphT,
          typename LambdaT>
-sycl::event advance(const GraphT& graph, frontier<FrontierSizeT>& in, frontier<FrontierSizeT>& out, LambdaT&& functor, size_t expected_size = 0) {
+sycl::event advance(const GraphT& graph, frontier<FrontierSizeT>& in, frontier<FrontierSizeT>& out, LambdaT&& functor) {
   using element_t = FrontierSizeT;
   
   sycl::queue& q = graph.get_queue();
@@ -207,19 +207,15 @@ sycl::event advance(const GraphT& graph, frontier<FrontierSizeT>& in, frontier<F
   auto graph_dev = graph.get_device_view();
 
   size_t coarsening_factor = 1; // it should be Compute Unit Size / num subgroups
-  
-  size_t element_bitsize = in_dev_frontier.get_element_bitsize();
-  sycl::range<1> local_range = {element_bitsize * coarsening_factor};
+
+  size_t element_bitsize = in_dev_frontier.get_element_bitsize(); // in bits
+  sycl::range<1> local_range = {element_bitsize * coarsening_factor}; 
   size_t global_size;
 
-  if (expected_size > 0) {
-      global_size = expected_size * element_bitsize;
-    } else {
-      global_size = 1024; // This parameter should be tuned according to the device capabilities
-    }
+  sycl::event to_wait = in.compute_active_frontier(); // kernel launch to compute active bitmap regions
+  auto offset_size = in.get_offsets_size().at_device(q, 0, {to_wait});
+  global_size = offset_size * element_bitsize;
 
-  sycl::event to_wait = in.compute_active_frontier();
-  
   sycl::range<1> global_range{(global_size % local_range[0] == 0) ? global_size : global_size + (local_range[0] - global_size % local_range[0])};
 
   Context<decltype(in_dev_frontier), decltype(out_dev_frontier)> context{num_nodes, in_dev_frontier, out_dev_frontier};
@@ -229,17 +225,17 @@ sycl::event advance(const GraphT& graph, frontier<FrontierSizeT>& in, frontier<F
 
   auto e = q.submit([&](sycl::handler& cgh) {
     cgh.depends_on(to_wait);
-    sycl::local_accessor<uint32_t, 1> n_edges_wg{local_range, cgh};
-    sycl::local_accessor<uint32_t, 1> n_edges_sg{local_range, cgh};
-    sycl::local_accessor<bool, 1> visited{local_range, cgh};
-    sycl::local_accessor<element_t, 1> subgroup_reduce{local_range, cgh};
-    sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail{max_num_subgroups, cgh};
-    sycl::local_accessor<uint32_t, 1> subgroup_ids{local_range, cgh};
-    sycl::local_accessor<element_t, 1> workgroup_reduce{local_range, cgh};
-    sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail{1, cgh};
-    sycl::local_accessor<uint32_t, 1> workgroup_ids{local_range, cgh};
-    sycl::local_accessor<element_t, 1> individual_reduce{local_range, cgh};
-    sycl::local_accessor<uint32_t, 1> individual_reduce_tail{1, cgh};
+    sycl::local_accessor<uint32_t, 1> n_edges_wg{local_range, cgh};                 // number of edges of vertices to process at work-group granularity
+    sycl::local_accessor<uint32_t, 1> n_edges_sg{local_range, cgh};                 // number of edges of vertices to process at sub-group granularity
+    sycl::local_accessor<bool, 1> visited{local_range, cgh};                        // tracks the vertices already visited at work-group and sub-group granularity
+    sycl::local_accessor<element_t, 1> subgroup_reduce{local_range, cgh};           // stores the vertices to process at sub-group granularity
+    sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail{max_num_subgroups, cgh}; // stores the tail of the subgroup reduction
+    sycl::local_accessor<uint32_t, 1> subgroup_ids{local_range, cgh};               // stores the thread id that found the vertex to process at sub-group level
+    sycl::local_accessor<element_t, 1> workgroup_reduce{local_range, cgh};          // stores the vertices to process at work-group granularity
+    sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail{1, cgh};                // stores the tail of the work-group reduction
+    sycl::local_accessor<uint32_t, 1> workgroup_ids{local_range, cgh};              // stores the thread id that found the vertex to process at work-group level
+    sycl::local_accessor<element_t, 1> individual_reduce{local_range, cgh};         // stores the vertices to process at individual thread granularity
+    sycl::local_accessor<uint32_t, 1> individual_reduce_tail{1, cgh};               // stores the tail of the individual thread reduction
 
 
     cgh.parallel_for(sycl::nd_range<1>{global_range, local_range},
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index bbda488a7f9..6287fbc2298 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -86,10 +86,11 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
     auto offsets_pointer = _offsets.get_mutable_data() + 1;
 
     uint32_t element_bitsize = bitmap.get_element_bitsize();
-    size_t local_range = propose_wg_size(this->_queue); 
-    size_t global_range =
-        _mlb_layer.get_count() + local_range - (_mlb_layer.get_count() % local_range);
+    size_t local_range = 256;// propose_wg_size(this->_queue); 
+    size_t mlb_count = _mlb_layer.get_count();
+    size_t global_range = (mlb_count % local_range == 0) ? mlb_count : (mlb_count + local_range - (mlb_count % local_range));
 
+    // check if local memory is enough
     bool use_local_mem =
         device_local_mem_size(this->_queue) >= static_cast<std::int64_t>(local_range * element_bitsize * sizeof(uint32_t));
 
@@ -102,7 +103,7 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
     auto e1 = this->_queue.submit([&](sycl::handler& cgh) {
         cgh.depends_on(e0);
 
-        if (!use_local_mem || true) { // Force to use global memory for simplicity
+        if (!use_local_mem) {   
             cgh.parallel_for(make_range_1d(_mlb_layer.get_count()),
                 [=,
                 offsets = offsets_pointer,
@@ -135,19 +136,19 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
                 offsets = offsets_pointer,
                 offsets_size = offsets_size_pointer,
                 data_layer = this->_mlb_layer.get_mutable_data(),
-                size = this->_num_items,
+                size = mlb_count,
                 buffer = this->_buffer.get_mutable_data(),
                 CAF_FLAG = this->_CAF_FLAG](sycl::nd_item<1> item) {
                     if (!buffer[CAF_FLAG]) return;
 
                     auto group = item.get_group();
                     sycl::atomic_ref<uint32_t,
-                                        sycl::memory_order::relaxed,
-                                        sycl::memory_scope::work_group>
+                                     sycl::memory_order::relaxed,
+                                     sycl::memory_scope::work_group>
                         local_size_ref{ local_size[0] };
                     sycl::atomic_ref<uint32_t,
-                                        sycl::memory_order::relaxed,
-                                        sycl::memory_scope::device>
+                                     sycl::memory_order::relaxed,
+                                     sycl::memory_scope::device>
                         offsets_size_ref{ offsets_size[0] };
 
                     if (group.leader()) {
@@ -155,7 +156,7 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
                     }
                     sycl::group_barrier(group);
                     for (uint32_t gid = item.get_global_linear_id(); gid < size;
-                            gid += local_range) {
+                            gid += item.get_global_range(0)) {
                         ElementType data = data_layer[gid];
                         for (size_t i = 0; i < element_bitsize; i++) {
                             if (data & (static_cast<ElementType>(1) << i)) {

From fcc4f75462edd019724672372b629a2cf429a141 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 27 Aug 2025 16:30:26 +0200
Subject: [PATCH 15/69] moved bitset to frontier folder

---
 cpp/oneapi/dal/backend/primitives/bitset.hpp                    | 1 -
 .../dal/backend/primitives/{bitset => frontier}/bitset.hpp      | 0
 cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp         | 2 +-
 cpp/oneapi/dal/backend/primitives/frontier/graph.hpp            | 2 +-
 4 files changed, 2 insertions(+), 3 deletions(-)
 delete mode 100644 cpp/oneapi/dal/backend/primitives/bitset.hpp
 rename cpp/oneapi/dal/backend/primitives/{bitset => frontier}/bitset.hpp (100%)

diff --git a/cpp/oneapi/dal/backend/primitives/bitset.hpp b/cpp/oneapi/dal/backend/primitives/bitset.hpp
deleted file mode 100644
index 905603885cb..00000000000
--- a/cpp/oneapi/dal/backend/primitives/bitset.hpp
+++ /dev/null
@@ -1 +0,0 @@
-#include "oneapi/dal/backend/primitives/bitset/bitset.hpp"
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
similarity index 100%
rename from cpp/oneapi/dal/backend/primitives/bitset/bitset.hpp
rename to cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index 5de56bc2fde..5ccfce81b74 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -4,7 +4,7 @@
 #include "oneapi/dal/backend/common.hpp"
 #include "oneapi/dal/graph/detail/common.hpp"
 #include "oneapi/dal/graph/detail/container.hpp"
-#include "oneapi/dal/backend/primitives/bitset.hpp"
+#include "oneapi/dal/backend/primitives/frontier/bitset.hpp"
 #include "oneapi/dal/backend/primitives/ndarray.hpp"
 
 namespace oneapi::dal::backend::primitives {
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index 825a119dbc5..f63ad131d9b 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -3,7 +3,7 @@
 #include "oneapi/dal/common.hpp"
 #include "oneapi/dal/graph/detail/common.hpp"
 #include "oneapi/dal/graph/detail/container.hpp"
-#include "oneapi/dal/backend/primitives/bitset.hpp"
+#include "oneapi/dal/backend/primitives/frontier/bitset.hpp"
 #include "oneapi/dal/backend/primitives/ndarray.hpp"
 
 namespace oneapi::dal::backend::primitives {

From 1e40aa94de1a1715bed9189617ad44ec9c137553 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 27 Aug 2025 16:32:22 +0200
Subject: [PATCH 16/69] applied clang-format

---
 .../primitives/frontier/advance_dpc.hpp       | 504 ++++++++++--------
 .../backend/primitives/frontier/bitset.hpp    |   9 +-
 .../backend/primitives/frontier/frontier.hpp  |  16 +-
 .../primitives/frontier/frontier_dpc.cpp      | 129 +++--
 .../dal/backend/primitives/frontier/graph.hpp | 252 ++++-----
 .../primitives/frontier/test/advance_dpc.cpp  |  81 ++-
 .../primitives/frontier/test/bfs_perf_dpc.cpp |  98 +++-
 .../primitives/frontier/test/frontier_dpc.cpp |   9 +-
 8 files changed, 637 insertions(+), 461 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
index 38551a07279..c9c121eab69 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
@@ -4,17 +4,16 @@
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 
-
 namespace oneapi::dal::backend::primitives {
 
 /// ContextState holds the state of the current processing group in the kernel
 /// It includes the group offset, coarsening factor, offsets size, and the SYCL
 /// nd_item for the current work item.
 struct ContextState {
-  size_t group_offset;
-  const uint16_t coarsening_factor;
-  const uint32_t offsets_size;
-  const sycl::nd_item<1> item;
+    size_t group_offset;
+    const uint16_t coarsening_factor;
+    const uint32_t offsets_size;
+    const sycl::nd_item<1> item;
 };
 
 /// Context is a template class that provides an interface for the kernel to
@@ -23,168 +22,195 @@ struct ContextState {
 /// the context state, check if there are more elements to process, get the
 /// assigned element, check if a vertex is in the frontier, and insert a vertex
 /// into the output frontier.
-template<typename InFrontierDevT, typename OutFrontierDevT>
+template <typename InFrontierDevT, typename OutFrontierDevT>
 struct Context {
-  size_t limit;
-  InFrontierDevT in_dev_frontier;
-  OutFrontierDevT out_dev_frontier;
-
-  Context(size_t limit, InFrontierDevT in_dev_frontier, OutFrontierDevT out_dev_frontier)
-      : limit(limit), in_dev_frontier(in_dev_frontier), out_dev_frontier(out_dev_frontier) {}
-
-  inline ContextState init(sycl::nd_item<1>& item) const {
-    return {
-        item.get_group_linear_id(),
-        static_cast<uint16_t>(item.get_local_range(0) / in_dev_frontier.get_element_bitsize()),
-        in_dev_frontier.get_offsets_size()[0],
-        item,
-    };
-  }
-
-  /// This method checks if there are more elements to process in the current group.
-  inline bool need_to_process(ContextState& state) const { return (state.group_offset * state.coarsening_factor < state.offsets_size); }
-
-  /// This method completes the current iteration by updating the group offset.
-  inline void complete_iteration(ContextState& state) const { state.group_offset += state.item.get_group_range(0); }
-
-  /// This method retrieves the assigned element for the current work item.
-  inline size_t get_assigned_element(const ContextState& state) const {
-    const uint16_t element_bitsize = in_dev_frontier.get_element_bitsize();
-    const uint32_t acutal_id_offset = (state.group_offset * state.coarsening_factor) + (state.item.get_local_linear_id() / element_bitsize);
-    const uint32_t* bitmap_offsets = in_dev_frontier.get_offsets();
-    // const size_t acutal_id_offset = (item.get_group_linear_id() * coarsening_factor) + (item.get_local_linear_id() / bitmap_range);
-    const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * element_bitsize) + (state.item.get_local_linear_id() % element_bitsize);
-    return assigned_vertex;
-  }
-
-  /// This method checks if a vertex is in the input frontier.
-  inline bool check(const ContextState& state, size_t vertex) const {
-    return vertex < limit && in_dev_frontier.check(vertex);
-  }
-
-  /// This method inserts a vertex into the output frontier.
-  inline void insert(const ContextState& state, size_t vertex) const {
-    out_dev_frontier.insert(vertex);
-  }
-};
-
-/// BitmapKernel is a template struct that defines the kernel to be executed on the device.
-/// It processes the input frontier and advances it based on the provided functor.
-template<typename T,
-         typename ContextT,
-         typename GraphDevT,
-         typename LambdaT>
-struct BitmapKernel {
-  void operator()(sycl::nd_item<1> item) const {
-    const size_t lid = item.get_local_linear_id();
-    const auto wgroup = item.get_group();
-    const size_t wgroup_size = wgroup.get_local_range(0);
-    const auto sgroup = item.get_sub_group();
-    const auto sgroup_id = sgroup.get_group_id();
-    const size_t sgroup_size = sgroup.get_local_range()[0];
-    const size_t llid = sgroup.get_local_linear_id();
-
-    auto state = context.init(item);
-
-    while (context.need_to_process(state)) {
-      const auto assigned_vertex = context.get_assigned_element(state);
-
-      if (sgroup.leader()) { subgroup_reduce_tail[sgroup_id] = 0; }
-      if (wgroup.leader()) { workgroup_reduce_tail[0] = 0; }
-
-      sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group> sg_tail{subgroup_reduce_tail[sgroup_id]};
-      sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group> wg_tail{workgroup_reduce_tail[0]};
-
-      // 1. distribute the workload based on the number of edges to the workgroup, subgroup or workitem
-      const uint32_t offset = sgroup_id * sgroup_size;
-      if (context.check(state, assigned_vertex)) {
-        uint32_t n_edges = graph_dev.get_degree(assigned_vertex); 
-        if (n_edges >= wgroup_size * wgroup_size) { // if the number of edges is large enough, we can assign the vertex to the workgroup
-          uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
-          n_edges_wg[loc] = n_edges;
-          workgroup_reduce[loc] = assigned_vertex;
-          workgroup_ids[loc] = lid;
-        } else if (n_edges >= sgroup_size) { // assign to the subgroup
-          uint32_t loc = sg_tail.fetch_add(static_cast<uint32_t>(1));
-          n_edges_sg[offset + loc] = n_edges;
-          subgroup_reduce[offset + loc] = assigned_vertex;
-          subgroup_ids[offset + loc] = lid;
-        }
-        visited[lid] = false;
-      } else {
-        visited[lid] = true;
-      }
-
-      sycl::group_barrier(wgroup);
-
-      // 2. process the the edge of one vertex at a time using the workgroup
-      for (size_t i = 0; i < wg_tail.load(); i++) {
-        auto vertex = workgroup_reduce[i];
-        size_t n_edges = n_edges_wg[i];
-        auto start = graph_dev.begin(vertex); 
-
-        for (auto j = lid; j < n_edges; j += wgroup_size) {
-          auto n = start + j;
-          auto edge = n.get_index(); 
-          auto weight = graph_dev.get_weight(edge); 
-          auto neighbor = *n;
-          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
-        }
+    size_t limit;
+    InFrontierDevT in_dev_frontier;
+    OutFrontierDevT out_dev_frontier;
+
+    Context(size_t limit, InFrontierDevT in_dev_frontier, OutFrontierDevT out_dev_frontier)
+            : limit(limit),
+              in_dev_frontier(in_dev_frontier),
+              out_dev_frontier(out_dev_frontier) {}
+
+    inline ContextState init(sycl::nd_item<1>& item) const {
+        return {
+            item.get_group_linear_id(),
+            static_cast<uint16_t>(item.get_local_range(0) / in_dev_frontier.get_element_bitsize()),
+            in_dev_frontier.get_offsets_size()[0],
+            item,
+        };
+    }
 
-        if (wgroup.leader()) { visited[workgroup_ids[i]] = true; }
-      }
+    /// This method checks if there are more elements to process in the current group.
+    inline bool need_to_process(ContextState& state) const {
+        return (state.group_offset * state.coarsening_factor < state.offsets_size);
+    }
 
-      sycl::group_barrier(sgroup);
+    /// This method completes the current iteration by updating the group offset.
+    inline void complete_iteration(ContextState& state) const {
+        state.group_offset += state.item.get_group_range(0);
+    }
 
-      // 3. process the edges of one vertex at a time using the subgroup
-      for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) { // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
-        size_t vertex_id = offset + i;
-        auto vertex = subgroup_reduce[vertex_id];
-        size_t n_edges = n_edges_sg[vertex_id];
+    /// This method retrieves the assigned element for the current work item.
+    inline size_t get_assigned_element(const ContextState& state) const {
+        const uint16_t element_bitsize = in_dev_frontier.get_element_bitsize();
+        const uint32_t acutal_id_offset = (state.group_offset * state.coarsening_factor) +
+                                          (state.item.get_local_linear_id() / element_bitsize);
+        const uint32_t* bitmap_offsets = in_dev_frontier.get_offsets();
+        // const size_t acutal_id_offset = (item.get_group_linear_id() * coarsening_factor) + (item.get_local_linear_id() / bitmap_range);
+        const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * element_bitsize) +
+                                     (state.item.get_local_linear_id() % element_bitsize);
+        return assigned_vertex;
+    }
 
-        auto start = graph_dev.begin(vertex); 
+    /// This method checks if a vertex is in the input frontier.
+    inline bool check(const ContextState& state, size_t vertex) const {
+        return vertex < limit && in_dev_frontier.check(vertex);
+    }
 
-        for (auto j = llid; j < n_edges; j += sgroup_size) {
-          auto n = start + j;
-          auto edge = n.get_index();
-          auto weight = graph_dev.get_weight(edge); 
-          auto neighbor = *n;
-          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
-        }
+    /// This method inserts a vertex into the output frontier.
+    inline void insert(const ContextState& state, size_t vertex) const {
+        out_dev_frontier.insert(vertex);
+    }
+};
 
-        if (sgroup.leader()) { visited[subgroup_ids[vertex_id]] = true; }
-      }
-      sycl::group_barrier(sgroup);
-
-      // 4. process the edges of the vertices that were not assigned to the workgroup or subgroup
-      if (!visited[lid]) {
-        auto vertex = assigned_vertex;
-        auto start = graph_dev.begin(vertex); 
-        auto end = graph_dev.end(vertex); 
-
-        for (auto n = start; n != end; ++n) {
-          auto edge = n.get_index(); 
-          auto weight = graph_dev.get_weight(edge); 
-          auto neighbor = *n;
-          if (functor(vertex, neighbor, edge, weight)) { context.insert(state, neighbor); }
+/// BitmapKernel is a template struct that defines the kernel to be executed on the device.
+/// It processes the input frontier and advances it based on the provided functor.
+template <typename T, typename ContextT, typename GraphDevT, typename LambdaT>
+struct BitmapKernel {
+    void operator()(sycl::nd_item<1> item) const {
+        const size_t lid = item.get_local_linear_id();
+        const auto wgroup = item.get_group();
+        const size_t wgroup_size = wgroup.get_local_range(0);
+        const auto sgroup = item.get_sub_group();
+        const auto sgroup_id = sgroup.get_group_id();
+        const size_t sgroup_size = sgroup.get_local_range()[0];
+        const size_t llid = sgroup.get_local_linear_id();
+
+        auto state = context.init(item);
+
+        while (context.need_to_process(state)) {
+            const auto assigned_vertex = context.get_assigned_element(state);
+
+            if (sgroup.leader()) {
+                subgroup_reduce_tail[sgroup_id] = 0;
+            }
+            if (wgroup.leader()) {
+                workgroup_reduce_tail[0] = 0;
+            }
+
+            sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group>
+                sg_tail{ subgroup_reduce_tail[sgroup_id] };
+            sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group>
+                wg_tail{ workgroup_reduce_tail[0] };
+
+            // 1. distribute the workload based on the number of edges to the workgroup, subgroup or workitem
+            const uint32_t offset = sgroup_id * sgroup_size;
+            if (context.check(state, assigned_vertex)) {
+                uint32_t n_edges = graph_dev.get_degree(assigned_vertex);
+                if (n_edges >=
+                    wgroup_size *
+                        wgroup_size) { // if the number of edges is large enough, we can assign the vertex to the workgroup
+                    uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
+                    n_edges_wg[loc] = n_edges;
+                    workgroup_reduce[loc] = assigned_vertex;
+                    workgroup_ids[loc] = lid;
+                }
+                else if (n_edges >= sgroup_size) { // assign to the subgroup
+                    uint32_t loc = sg_tail.fetch_add(static_cast<uint32_t>(1));
+                    n_edges_sg[offset + loc] = n_edges;
+                    subgroup_reduce[offset + loc] = assigned_vertex;
+                    subgroup_ids[offset + loc] = lid;
+                }
+                visited[lid] = false;
+            }
+            else {
+                visited[lid] = true;
+            }
+
+            sycl::group_barrier(wgroup);
+
+            // 2. process the the edge of one vertex at a time using the workgroup
+            for (size_t i = 0; i < wg_tail.load(); i++) {
+                auto vertex = workgroup_reduce[i];
+                size_t n_edges = n_edges_wg[i];
+                auto start = graph_dev.begin(vertex);
+
+                for (auto j = lid; j < n_edges; j += wgroup_size) {
+                    auto n = start + j;
+                    auto edge = n.get_index();
+                    auto weight = graph_dev.get_weight(edge);
+                    auto neighbor = *n;
+                    if (functor(vertex, neighbor, edge, weight)) {
+                        context.insert(state, neighbor);
+                    }
+                }
+
+                if (wgroup.leader()) {
+                    visited[workgroup_ids[i]] = true;
+                }
+            }
+
+            sycl::group_barrier(sgroup);
+
+            // 3. process the edges of one vertex at a time using the subgroup
+            for (
+                size_t i = 0; i < subgroup_reduce_tail[sgroup_id];
+                i++) { // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
+                size_t vertex_id = offset + i;
+                auto vertex = subgroup_reduce[vertex_id];
+                size_t n_edges = n_edges_sg[vertex_id];
+
+                auto start = graph_dev.begin(vertex);
+
+                for (auto j = llid; j < n_edges; j += sgroup_size) {
+                    auto n = start + j;
+                    auto edge = n.get_index();
+                    auto weight = graph_dev.get_weight(edge);
+                    auto neighbor = *n;
+                    if (functor(vertex, neighbor, edge, weight)) {
+                        context.insert(state, neighbor);
+                    }
+                }
+
+                if (sgroup.leader()) {
+                    visited[subgroup_ids[vertex_id]] = true;
+                }
+            }
+            sycl::group_barrier(sgroup);
+
+            // 4. process the edges of the vertices that were not assigned to the workgroup or subgroup
+            if (!visited[lid]) {
+                auto vertex = assigned_vertex;
+                auto start = graph_dev.begin(vertex);
+                auto end = graph_dev.end(vertex);
+
+                for (auto n = start; n != end; ++n) {
+                    auto edge = n.get_index();
+                    auto weight = graph_dev.get_weight(edge);
+                    auto neighbor = *n;
+                    if (functor(vertex, neighbor, edge, weight)) {
+                        context.insert(state, neighbor);
+                    }
+                }
+            }
+            context.complete_iteration(state); // complete the current iteration
         }
-      }
-      context.complete_iteration(state); // complete the current iteration
     }
-  }
-
-  const ContextT context;
-  const GraphDevT graph_dev;
-  const sycl::local_accessor<uint32_t, 1> n_edges_wg;
-  const sycl::local_accessor<uint32_t, 1> n_edges_sg;
-  const sycl::local_accessor<bool, 1> visited;
-  const sycl::local_accessor<T, 1> subgroup_reduce;
-  const sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail;
-  const sycl::local_accessor<uint32_t, 1> subgroup_ids;
-  const sycl::local_accessor<T, 1> workgroup_reduce;
-  const sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail;
-  const sycl::local_accessor<uint32_t, 1> workgroup_ids;
-  const LambdaT functor;
+
+    const ContextT context;
+    const GraphDevT graph_dev;
+    const sycl::local_accessor<uint32_t, 1> n_edges_wg;
+    const sycl::local_accessor<uint32_t, 1> n_edges_sg;
+    const sycl::local_accessor<bool, 1> visited;
+    const sycl::local_accessor<T, 1> subgroup_reduce;
+    const sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail;
+    const sycl::local_accessor<uint32_t, 1> subgroup_ids;
+    const sycl::local_accessor<T, 1> workgroup_reduce;
+    const sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail;
+    const sycl::local_accessor<uint32_t, 1> workgroup_ids;
+    const LambdaT functor;
 };
 
 /// advance is a function that launches the BitmapKernel on the device to advance the frontier.
@@ -192,67 +218,107 @@ struct BitmapKernel {
 /// The expected_size parameter is used to specify the expected size of the input frontier, in order
 /// to optimize the kernel launch parameters. If expected_size is zero, a default size is used.
 /// It returns a sycl::event that can be used to synchronize the execution.
-template<typename FrontierSizeT,
-         typename GraphT,
-         typename LambdaT>
-sycl::event advance(const GraphT& graph, frontier<FrontierSizeT>& in, frontier<FrontierSizeT>& out, LambdaT&& functor) {
-  using element_t = FrontierSizeT;
-  
-  sycl::queue& q = graph.get_queue();
-
-  size_t num_nodes = graph.get_vertex_count();
-
-  auto in_dev_frontier = in.get_device_view();
-  auto out_dev_frontier = out.get_device_view();
-  auto graph_dev = graph.get_device_view();
-
-  size_t coarsening_factor = 1; // it should be Compute Unit Size / num subgroups
-
-  size_t element_bitsize = in_dev_frontier.get_element_bitsize(); // in bits
-  sycl::range<1> local_range = {element_bitsize * coarsening_factor}; 
-  size_t global_size;
-
-  sycl::event to_wait = in.compute_active_frontier(); // kernel launch to compute active bitmap regions
-  auto offset_size = in.get_offsets_size().at_device(q, 0, {to_wait});
-  global_size = offset_size * element_bitsize;
-
-  sycl::range<1> global_range{(global_size % local_range[0] == 0) ? global_size : global_size + (local_range[0] - global_size % local_range[0])};
-
-  Context<decltype(in_dev_frontier), decltype(out_dev_frontier)> context{num_nodes, in_dev_frontier, out_dev_frontier};
-  using bitmap_kernel_t = BitmapKernel<element_t, decltype(context), decltype(graph_dev), LambdaT>;
-
-  const uint32_t max_num_subgroups = device_max_sg_count(q);
-
-  auto e = q.submit([&](sycl::handler& cgh) {
-    cgh.depends_on(to_wait);
-    sycl::local_accessor<uint32_t, 1> n_edges_wg{local_range, cgh};                 // number of edges of vertices to process at work-group granularity
-    sycl::local_accessor<uint32_t, 1> n_edges_sg{local_range, cgh};                 // number of edges of vertices to process at sub-group granularity
-    sycl::local_accessor<bool, 1> visited{local_range, cgh};                        // tracks the vertices already visited at work-group and sub-group granularity
-    sycl::local_accessor<element_t, 1> subgroup_reduce{local_range, cgh};           // stores the vertices to process at sub-group granularity
-    sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail{max_num_subgroups, cgh}; // stores the tail of the subgroup reduction
-    sycl::local_accessor<uint32_t, 1> subgroup_ids{local_range, cgh};               // stores the thread id that found the vertex to process at sub-group level
-    sycl::local_accessor<element_t, 1> workgroup_reduce{local_range, cgh};          // stores the vertices to process at work-group granularity
-    sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail{1, cgh};                // stores the tail of the work-group reduction
-    sycl::local_accessor<uint32_t, 1> workgroup_ids{local_range, cgh};              // stores the thread id that found the vertex to process at work-group level
-    sycl::local_accessor<element_t, 1> individual_reduce{local_range, cgh};         // stores the vertices to process at individual thread granularity
-    sycl::local_accessor<uint32_t, 1> individual_reduce_tail{1, cgh};               // stores the tail of the individual thread reduction
-
-
-    cgh.parallel_for(sycl::nd_range<1>{global_range, local_range},
-      bitmap_kernel_t{context,
-                      graph_dev,
-                      n_edges_wg,
-                      n_edges_sg,
-                      visited,
-                      subgroup_reduce,
-                      subgroup_reduce_tail,
-                      subgroup_ids,
-                      workgroup_reduce,
-                      workgroup_reduce_tail,
-                      workgroup_ids,
-                      std::forward<LambdaT>(functor)});
-  });
-  return {e};
+template <typename FrontierSizeT, typename GraphT, typename LambdaT>
+sycl::event advance(const GraphT& graph,
+                    frontier<FrontierSizeT>& in,
+                    frontier<FrontierSizeT>& out,
+                    LambdaT&& functor) {
+    using element_t = FrontierSizeT;
+
+    sycl::queue& q = graph.get_queue();
+
+    size_t num_nodes = graph.get_vertex_count();
+
+    auto in_dev_frontier = in.get_device_view();
+    auto out_dev_frontier = out.get_device_view();
+    auto graph_dev = graph.get_device_view();
+
+    size_t coarsening_factor = 1; // it should be Compute Unit Size / num subgroups
+
+    size_t element_bitsize = in_dev_frontier.get_element_bitsize(); // in bits
+    sycl::range<1> local_range = { element_bitsize * coarsening_factor };
+    size_t global_size;
+
+    sycl::event to_wait =
+        in.compute_active_frontier(); // kernel launch to compute active bitmap regions
+    auto offset_size = in.get_offsets_size().at_device(q, 0, { to_wait });
+    global_size = offset_size * element_bitsize;
+
+    sycl::range<1> global_range{ (global_size % local_range[0] == 0)
+                                     ? global_size
+                                     : global_size +
+                                           (local_range[0] - global_size % local_range[0]) };
+
+    Context<decltype(in_dev_frontier), decltype(out_dev_frontier)> context{ num_nodes,
+                                                                            in_dev_frontier,
+                                                                            out_dev_frontier };
+    using bitmap_kernel_t =
+        BitmapKernel<element_t, decltype(context), decltype(graph_dev), LambdaT>;
+
+    const uint32_t max_num_subgroups = device_max_sg_count(q);
+
+    auto e = q.submit([&](sycl::handler& cgh) {
+        cgh.depends_on(to_wait);
+        sycl::local_accessor<uint32_t, 1> n_edges_wg{
+            local_range,
+            cgh
+        }; // number of edges of vertices to process at work-group granularity
+        sycl::local_accessor<uint32_t, 1> n_edges_sg{
+            local_range,
+            cgh
+        }; // number of edges of vertices to process at sub-group granularity
+        sycl::local_accessor<bool, 1> visited{
+            local_range,
+            cgh
+        }; // tracks the vertices already visited at work-group and sub-group granularity
+        sycl::local_accessor<element_t, 1> subgroup_reduce{
+            local_range,
+            cgh
+        }; // stores the vertices to process at sub-group granularity
+        sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail{
+            max_num_subgroups,
+            cgh
+        }; // stores the tail of the subgroup reduction
+        sycl::local_accessor<uint32_t, 1> subgroup_ids{
+            local_range,
+            cgh
+        }; // stores the thread id that found the vertex to process at sub-group level
+        sycl::local_accessor<element_t, 1> workgroup_reduce{
+            local_range,
+            cgh
+        }; // stores the vertices to process at work-group granularity
+        sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail{
+            1,
+            cgh
+        }; // stores the tail of the work-group reduction
+        sycl::local_accessor<uint32_t, 1> workgroup_ids{
+            local_range,
+            cgh
+        }; // stores the thread id that found the vertex to process at work-group level
+        sycl::local_accessor<element_t, 1> individual_reduce{
+            local_range,
+            cgh
+        }; // stores the vertices to process at individual thread granularity
+        sycl::local_accessor<uint32_t, 1> individual_reduce_tail{
+            1,
+            cgh
+        }; // stores the tail of the individual thread reduction
+
+        cgh.parallel_for(sycl::nd_range<1>{ global_range, local_range },
+                         bitmap_kernel_t{ context,
+                                          graph_dev,
+                                          n_edges_wg,
+                                          n_edges_sg,
+                                          visited,
+                                          subgroup_reduce,
+                                          subgroup_reduce_tail,
+                                          subgroup_ids,
+                                          workgroup_reduce,
+                                          workgroup_reduce_tail,
+                                          workgroup_ids,
+                                          std::forward<LambdaT>(functor) });
+    });
+    return { e };
 }
 
 } // namespace oneapi::dal::backend::primitives
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index a6479a2864e..c4a75a1d704 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -42,8 +42,7 @@ class bitset {
     inline void atomic_set(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
-        sycl::atomic_ref<element_t, mem_order, mem_scope>
-            atomic_element(_data[element_index]);
+        sycl::atomic_ref<element_t, mem_order, mem_scope> atomic_element(_data[element_index]);
         atomic_element |= (element_t(1) << bit_index);
     }
 
@@ -53,8 +52,7 @@ class bitset {
     inline void atomic_unset(std::uint32_t index) {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
-        sycl::atomic_ref<element_t, mem_order, mem_scope>
-            atomic_element(_data[element_index]);
+        sycl::atomic_ref<element_t, mem_order, mem_scope> atomic_element(_data[element_index]);
         atomic_element &= ~(element_t(1) << bit_index);
     }
 
@@ -64,8 +62,7 @@ class bitset {
     inline bool atomic_test(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
-        sycl::atomic_ref<element_t, mem_order, mem_scope>
-            atomic_element(_data[element_index]);
+        sycl::atomic_ref<element_t, mem_order, mem_scope> atomic_element(_data[element_index]);
         return (atomic_element.load() & (element_t(1) << bit_index)) != 0;
     }
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index 5ccfce81b74..eda1028746c 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -23,8 +23,8 @@ class frontier_view {
                   std::uint32_t* offsets_size,
                   size_t num_items)
             : _num_items(num_items),
-              _data_layer(bitset<bitmap_t>{data_layer}),
-              _mlb_layer(bitset<bitmap_t>{mlb_layer}),
+              _data_layer(bitset<bitmap_t>{ data_layer }),
+              _mlb_layer(bitset<bitmap_t>{ mlb_layer }),
               _offsets(offsets),
               _offsets_size(offsets_size) {}
 
@@ -73,17 +73,19 @@ class frontier {
     using buffer_t = std::uint32_t;
 
 public:
-    frontier(sycl::queue& queue, std::size_t num_items, sycl::usm::alloc alloc = sycl::usm::alloc::shared);
+    frontier(sycl::queue& queue,
+             std::size_t num_items,
+             sycl::usm::alloc alloc = sycl::usm::alloc::shared);
 
     const frontier_view<ElementType> get_device_view() const {
         auto offsets_size_pointer = _offsets.get_mutable_data();
         auto offsets_pointer = _offsets.get_mutable_data() + 1;
 
         return { _data_layer.get_mutable_data(),
-                _mlb_layer.get_mutable_data(),
-                offsets_pointer,
-                offsets_size_pointer,
-                static_cast<std::size_t>(_data_layer.get_count()) };
+                 _mlb_layer.get_mutable_data(),
+                 offsets_pointer,
+                 offsets_size_pointer,
+                 static_cast<std::size_t>(_data_layer.get_count()) };
     }
 
     inline ndview<ElementType, 1> get_data() const {
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index 6287fbc2298..7805d1fef4f 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -7,19 +7,21 @@
 namespace oneapi::dal::backend::primitives {
 
 #ifdef ONEDAL_DATA_PARALLEL
-    
+
 template <typename ElementType>
-frontier<ElementType>::frontier(sycl::queue& queue, std::size_t num_items, sycl::usm::alloc alloc) : _queue(queue), _num_items(num_items) {
-    std::int64_t array_size =
-        (num_items + bitset<ElementType>::element_bitsize - 1) / bitset<ElementType>::element_bitsize;
+frontier<ElementType>::frontier(sycl::queue& queue, std::size_t num_items, sycl::usm::alloc alloc)
+        : _queue(queue),
+          _num_items(num_items) {
+    std::int64_t array_size = (num_items + bitset<ElementType>::element_bitsize - 1) /
+                              bitset<ElementType>::element_bitsize;
     std::int64_t mlb_size = (array_size + bitset<ElementType>::element_bitsize - 1) /
-                    bitset<ElementType>::element_bitsize;
-    _data_layer =
-        ndarray<ElementType, 1>::empty(_queue, { array_size }, alloc);
-    _mlb_layer =
-        ndarray<ElementType, 1>::empty(_queue, { mlb_size }, alloc);
-    _offsets =
-        ndarray<std::uint32_t, 1>::empty(_queue, { array_size + 1 }, alloc); /// First offset is to keep the size of the frontier
+                            bitset<ElementType>::element_bitsize;
+    _data_layer = ndarray<ElementType, 1>::empty(_queue, { array_size }, alloc);
+    _mlb_layer = ndarray<ElementType, 1>::empty(_queue, { mlb_size }, alloc);
+    _offsets = ndarray<std::uint32_t, 1>::empty(
+        _queue,
+        { array_size + 1 },
+        alloc); /// First offset is to keep the size of the frontier
     _buffer = ndarray<std::uint32_t, 1>::empty(_queue, { 10 }, alloc);
 
     sycl::event e1, e2, e3;
@@ -55,17 +57,21 @@ bool frontier<ElementType>::empty() {
 template <typename ElementType>
 inline void frontier<ElementType>::insert(ElementType idx) {
     auto view = this->get_device_view();
-    _queue.submit([&](sycl::handler& cgh) {
-        cgh.single_task([=]() {
-            view.insert(idx);
-        });
-    }).wait_and_throw();
+    _queue
+        .submit([&](sycl::handler& cgh) {
+            cgh.single_task([=]() {
+                view.insert(idx);
+            });
+        })
+        .wait_and_throw();
 }
 
 template <typename ElementType>
 inline bool frontier<ElementType>::check(ElementType idx) {
-    ElementType tmp_data = _data_layer.at_device(_queue, idx / bitset<ElementType>::element_bitsize);
-    return (tmp_data & (static_cast<ElementType>(1) << (idx % bitset<ElementType>::element_bitsize))) != 0;
+    ElementType tmp_data =
+        _data_layer.at_device(_queue, idx / bitset<ElementType>::element_bitsize);
+    return (tmp_data &
+            (static_cast<ElementType>(1) << (idx % bitset<ElementType>::element_bitsize))) != 0;
 }
 
 template <typename ElementType>
@@ -86,16 +92,22 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
     auto offsets_pointer = _offsets.get_mutable_data() + 1;
 
     uint32_t element_bitsize = bitmap.get_element_bitsize();
-    size_t local_range = 256;// propose_wg_size(this->_queue); 
+    size_t local_range = 256; // propose_wg_size(this->_queue);
     size_t mlb_count = _mlb_layer.get_count();
-    size_t global_range = (mlb_count % local_range == 0) ? mlb_count : (mlb_count + local_range - (mlb_count % local_range));
+    size_t global_range = (mlb_count % local_range == 0)
+                              ? mlb_count
+                              : (mlb_count + local_range - (mlb_count % local_range));
 
     // check if local memory is enough
     bool use_local_mem =
-        device_local_mem_size(this->_queue) >= static_cast<std::int64_t>(local_range * element_bitsize * sizeof(uint32_t));
+        device_local_mem_size(this->_queue) >=
+        static_cast<std::int64_t>(local_range * element_bitsize * sizeof(uint32_t));
 
     auto e0 = _queue.submit([&](sycl::handler& cgh) {
-        cgh.single_task([=, offsets_size = this->get_offsets_size().get_mutable_data(), buffer_ptr = this->_buffer.get_mutable_data(), CAF_FLAG = this->_CAF_FLAG]() {
+        cgh.single_task([=,
+                         offsets_size = this->get_offsets_size().get_mutable_data(),
+                         buffer_ptr = this->_buffer.get_mutable_data(),
+                         CAF_FLAG = this->_CAF_FLAG]() {
             buffer_ptr[CAF_FLAG] = offsets_size[0] == 0 ? 1 : 0;
         });
     });
@@ -103,43 +115,45 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
     auto e1 = this->_queue.submit([&](sycl::handler& cgh) {
         cgh.depends_on(e0);
 
-        if (!use_local_mem) {   
+        if (!use_local_mem) {
             cgh.parallel_for(make_range_1d(_mlb_layer.get_count()),
-                [=,
-                offsets = offsets_pointer,
-                offsets_size = offsets_size_pointer,
-                data_layer = this->_mlb_layer.get_mutable_data(),
-                buffer = this->_buffer.get_mutable_data(),
-                CAF_FLAG = this->_CAF_FLAG](sycl::id<1> idx) {
-
-                    if (!buffer[CAF_FLAG]) return;
-
-                    sycl::atomic_ref<uint32_t,
-                                    sycl::memory_order::relaxed,
-                                    sycl::memory_scope::device>
-                        offsets_size_ref{ offsets_size[0] };
-
-                    ElementType data = data_layer[idx];
-                    for (size_t i = 0; i < element_bitsize; i++) {
-                        if (data & (static_cast<ElementType>(1) << i)) {
-                            offsets[offsets_size_ref++] = i + idx * element_bitsize;
-                        }
-                    }
-            });
-        } else {
+                             [=,
+                              offsets = offsets_pointer,
+                              offsets_size = offsets_size_pointer,
+                              data_layer = this->_mlb_layer.get_mutable_data(),
+                              buffer = this->_buffer.get_mutable_data(),
+                              CAF_FLAG = this->_CAF_FLAG](sycl::id<1> idx) {
+                                 if (!buffer[CAF_FLAG])
+                                     return;
+
+                                 sycl::atomic_ref<uint32_t,
+                                                  sycl::memory_order::relaxed,
+                                                  sycl::memory_scope::device>
+                                     offsets_size_ref{ offsets_size[0] };
+
+                                 ElementType data = data_layer[idx];
+                                 for (size_t i = 0; i < element_bitsize; i++) {
+                                     if (data & (static_cast<ElementType>(1) << i)) {
+                                         offsets[offsets_size_ref++] = i + idx * element_bitsize;
+                                     }
+                                 }
+                             });
+        }
+        else {
             sycl::local_accessor<uint32_t, 1> local_offsets(local_range * element_bitsize, cgh);
             sycl::local_accessor<uint32_t, 1> local_size(1, cgh);
 
             cgh.parallel_for(
                 make_multiple_nd_range_1d(global_range, local_range),
                 [=,
-                offsets = offsets_pointer,
-                offsets_size = offsets_size_pointer,
-                data_layer = this->_mlb_layer.get_mutable_data(),
-                size = mlb_count,
-                buffer = this->_buffer.get_mutable_data(),
-                CAF_FLAG = this->_CAF_FLAG](sycl::nd_item<1> item) {
-                    if (!buffer[CAF_FLAG]) return;
+                 offsets = offsets_pointer,
+                 offsets_size = offsets_size_pointer,
+                 data_layer = this->_mlb_layer.get_mutable_data(),
+                 size = mlb_count,
+                 buffer = this->_buffer.get_mutable_data(),
+                 CAF_FLAG = this->_CAF_FLAG](sycl::nd_item<1> item) {
+                    if (!buffer[CAF_FLAG])
+                        return;
 
                     auto group = item.get_group();
                     sycl::atomic_ref<uint32_t,
@@ -156,7 +170,7 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
                     }
                     sycl::group_barrier(group);
                     for (uint32_t gid = item.get_global_linear_id(); gid < size;
-                            gid += item.get_global_range(0)) {
+                         gid += item.get_global_range(0)) {
                         ElementType data = data_layer[gid];
                         for (size_t i = 0; i < element_bitsize; i++) {
                             if (data & (static_cast<ElementType>(1) << i)) {
@@ -173,20 +187,17 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
                     }
                     data_offset = sycl::group_broadcast(group, data_offset, 0);
                     for (size_t i = item.get_local_linear_id(); i < local_size_ref.load();
-                            i += item.get_local_range(0)) {
+                         i += item.get_local_range(0)) {
                         offsets[data_offset + i] = local_offsets[i];
                     }
                 });
         }
-
     });
     return e1;
-
 }
 
-#define INSTANTIATE(F) \
-    template class frontier<F>;
-    
+#define INSTANTIATE(F) template class frontier<F>;
+
 INSTANTIATE(std::uint64_t)
 INSTANTIATE(std::uint32_t)
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index f63ad131d9b..5e1e12d26d8 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -8,151 +8,153 @@
 
 namespace oneapi::dal::backend::primitives {
 
-template<typename VertexT = std::uint32_t, typename EdgeT = std::uint32_t, typename WeightT = std::uint32_t>
+template <typename VertexT = std::uint32_t,
+          typename EdgeT = std::uint32_t,
+          typename WeightT = std::uint32_t>
 class csr_graph_view {
-  using vertex_t = VertexT;
-  using edge_t = EdgeT;
-  using weight_t = WeightT;
-
-  struct neighbor_iterator_t {
-    neighbor_iterator_t(const vertex_t* start_ptr, vertex_t* ptr)
-      : _ptr(ptr), _start_ptr(start_ptr) {}
-    
-    SYCL_EXTERNAL bool operator==(const neighbor_iterator_t& other) const {
-      return _ptr == other._ptr;
-    }
+    using vertex_t = VertexT;
+    using edge_t = EdgeT;
+    using weight_t = WeightT;
+
+    struct neighbor_iterator_t {
+        neighbor_iterator_t(const vertex_t* start_ptr, vertex_t* ptr)
+                : _ptr(ptr),
+                  _start_ptr(start_ptr) {}
+
+        SYCL_EXTERNAL bool operator==(const neighbor_iterator_t& other) const {
+            return _ptr == other._ptr;
+        }
+
+        SYCL_EXTERNAL bool operator!=(const neighbor_iterator_t& other) const {
+            return _ptr != other._ptr;
+        }
+
+        SYCL_EXTERNAL neighbor_iterator_t& operator++() {
+            ++_ptr;
+            return *this;
+        }
+
+        SYCL_EXTERNAL neighbor_iterator_t operator+(int n) const {
+            neighbor_iterator_t tmp = *this;
+            tmp._ptr += n;
+            return tmp;
+        }
+
+        SYCL_EXTERNAL vertex_t operator*() const {
+            return *_ptr;
+        }
+
+        SYCL_EXTERNAL edge_t get_index() const {
+            return static_cast<edge_t>(_ptr - _start_ptr);
+        }
+
+        vertex_t* _ptr;
+        const vertex_t* _start_ptr;
+    };
 
-    SYCL_EXTERNAL bool operator!=(const neighbor_iterator_t& other) const {
-      return _ptr != other._ptr;
+public:
+    csr_graph_view(std::size_t num_nodes, vertex_t* row_ptr, edge_t* col_indices, weight_t* weights)
+            : _num_nodes(num_nodes),
+              _row_ptr(row_ptr),
+              _col_indices(col_indices),
+              _weights(weights) {
+        ONEDAL_ASSERT(_row_ptr != nullptr, "Row pointer must not be null");
+        ONEDAL_ASSERT(_col_indices != nullptr, "Column indices must not be null");
+        ONEDAL_ASSERT(_weights != nullptr, "Weights must not be null");
     }
 
-    SYCL_EXTERNAL neighbor_iterator_t& operator++() {
-      ++_ptr;
-      return *this;
+    SYCL_EXTERNAL inline std::uint32_t get_degree(const vertex_t vertex) const {
+        ONEDAL_ASSERT(vertex < _num_nodes, "Vertex index out of bounds");
+        return static_cast<std::uint32_t>(_row_ptr[vertex + 1] - _row_ptr[vertex]);
     }
 
-    SYCL_EXTERNAL neighbor_iterator_t operator+(int n) const {
-      neighbor_iterator_t tmp = *this;
-      tmp._ptr += n;
-      return tmp;
+    SYCL_EXTERNAL inline weight_t get_weight(const edge_t edge) const {
+        return _weights[edge];
     }
 
-    SYCL_EXTERNAL vertex_t operator*() const {
-      return *_ptr;
+    SYCL_EXTERNAL inline neighbor_iterator_t begin(vertex_t vertex) const {
+        ONEDAL_ASSERT(vertex < _num_nodes, "Vertex index out of bounds");
+        return neighbor_iterator_t(_col_indices, _col_indices + _row_ptr[vertex]);
     }
 
-    SYCL_EXTERNAL edge_t get_index() const {
-      return static_cast<edge_t>(_ptr - _start_ptr);
+    SYCL_EXTERNAL inline neighbor_iterator_t end(vertex_t vertex) const {
+        ONEDAL_ASSERT(vertex < _num_nodes, "Vertex index out of bounds");
+        return neighbor_iterator_t(_col_indices, _col_indices + _row_ptr[vertex + 1]);
     }
 
-    vertex_t* _ptr;
-    const vertex_t* _start_ptr;
-  };
-
-public:
-  csr_graph_view(std::size_t num_nodes,
-                 vertex_t* row_ptr,
-                 edge_t* col_indices,
-                 weight_t* weights)
-      : _num_nodes(num_nodes),
-        _row_ptr(row_ptr),
-        _col_indices(col_indices),
-        _weights(weights) {
-    ONEDAL_ASSERT(_row_ptr != nullptr, "Row pointer must not be null");
-    ONEDAL_ASSERT(_col_indices != nullptr, "Column indices must not be null");
-    ONEDAL_ASSERT(_weights != nullptr, "Weights must not be null");
-  }
-
-  SYCL_EXTERNAL inline std::uint32_t get_degree(const vertex_t vertex) const {
-    ONEDAL_ASSERT(vertex < _num_nodes, "Vertex index out of bounds");
-    return static_cast<std::uint32_t>(_row_ptr[vertex + 1] - _row_ptr[vertex]);
-  }
-
-  SYCL_EXTERNAL inline weight_t get_weight(const edge_t edge) const {
-    return _weights[edge];
-  }
-
-  SYCL_EXTERNAL inline neighbor_iterator_t begin(vertex_t vertex) const {
-    ONEDAL_ASSERT(vertex < _num_nodes, "Vertex index out of bounds");
-    return neighbor_iterator_t(_col_indices, _col_indices + _row_ptr[vertex]);
-  }
-
-  SYCL_EXTERNAL inline neighbor_iterator_t end(vertex_t vertex) const {
-    ONEDAL_ASSERT(vertex < _num_nodes, "Vertex index out of bounds");
-    return neighbor_iterator_t(_col_indices, _col_indices + _row_ptr[vertex + 1]);
-  }
-
 private:
-  std::size_t _num_nodes;
-  vertex_t* _row_ptr;
-  edge_t* _col_indices;
-  weight_t* _weights;
+    std::size_t _num_nodes;
+    vertex_t* _row_ptr;
+    edge_t* _col_indices;
+    weight_t* _weights;
 };
 
-template<typename VertexT = std::uint32_t, typename EdgeT = std::uint32_t, typename WeightT = std::uint32_t>
+template <typename VertexT = std::uint32_t,
+          typename EdgeT = std::uint32_t,
+          typename WeightT = std::uint32_t>
 class csr_graph {
-  using vertex_t = VertexT;
-  using edge_t = EdgeT;
-  using weight_t = WeightT;
-  using graph_view_t = csr_graph_view<vertex_t, edge_t, weight_t>;
+    using vertex_t = VertexT;
+    using edge_t = EdgeT;
+    using weight_t = WeightT;
+    using graph_view_t = csr_graph_view<vertex_t, edge_t, weight_t>;
 
 public:
-  csr_graph(sycl::queue& queue,
-            std::vector<VertexT> row_ptr,
-            std::vector<EdgeT> col_indices,
-            std::vector<WeightT> weights = {},
-            sycl::usm::alloc alloc = sycl::usm::alloc::shared) 
-            : _queue(queue), _num_nodes(row_ptr.size() - 1) {
-
-    std::int64_t row_ptr_size = static_cast<std::int64_t>(row_ptr.size());
-    std::int64_t col_indices_size = static_cast<std::int64_t>(col_indices.size());
-    std::int64_t weights_size = static_cast<std::int64_t>(weights.size());
-
-    _row_ptr = ndarray<vertex_t, 1>::empty(_queue, {row_ptr_size}, alloc);
-    _col_indices = ndarray<edge_t, 1>::empty(_queue, {col_indices_size}, alloc);
-    _weights = ndarray<weight_t, 1>::empty(_queue, {weights_size}, alloc);
-
-    auto e1 = dal::backend::copy_host2usm(_queue,
-                              _row_ptr.get_mutable_data(),
-                              row_ptr.data(),
-                              row_ptr.size());
-
-    auto e2 = dal::backend::copy_host2usm(_queue,
-                              _col_indices.get_mutable_data(),
-                              col_indices.data(),
-                              col_indices.size());
-
-    auto e3 = dal::backend::copy_host2usm(_queue,
-                              _weights.get_mutable_data(),
-                              weights.data(),
-                              weights.size());
-
-    e1.wait_and_throw();
-    e2.wait_and_throw();
-    e3.wait_and_throw();
-  }
-
-  graph_view_t get_device_view() const {
-    return { _num_nodes, 
-             _row_ptr.get_mutable_data(), 
-             _col_indices.get_mutable_data(), 
-             _weights.get_mutable_data() };
-  }
-
-  sycl::queue& get_queue() const {
-    return _queue;
-  }
-
-  std::size_t get_vertex_count() const {
-    return _num_nodes;
-  }
+    csr_graph(sycl::queue& queue,
+              std::vector<VertexT> row_ptr,
+              std::vector<EdgeT> col_indices,
+              std::vector<WeightT> weights = {},
+              sycl::usm::alloc alloc = sycl::usm::alloc::shared)
+            : _queue(queue),
+              _num_nodes(row_ptr.size() - 1) {
+        std::int64_t row_ptr_size = static_cast<std::int64_t>(row_ptr.size());
+        std::int64_t col_indices_size = static_cast<std::int64_t>(col_indices.size());
+        std::int64_t weights_size = static_cast<std::int64_t>(weights.size());
+
+        _row_ptr = ndarray<vertex_t, 1>::empty(_queue, { row_ptr_size }, alloc);
+        _col_indices = ndarray<edge_t, 1>::empty(_queue, { col_indices_size }, alloc);
+        _weights = ndarray<weight_t, 1>::empty(_queue, { weights_size }, alloc);
+
+        auto e1 = dal::backend::copy_host2usm(_queue,
+                                              _row_ptr.get_mutable_data(),
+                                              row_ptr.data(),
+                                              row_ptr.size());
+
+        auto e2 = dal::backend::copy_host2usm(_queue,
+                                              _col_indices.get_mutable_data(),
+                                              col_indices.data(),
+                                              col_indices.size());
+
+        auto e3 = dal::backend::copy_host2usm(_queue,
+                                              _weights.get_mutable_data(),
+                                              weights.data(),
+                                              weights.size());
+
+        e1.wait_and_throw();
+        e2.wait_and_throw();
+        e3.wait_and_throw();
+    }
+
+    graph_view_t get_device_view() const {
+        return { _num_nodes,
+                 _row_ptr.get_mutable_data(),
+                 _col_indices.get_mutable_data(),
+                 _weights.get_mutable_data() };
+    }
+
+    sycl::queue& get_queue() const {
+        return _queue;
+    }
+
+    std::size_t get_vertex_count() const {
+        return _num_nodes;
+    }
 
 private:
-  sycl::queue& _queue;
-  std::size_t _num_nodes;
-  ndarray<vertex_t, 1> _row_ptr;
-  ndarray<edge_t, 1> _col_indices;
-  ndarray<weight_t, 1> _weights;
+    sycl::queue& _queue;
+    std::size_t _num_nodes;
+    ndarray<vertex_t, 1> _row_ptr;
+    ndarray<edge_t, 1> _col_indices;
+    ndarray<weight_t, 1> _weights;
 };
 
 } // namespace oneapi::dal::backend::primitives
\ No newline at end of file
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index 0008d0196a6..f037ebb0db2 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -20,7 +20,7 @@ void print_device_name(sycl::queue& queue) {
     std::cout << "Running on device: " << device_name << std::endl;
 }
 
-template<typename T>
+template <typename T>
 void print_frontier(const T* data, size_t count, size_t num_items) {
     size_t element_bitsize = sizeof(T) * 8;
     for (size_t i = 0; i < count; ++i) {
@@ -31,8 +31,8 @@ void print_frontier(const T* data, size_t count, size_t num_items) {
 }
 
 std::vector<uint32_t> compute_next_frontier(std::vector<uint32_t>& row_ptr,
-                                       std::vector<uint32_t>& col_indices,
-                                       std::vector<uint32_t>& frontier) {
+                                            std::vector<uint32_t>& col_indices,
+                                            std::vector<uint32_t>& frontier) {
     std::vector<uint32_t> next_frontier;
 
     for (auto node : frontier) {
@@ -46,18 +46,19 @@ std::vector<uint32_t> compute_next_frontier(std::vector<uint32_t>& row_ptr,
     }
     // Remove duplicates
     std::sort(next_frontier.begin(), next_frontier.end());
-    next_frontier.erase(std::unique(next_frontier.begin(), next_frontier.end()), next_frontier.end());
+    next_frontier.erase(std::unique(next_frontier.begin(), next_frontier.end()),
+                        next_frontier.end());
     return next_frontier;
 }
 
-template<typename T>
+template <typename T>
 void compare_frontiers(T& device_frontier, std::vector<uint32_t>& host_frontier, size_t num_nodes) {
     for (size_t i = 0; i < num_nodes; ++i) {
         bool tmpd = device_frontier.check(i);
         bool tmph = std::find(host_frontier.begin(), host_frontier.end(), i) != host_frontier.end();
         if (tmpd != tmph) {
-            std::cout << "Mismatch at vertex " << i << ": device = " << tmpd << ", host = " << tmph << std::endl;
-
+            std::cout << "Mismatch at vertex " << i << ": device = " << tmpd << ", host = " << tmph
+                      << std::endl;
         }
         REQUIRE(tmpd == tmph);
     }
@@ -71,26 +72,70 @@ TEST("test advance operation", "[advance]") {
     // std::vector<std::uint32_t> row_ptr = {0, 2, 4, 6};
     // std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 0, 1};
     // std::vector<std::uint32_t> weights = {1, 1, 1, 1, 1, 1};
-    std::vector<std::uint32_t> row_ptr = {0, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225, 229, 233, 237, 241, 245, 249, 253, 257, 261, 265, 269, 273, 277, 281, 285, 289, 293, 297, 301, 305, 309, 313, 317, 321, 325, 329, 333, 337, 341, 345, 349, 353, 357, 361, 365, 369, 373, 377, 381, 385, 389, 393, 397, 401, 405, 409, 413, 417, 421, 425, 429, 433, 437, 441, 445, 449, 453, 457, 461, 465, 469, 473, 477, 481, 485, 489, 493, 497, 501, 504, 506};
-    std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 3, 0, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 6, 3, 4, 6, 7, 4, 5, 7, 8, 5, 6, 8, 9, 6, 7, 9, 10, 7, 8, 10, 11, 8, 9, 11, 12, 9, 10, 12, 13, 10, 11, 13, 14, 11, 12, 14, 15, 12, 13, 15, 16, 13, 14, 16, 17, 14, 15, 17, 18, 15, 16, 18, 19, 16, 17, 19, 20, 17, 18, 20, 21, 18, 19, 21, 22, 19, 20, 22, 23, 20, 21, 23, 24, 21, 22, 24, 25, 22, 23, 25, 26, 23, 24, 26, 27, 24, 25, 27, 28, 25, 26, 28, 29, 26, 27, 29, 30, 27, 28, 30, 31, 28, 29, 31, 32, 29, 30, 32, 33, 30, 31, 33, 34, 31, 32, 34, 35, 32, 33, 35, 36, 33, 34, 36, 37, 34, 35, 37, 38, 35, 36, 38, 39, 36, 37, 39, 40, 37, 38, 40, 41, 38, 39, 41, 42, 39, 40, 42, 43, 40, 41, 43, 44, 41, 42, 44, 45, 42, 43, 45, 46, 43, 44, 46, 47, 44, 45, 47, 48, 45, 46, 48, 49, 46, 47, 49, 50, 47, 48, 50, 51, 48, 49, 51, 52, 49, 50, 52, 53, 50, 51, 53, 54, 51, 52, 54, 55, 52, 53, 55, 56, 53, 54, 56, 57, 54, 55, 57, 58, 55, 56, 58, 59, 56, 57, 59, 60, 57, 58, 60, 61, 58, 59, 61, 62, 59, 60, 62, 63, 60, 61, 63, 64, 61, 62, 64, 65, 62, 63, 65, 66, 63, 64, 66, 67, 64, 65, 67, 68, 65, 66, 68, 69, 66, 67, 69, 70, 67, 68, 70, 71, 68, 69, 71, 72, 69, 70, 72, 73, 70, 71, 73, 74, 71, 72, 74, 75, 72, 73, 75, 76, 73, 74, 76, 77, 74, 75, 77, 78, 75, 76, 78, 79, 76, 77, 79, 80, 77, 78, 80, 81, 78, 79, 81, 82, 79, 80, 82, 83, 80, 81, 83, 84, 81, 82, 84, 85, 82, 83, 85, 86, 83, 84, 86, 87, 84, 85, 87, 88, 85, 86, 88, 89, 86, 87, 89, 90, 87, 88, 90, 91, 88, 89, 91, 92, 89, 90, 92, 93, 90, 91, 93, 94, 91, 92, 94, 95, 92, 93, 95, 96, 93, 94, 96, 97, 94, 95, 97, 98, 95, 96, 98, 99, 96, 97, 99, 100, 97, 98, 100, 101, 98, 99, 101, 102, 99, 100, 102, 103, 100, 101, 103, 104, 101, 102, 104, 105, 102, 103, 105, 106, 103, 104, 106, 107, 104, 105, 107, 108, 105, 106, 108, 109, 106, 107, 109, 110, 107, 108, 110, 111, 108, 109, 111, 112, 109, 110, 112, 113, 110, 111, 113, 114, 111, 112, 114, 115, 112, 113, 115, 116, 113, 114, 116, 117, 114, 115, 117, 118, 115, 116, 118, 119, 116, 117, 119, 120, 117, 118, 120, 121, 118, 119, 121, 122, 119, 120, 122, 123, 120, 121, 123, 124, 121, 122, 124, 125, 122, 123, 125, 126, 123, 124, 126, 127, 124, 125, 127, 125, 126};
+    std::vector<std::uint32_t> row_ptr = {
+        0,   2,   5,   9,   13,  17,  21,  25,  29,  33,  37,  41,  45,  49,  53,  57,  61,
+        65,  69,  73,  77,  81,  85,  89,  93,  97,  101, 105, 109, 113, 117, 121, 125, 129,
+        133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197,
+        201, 205, 209, 213, 217, 221, 225, 229, 233, 237, 241, 245, 249, 253, 257, 261, 265,
+        269, 273, 277, 281, 285, 289, 293, 297, 301, 305, 309, 313, 317, 321, 325, 329, 333,
+        337, 341, 345, 349, 353, 357, 361, 365, 369, 373, 377, 381, 385, 389, 393, 397, 401,
+        405, 409, 413, 417, 421, 425, 429, 433, 437, 441, 445, 449, 453, 457, 461, 465, 469,
+        473, 477, 481, 485, 489, 493, 497, 501, 504, 506
+    };
+    std::vector<std::uint32_t> col_indices = {
+        1,   2,   0,   2,   3,   0,   1,   3,   4,   1,   2,   4,   5,   2,   3,   5,   6,   3,
+        4,   6,   7,   4,   5,   7,   8,   5,   6,   8,   9,   6,   7,   9,   10,  7,   8,   10,
+        11,  8,   9,   11,  12,  9,   10,  12,  13,  10,  11,  13,  14,  11,  12,  14,  15,  12,
+        13,  15,  16,  13,  14,  16,  17,  14,  15,  17,  18,  15,  16,  18,  19,  16,  17,  19,
+        20,  17,  18,  20,  21,  18,  19,  21,  22,  19,  20,  22,  23,  20,  21,  23,  24,  21,
+        22,  24,  25,  22,  23,  25,  26,  23,  24,  26,  27,  24,  25,  27,  28,  25,  26,  28,
+        29,  26,  27,  29,  30,  27,  28,  30,  31,  28,  29,  31,  32,  29,  30,  32,  33,  30,
+        31,  33,  34,  31,  32,  34,  35,  32,  33,  35,  36,  33,  34,  36,  37,  34,  35,  37,
+        38,  35,  36,  38,  39,  36,  37,  39,  40,  37,  38,  40,  41,  38,  39,  41,  42,  39,
+        40,  42,  43,  40,  41,  43,  44,  41,  42,  44,  45,  42,  43,  45,  46,  43,  44,  46,
+        47,  44,  45,  47,  48,  45,  46,  48,  49,  46,  47,  49,  50,  47,  48,  50,  51,  48,
+        49,  51,  52,  49,  50,  52,  53,  50,  51,  53,  54,  51,  52,  54,  55,  52,  53,  55,
+        56,  53,  54,  56,  57,  54,  55,  57,  58,  55,  56,  58,  59,  56,  57,  59,  60,  57,
+        58,  60,  61,  58,  59,  61,  62,  59,  60,  62,  63,  60,  61,  63,  64,  61,  62,  64,
+        65,  62,  63,  65,  66,  63,  64,  66,  67,  64,  65,  67,  68,  65,  66,  68,  69,  66,
+        67,  69,  70,  67,  68,  70,  71,  68,  69,  71,  72,  69,  70,  72,  73,  70,  71,  73,
+        74,  71,  72,  74,  75,  72,  73,  75,  76,  73,  74,  76,  77,  74,  75,  77,  78,  75,
+        76,  78,  79,  76,  77,  79,  80,  77,  78,  80,  81,  78,  79,  81,  82,  79,  80,  82,
+        83,  80,  81,  83,  84,  81,  82,  84,  85,  82,  83,  85,  86,  83,  84,  86,  87,  84,
+        85,  87,  88,  85,  86,  88,  89,  86,  87,  89,  90,  87,  88,  90,  91,  88,  89,  91,
+        92,  89,  90,  92,  93,  90,  91,  93,  94,  91,  92,  94,  95,  92,  93,  95,  96,  93,
+        94,  96,  97,  94,  95,  97,  98,  95,  96,  98,  99,  96,  97,  99,  100, 97,  98,  100,
+        101, 98,  99,  101, 102, 99,  100, 102, 103, 100, 101, 103, 104, 101, 102, 104, 105, 102,
+        103, 105, 106, 103, 104, 106, 107, 104, 105, 107, 108, 105, 106, 108, 109, 106, 107, 109,
+        110, 107, 108, 110, 111, 108, 109, 111, 112, 109, 110, 112, 113, 110, 111, 113, 114, 111,
+        112, 114, 115, 112, 113, 115, 116, 113, 114, 116, 117, 114, 115, 117, 118, 115, 116, 118,
+        119, 116, 117, 119, 120, 117, 118, 120, 121, 118, 119, 121, 122, 119, 120, 122, 123, 120,
+        121, 123, 124, 121, 122, 124, 125, 122, 123, 125, 126, 123, 124, 126, 127, 124, 125, 127,
+        125, 126
+    };
     std::vector<std::uint32_t> weights(col_indices.size(), 1);
     size_t num_nodes = row_ptr.size() - 1;
 
-    
     auto graph = pr::csr_graph(queue, row_ptr, col_indices, weights);
-    auto in_frontier = pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
-    auto out_frontier = pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
-    
+    auto in_frontier =
+        pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+    auto out_frontier =
+        pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+
     in_frontier.insert(3);
     in_frontier.insert(4);
     in_frontier.insert(52);
     in_frontier.insert(100);
-    std::vector<std::uint32_t> host_frontier = {3, 4, 52, 100};
+    std::vector<std::uint32_t> host_frontier = { 3, 4, 52, 100 };
+
+    pr::advance(graph,
+                in_frontier,
+                out_frontier,
+                [=](auto vertex, auto neighbor, auto edge, auto weight) {
+                    return true; // Always advance
+                })
+        .wait_and_throw();
 
-    pr::advance(graph, in_frontier, out_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
-        return true; // Always advance
-    }).wait_and_throw();
-    
     auto tmp_frontier = compute_next_frontier(row_ptr, col_indices, host_frontier);
     compare_frontiers(out_frontier, tmp_frontier, num_nodes);
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
index 579861e2841..396d29c59ce 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
@@ -27,7 +27,8 @@ class PerformanceTester {
 
     void set_end() {
         auto end_time = std::chrono::high_resolution_clock::now();
-        auto duration = std::chrono::duration_cast<std::chrono::milliseconds>(end_time - start_time_).count();
+        auto duration =
+            std::chrono::duration_cast<std::chrono::milliseconds>(end_time - start_time_).count();
         std::cout << "Total execution time: " << duration << " ms" << std::endl;
     }
 
@@ -35,8 +36,9 @@ class PerformanceTester {
         for (const auto& [name, events] : timings_) {
             std::cout << "Performance for " << name << ": ";
             for (const auto& event : events) {
-                auto duration = event.get_profiling_info<sycl::info::event_profiling::command_end>() -
-                                event.get_profiling_info<sycl::info::event_profiling::command_start>();
+                auto duration =
+                    event.get_profiling_info<sycl::info::event_profiling::command_end>() -
+                    event.get_profiling_info<sycl::info::event_profiling::command_start>();
                 std::cout << duration / 1e6 << " ms ";
             }
             std::cout << std::endl;
@@ -55,9 +57,12 @@ void print_device_name(sycl::queue& queue) {
     std::cout << "Running on device: " << device_name << std::endl;
 }
 
-template<typename T>
-std::vector<std::uint32_t> host_bfs(std::vector<T>& row_offsets, std::vector<T>& col_indices, T src) {
-    std::vector<std::uint32_t> distances(row_offsets.size() - 1, std::numeric_limits<std::uint32_t>::max());
+template <typename T>
+std::vector<std::uint32_t> host_bfs(std::vector<T>& row_offsets,
+                                    std::vector<T>& col_indices,
+                                    T src) {
+    std::vector<std::uint32_t> distances(row_offsets.size() - 1,
+                                         std::numeric_limits<std::uint32_t>::max());
     std::queue<T> q;
     q.push(src);
     distances[src] = 0;
@@ -84,38 +89,85 @@ TEST("test advance operation", "[advance]") {
 
     PerformanceTester perf_tester;
 
-    std::vector<std::uint32_t> row_ptr = {0, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225, 229, 233, 237, 241, 245, 249, 253, 257, 261, 265, 269, 273, 277, 281, 285, 289, 293, 297, 301, 305, 309, 313, 317, 321, 325, 329, 333, 337, 341, 345, 349, 353, 357, 361, 365, 369, 373, 377, 381, 385, 389, 393, 397, 401, 405, 409, 413, 417, 421, 425, 429, 433, 437, 441, 445, 449, 453, 457, 461, 465, 469, 473, 477, 481, 485, 489, 493, 497, 501, 504, 506};
-    std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 3, 0, 1, 3, 4, 1, 2, 4, 5, 2, 3, 5, 6, 3, 4, 6, 7, 4, 5, 7, 8, 5, 6, 8, 9, 6, 7, 9, 10, 7, 8, 10, 11, 8, 9, 11, 12, 9, 10, 12, 13, 10, 11, 13, 14, 11, 12, 14, 15, 12, 13, 15, 16, 13, 14, 16, 17, 14, 15, 17, 18, 15, 16, 18, 19, 16, 17, 19, 20, 17, 18, 20, 21, 18, 19, 21, 22, 19, 20, 22, 23, 20, 21, 23, 24, 21, 22, 24, 25, 22, 23, 25, 26, 23, 24, 26, 27, 24, 25, 27, 28, 25, 26, 28, 29, 26, 27, 29, 30, 27, 28, 30, 31, 28, 29, 31, 32, 29, 30, 32, 33, 30, 31, 33, 34, 31, 32, 34, 35, 32, 33, 35, 36, 33, 34, 36, 37, 34, 35, 37, 38, 35, 36, 38, 39, 36, 37, 39, 40, 37, 38, 40, 41, 38, 39, 41, 42, 39, 40, 42, 43, 40, 41, 43, 44, 41, 42, 44, 45, 42, 43, 45, 46, 43, 44, 46, 47, 44, 45, 47, 48, 45, 46, 48, 49, 46, 47, 49, 50, 47, 48, 50, 51, 48, 49, 51, 52, 49, 50, 52, 53, 50, 51, 53, 54, 51, 52, 54, 55, 52, 53, 55, 56, 53, 54, 56, 57, 54, 55, 57, 58, 55, 56, 58, 59, 56, 57, 59, 60, 57, 58, 60, 61, 58, 59, 61, 62, 59, 60, 62, 63, 60, 61, 63, 64, 61, 62, 64, 65, 62, 63, 65, 66, 63, 64, 66, 67, 64, 65, 67, 68, 65, 66, 68, 69, 66, 67, 69, 70, 67, 68, 70, 71, 68, 69, 71, 72, 69, 70, 72, 73, 70, 71, 73, 74, 71, 72, 74, 75, 72, 73, 75, 76, 73, 74, 76, 77, 74, 75, 77, 78, 75, 76, 78, 79, 76, 77, 79, 80, 77, 78, 80, 81, 78, 79, 81, 82, 79, 80, 82, 83, 80, 81, 83, 84, 81, 82, 84, 85, 82, 83, 85, 86, 83, 84, 86, 87, 84, 85, 87, 88, 85, 86, 88, 89, 86, 87, 89, 90, 87, 88, 90, 91, 88, 89, 91, 92, 89, 90, 92, 93, 90, 91, 93, 94, 91, 92, 94, 95, 92, 93, 95, 96, 93, 94, 96, 97, 94, 95, 97, 98, 95, 96, 98, 99, 96, 97, 99, 100, 97, 98, 100, 101, 98, 99, 101, 102, 99, 100, 102, 103, 100, 101, 103, 104, 101, 102, 104, 105, 102, 103, 105, 106, 103, 104, 106, 107, 104, 105, 107, 108, 105, 106, 108, 109, 106, 107, 109, 110, 107, 108, 110, 111, 108, 109, 111, 112, 109, 110, 112, 113, 110, 111, 113, 114, 111, 112, 114, 115, 112, 113, 115, 116, 113, 114, 116, 117, 114, 115, 117, 118, 115, 116, 118, 119, 116, 117, 119, 120, 117, 118, 120, 121, 118, 119, 121, 122, 119, 120, 122, 123, 120, 121, 123, 124, 121, 122, 124, 125, 122, 123, 125, 126, 123, 124, 126, 127, 124, 125, 127, 125, 126};
+    std::vector<std::uint32_t> row_ptr = {
+        0,   2,   5,   9,   13,  17,  21,  25,  29,  33,  37,  41,  45,  49,  53,  57,  61,
+        65,  69,  73,  77,  81,  85,  89,  93,  97,  101, 105, 109, 113, 117, 121, 125, 129,
+        133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197,
+        201, 205, 209, 213, 217, 221, 225, 229, 233, 237, 241, 245, 249, 253, 257, 261, 265,
+        269, 273, 277, 281, 285, 289, 293, 297, 301, 305, 309, 313, 317, 321, 325, 329, 333,
+        337, 341, 345, 349, 353, 357, 361, 365, 369, 373, 377, 381, 385, 389, 393, 397, 401,
+        405, 409, 413, 417, 421, 425, 429, 433, 437, 441, 445, 449, 453, 457, 461, 465, 469,
+        473, 477, 481, 485, 489, 493, 497, 501, 504, 506
+    };
+    std::vector<std::uint32_t> col_indices = {
+        1,   2,   0,   2,   3,   0,   1,   3,   4,   1,   2,   4,   5,   2,   3,   5,   6,   3,
+        4,   6,   7,   4,   5,   7,   8,   5,   6,   8,   9,   6,   7,   9,   10,  7,   8,   10,
+        11,  8,   9,   11,  12,  9,   10,  12,  13,  10,  11,  13,  14,  11,  12,  14,  15,  12,
+        13,  15,  16,  13,  14,  16,  17,  14,  15,  17,  18,  15,  16,  18,  19,  16,  17,  19,
+        20,  17,  18,  20,  21,  18,  19,  21,  22,  19,  20,  22,  23,  20,  21,  23,  24,  21,
+        22,  24,  25,  22,  23,  25,  26,  23,  24,  26,  27,  24,  25,  27,  28,  25,  26,  28,
+        29,  26,  27,  29,  30,  27,  28,  30,  31,  28,  29,  31,  32,  29,  30,  32,  33,  30,
+        31,  33,  34,  31,  32,  34,  35,  32,  33,  35,  36,  33,  34,  36,  37,  34,  35,  37,
+        38,  35,  36,  38,  39,  36,  37,  39,  40,  37,  38,  40,  41,  38,  39,  41,  42,  39,
+        40,  42,  43,  40,  41,  43,  44,  41,  42,  44,  45,  42,  43,  45,  46,  43,  44,  46,
+        47,  44,  45,  47,  48,  45,  46,  48,  49,  46,  47,  49,  50,  47,  48,  50,  51,  48,
+        49,  51,  52,  49,  50,  52,  53,  50,  51,  53,  54,  51,  52,  54,  55,  52,  53,  55,
+        56,  53,  54,  56,  57,  54,  55,  57,  58,  55,  56,  58,  59,  56,  57,  59,  60,  57,
+        58,  60,  61,  58,  59,  61,  62,  59,  60,  62,  63,  60,  61,  63,  64,  61,  62,  64,
+        65,  62,  63,  65,  66,  63,  64,  66,  67,  64,  65,  67,  68,  65,  66,  68,  69,  66,
+        67,  69,  70,  67,  68,  70,  71,  68,  69,  71,  72,  69,  70,  72,  73,  70,  71,  73,
+        74,  71,  72,  74,  75,  72,  73,  75,  76,  73,  74,  76,  77,  74,  75,  77,  78,  75,
+        76,  78,  79,  76,  77,  79,  80,  77,  78,  80,  81,  78,  79,  81,  82,  79,  80,  82,
+        83,  80,  81,  83,  84,  81,  82,  84,  85,  82,  83,  85,  86,  83,  84,  86,  87,  84,
+        85,  87,  88,  85,  86,  88,  89,  86,  87,  89,  90,  87,  88,  90,  91,  88,  89,  91,
+        92,  89,  90,  92,  93,  90,  91,  93,  94,  91,  92,  94,  95,  92,  93,  95,  96,  93,
+        94,  96,  97,  94,  95,  97,  98,  95,  96,  98,  99,  96,  97,  99,  100, 97,  98,  100,
+        101, 98,  99,  101, 102, 99,  100, 102, 103, 100, 101, 103, 104, 101, 102, 104, 105, 102,
+        103, 105, 106, 103, 104, 106, 107, 104, 105, 107, 108, 105, 106, 108, 109, 106, 107, 109,
+        110, 107, 108, 110, 111, 108, 109, 111, 112, 109, 110, 112, 113, 110, 111, 113, 114, 111,
+        112, 114, 115, 112, 113, 115, 116, 113, 114, 116, 117, 114, 115, 117, 118, 115, 116, 118,
+        119, 116, 117, 119, 120, 117, 118, 120, 121, 118, 119, 121, 122, 119, 120, 122, 123, 120,
+        121, 123, 124, 121, 122, 124, 125, 122, 123, 125, 126, 123, 124, 126, 127, 124, 125, 127,
+        125, 126
+    };
     std::vector<std::uint32_t> weights(col_indices.size(), 1);
-    
+
     auto graph = pr::csr_graph(queue, row_ptr, col_indices, weights);
     size_t num_nodes = row_ptr.size() - 1;
     auto in_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
     auto out_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
-    pr::ndarray<std::uint32_t, 1> distance = pr::ndarray<std::uint32_t, 1>::empty(queue, {static_cast<std::int64_t>(num_nodes)}, sycl::usm::alloc::device);
+    pr::ndarray<std::uint32_t, 1> distance =
+        pr::ndarray<std::uint32_t, 1>::empty(queue,
+                                             { static_cast<std::int64_t>(num_nodes) },
+                                             sycl::usm::alloc::device);
     auto distance_ptr = distance.get_mutable_data();
 
     const std::uint32_t src = 0;
 
-    queue.submit([&](sycl::handler& cgh) {
-        cgh.parallel_for(sycl::range<1>(num_nodes), [=](sycl::id<1> idx) {
-            distance_ptr[idx] = idx[0] == src ? 0 : num_nodes + 1;
-        });
-    }).wait_and_throw();
-    
+    queue
+        .submit([&](sycl::handler& cgh) {
+            cgh.parallel_for(sycl::range<1>(num_nodes), [=](sycl::id<1> idx) {
+                distance_ptr[idx] = idx[0] == src ? 0 : num_nodes + 1;
+            });
+        })
+        .wait_and_throw();
+
     in_frontier.insert(src);
     size_t iter = 0;
 
     /// Start BFS
     perf_tester.set_start();
     while (!in_frontier.empty()) {
-        auto e = pr::advance(graph, in_frontier, out_frontier, [=](auto vertex, auto neighbor, auto edge, auto weight) {
-            bool visited = distance_ptr[neighbor] < num_nodes + 1;
-            if (!visited) {
-                distance_ptr[neighbor] = iter + 1;
-            }
-            return !visited;
-        });
+        auto e = pr::advance(graph,
+                             in_frontier,
+                             out_frontier,
+                             [=](auto vertex, auto neighbor, auto edge, auto weight) {
+                                 bool visited = distance_ptr[neighbor] < num_nodes + 1;
+                                 if (!visited) {
+                                     distance_ptr[neighbor] = iter + 1;
+                                 }
+                                 return !visited;
+                             });
         perf_tester.add("advance", e);
         e.wait_and_throw();
         iter++;
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
index 6117bf61ee2..a214dea6473 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
@@ -14,7 +14,7 @@ void print_device_name(sycl::queue& queue) {
     std::cout << "Running on device: " << device_name << std::endl;
 }
 
-template<typename T>
+template <typename T>
 void print_frontier(const T* data, size_t count, size_t num_items) {
     size_t element_bitsize = sizeof(T) * 8;
     for (size_t i = 0; i < count; ++i) {
@@ -50,11 +50,12 @@ TEST("frontier queue basic operations", "[frontier]") {
     REQUIRE(f.check(3) == false);
     REQUIRE(f.check(bitset<std::uint32_t>::element_bitsize) == true);
     REQUIRE(f.check(bitset<std::uint32_t>::element_bitsize + 1) == false);
-    
+
     auto e = f.compute_active_frontier();
-    REQUIRE(f.get_offsets_size().at_device(queue, 0, {e}) == 3);
+    REQUIRE(f.get_offsets_size().at_device(queue, 0, { e }) == 3);
     for (int i = 0; i < 3; i++) {
-        std::cout << "Active frontier item " << i << ": " << f.get_offsets().at_device(queue, i) << std::endl;
+        std::cout << "Active frontier item " << i << ": " << f.get_offsets().at_device(queue, i)
+                  << std::endl;
     }
 
     f.clear();

From d471d0a594e39be9620917d95ca975c1e9166822 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Mon, 1 Sep 2025 14:12:46 +0200
Subject: [PATCH 17/69] added trailing new line to source files to complie with
 the CI formatter.

---
 cpp/oneapi/dal/backend/primitives/frontier.hpp              | 2 +-
 cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp  | 2 +-
 cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp       | 2 +-
 cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp | 2 +-
 cpp/oneapi/dal/backend/primitives/frontier/graph.hpp        | 2 +-
 5 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier.hpp
index 245ef5b7f91..8fc3b7fca39 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier.hpp
@@ -1,3 +1,3 @@
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 #include "oneapi/dal/backend/primitives/frontier/advance_dpc.hpp"
-#include "oneapi/dal/backend/primitives/frontier/graph.hpp"
\ No newline at end of file
+#include "oneapi/dal/backend/primitives/frontier/graph.hpp"
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
index c9c121eab69..9c5ee1ad2e6 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
@@ -321,4 +321,4 @@ sycl::event advance(const GraphT& graph,
     return { e };
 }
 
-} // namespace oneapi::dal::backend::primitives
\ No newline at end of file
+} // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index c4a75a1d704..e554f11c1ee 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -89,4 +89,4 @@ class bitset {
     element_t* _data;
 };
 
-} // namespace oneapi::dal::backend::primitives
\ No newline at end of file
+} // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index 7805d1fef4f..faa0e2e7842 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -203,4 +203,4 @@ INSTANTIATE(std::uint32_t)
 
 #endif
 
-} // namespace oneapi::dal::backend::primitives
\ No newline at end of file
+} // namespace oneapi::dal::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index 5e1e12d26d8..11a9a529f8f 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -157,4 +157,4 @@ class csr_graph {
     ndarray<weight_t, 1> _weights;
 };
 
-} // namespace oneapi::dal::backend::primitives
\ No newline at end of file
+} // namespace oneapi::dal::backend::primitives

From f720a870d251a38411cb8c38b0119a39ecb74081 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 3 Sep 2025 12:04:54 +0200
Subject: [PATCH 18/69] update headers to comply with the oneDAL naming style

---
 cpp/oneapi/dal/backend/primitives/frontier.hpp                  | 2 +-
 .../primitives/frontier/{advance_dpc.hpp => advance.hpp}        | 0
 cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp | 2 +-
 3 files changed, 2 insertions(+), 2 deletions(-)
 rename cpp/oneapi/dal/backend/primitives/frontier/{advance_dpc.hpp => advance.hpp} (100%)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier.hpp
index 8fc3b7fca39..69fe3aab466 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier.hpp
@@ -1,3 +1,3 @@
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
-#include "oneapi/dal/backend/primitives/frontier/advance_dpc.hpp"
+#include "oneapi/dal/backend/primitives/frontier/advance.hpp"
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
similarity index 100%
rename from cpp/oneapi/dal/backend/primitives/frontier/advance_dpc.hpp
rename to cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index f037ebb0db2..2f421e997b2 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -1,5 +1,5 @@
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
-#include "oneapi/dal/backend/primitives/frontier/advance_dpc.hpp"
+#include "oneapi/dal/backend/primitives/frontier/advance.hpp"
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"
 
 #include "oneapi/dal/test/engine/common.hpp"

From 10813a6916ab428c0f1a7ec06a54ddeb6110832b Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 3 Sep 2025 15:15:27 +0200
Subject: [PATCH 19/69] primitives/frontier: remove unused dependencies from
 BUILD

---
 cpp/oneapi/dal/backend/primitives/frontier/BUILD | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/BUILD b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
index ef392864d39..db480e28ed8 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/BUILD
+++ b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
@@ -9,9 +9,6 @@ dal_module (
     auto = True,
     dal_deps = [
         "@onedal//cpp/oneapi/dal/backend/primitives:common",
-        "@onedal//cpp/oneapi/dal/backend/primitives:blas",
-        "@onedal//cpp/oneapi/dal/backend/primitives/optimizers",
-        "@onedal//cpp/oneapi/dal/backend/primitives:sparse_blas",
     ],
 )
 

From 4da1b4ce4508b4ef8e81639fca7211ef461c7be8 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 3 Sep 2025 15:15:27 +0200
Subject: [PATCH 20/69] primitives/frontier: small code cleanup in advance.hpp
 (comment removal and add explanatory comment)

---
 cpp/oneapi/dal/backend/primitives/frontier/advance.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index 9c5ee1ad2e6..3c8b2325e44 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -58,7 +58,6 @@ struct Context {
         const uint32_t acutal_id_offset = (state.group_offset * state.coarsening_factor) +
                                           (state.item.get_local_linear_id() / element_bitsize);
         const uint32_t* bitmap_offsets = in_dev_frontier.get_offsets();
-        // const size_t acutal_id_offset = (item.get_group_linear_id() * coarsening_factor) + (item.get_local_linear_id() / bitmap_range);
         const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * element_bitsize) +
                                      (state.item.get_local_linear_id() % element_bitsize);
         return assigned_vertex;
@@ -233,7 +232,8 @@ sycl::event advance(const GraphT& graph,
     auto out_dev_frontier = out.get_device_view();
     auto graph_dev = graph.get_device_view();
 
-    size_t coarsening_factor = 1; // it should be Compute Unit Size / num subgroups
+    /// The coarsening factor represents the number of integers a single work-group should handle.
+    size_t coarsening_factor = 1; // it should be Compute Unit Size / num subgroups;
 
     size_t element_bitsize = in_dev_frontier.get_element_bitsize(); // in bits
     sycl::range<1> local_range = { element_bitsize * coarsening_factor };

From 923f2fa4bf0a324a95fe222f55580fef1b235cb3 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 3 Sep 2025 15:15:27 +0200
Subject: [PATCH 21/69] primitives/frontier: remove unused includes and stray
 blank lines in headers, sources and tests

---
 cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp    | 2 --
 .../dal/backend/primitives/frontier/frontier_dpc.cpp       | 4 ----
 .../dal/backend/primitives/frontier/test/advance_dpc.cpp   | 7 -------
 .../dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp  | 1 -
 .../dal/backend/primitives/frontier/test/frontier_dpc.cpp  | 3 ---
 5 files changed, 17 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index eda1028746c..9efe5365792 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -2,8 +2,6 @@
 
 #include "oneapi/dal/common.hpp"
 #include "oneapi/dal/backend/common.hpp"
-#include "oneapi/dal/graph/detail/common.hpp"
-#include "oneapi/dal/graph/detail/container.hpp"
 #include "oneapi/dal/backend/primitives/frontier/bitset.hpp"
 #include "oneapi/dal/backend/primitives/ndarray.hpp"
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index faa0e2e7842..4c142e2b83c 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -1,8 +1,4 @@
-
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
-#include "oneapi/dal/backend/common.hpp"
-#include "oneapi/dal/backend/primitives/ndarray.hpp"
-#include "oneapi/dal/graph/detail/common.hpp"
 
 namespace oneapi::dal::backend::primitives {
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index 2f421e997b2..7e35eeb7683 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -3,12 +3,6 @@
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"
 
 #include "oneapi/dal/test/engine/common.hpp"
-#include "oneapi/dal/test/engine/fixtures.hpp"
-#include "oneapi/dal/test/engine/dataframe.hpp"
-
-#include "oneapi/dal/test/engine/common.hpp"
-#include "oneapi/dal/test/engine/fixtures.hpp"
-#include "oneapi/dal/test/engine/dataframe.hpp"
 
 namespace oneapi::dal::backend::primitives::test {
 
@@ -138,7 +132,6 @@ TEST("test advance operation", "[advance]") {
 
     auto tmp_frontier = compute_next_frontier(row_ptr, col_indices, host_frontier);
     compare_frontiers(out_frontier, tmp_frontier, num_nodes);
-
 } // TEST "test advance operation"
 
 } // namespace oneapi::dal::backend::primitives::test
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
index 396d29c59ce..7b9c12b3ea8 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
@@ -184,7 +184,6 @@ TEST("test advance operation", "[advance]") {
     for (size_t i = 0; i < num_nodes; ++i) {
         REQUIRE(actual_distances[i] == expected_distances[i]);
     }
-
 } // TEST "test advance operation"
 
 } // namespace oneapi::dal::backend::primitives::test
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
index a214dea6473..c3d089afb6d 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
@@ -1,8 +1,6 @@
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 
 #include "oneapi/dal/test/engine/common.hpp"
-#include "oneapi/dal/test/engine/fixtures.hpp"
-#include "oneapi/dal/test/engine/dataframe.hpp"
 
 namespace oneapi::dal::backend::primitives::test {
 
@@ -60,7 +58,6 @@ TEST("frontier queue basic operations", "[frontier]") {
 
     f.clear();
     REQUIRE(f.empty() == true);
-
 } // TEST "frontier queue operations"
 
 } // namespace oneapi::dal::backend::primitives::test

From 7af91f5c5a79d1393357d308f5aad40cd77ddae5 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Fri, 19 Sep 2025 15:04:34 +0200
Subject: [PATCH 22/69] Remove perf_tests target from frontier BUILD

---
 cpp/oneapi/dal/backend/primitives/frontier/BUILD | 13 -------------
 1 file changed, 13 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/BUILD b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
index db480e28ed8..83d8a7dd277 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/BUILD
+++ b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
@@ -26,16 +26,3 @@ dal_test_suite (
         ":frontier",
     ],
 )
-
-dal_test_suite(
-    name = "perf_tests",
-    framework = "catch2",
-    compile_as = [ "dpc++" ],
-    private = True,
-    srcs = glob([
-        "test/*perf_dpc.cpp",
-    ]),
-    dal_deps = [
-        ":frontier",
-    ],
-)
\ No newline at end of file

From 635619892142c69a40f2a84606e570237f5bc20e Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Fri, 19 Sep 2025 15:04:35 +0200
Subject: [PATCH 23/69] Refactor frontier context and bitmap kernel: rename
 Context/ContextState and introduce hierarchical reductions

---
 .../backend/primitives/frontier/advance.hpp   | 250 ++++++++++--------
 1 file changed, 143 insertions(+), 107 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index 3c8b2325e44..b4e191ee34f 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -6,34 +6,31 @@
 
 namespace oneapi::dal::backend::primitives {
 
-/// ContextState holds the state of the current processing group in the kernel
+/// frontier_context_state holds the state of the current processing group in the kernel
 /// It includes the group offset, coarsening factor, offsets size, and the SYCL
 /// nd_item for the current work item.
-struct ContextState {
+struct frontier_context_state {
     size_t group_offset;
     const uint16_t coarsening_factor;
     const uint32_t offsets_size;
     const sycl::nd_item<1> item;
 };
 
-/// Context is a template class that provides an interface for the kernel to
+/// frontier_context is a template class that provides an interface for the kernel to
 /// interact with the frontier data structure. It holds the limit of the graph,
 /// the input frontier, and the output frontier. It provides methods to initialize
 /// the context state, check if there are more elements to process, get the
 /// assigned element, check if a vertex is in the frontier, and insert a vertex
 /// into the output frontier.
 template <typename InFrontierDevT, typename OutFrontierDevT>
-struct Context {
-    size_t limit;
-    InFrontierDevT in_dev_frontier;
-    OutFrontierDevT out_dev_frontier;
-
-    Context(size_t limit, InFrontierDevT in_dev_frontier, OutFrontierDevT out_dev_frontier)
+class frontier_context {
+public:
+    frontier_context(size_t limit, InFrontierDevT in_dev_frontier, OutFrontierDevT out_dev_frontier)
             : limit(limit),
               in_dev_frontier(in_dev_frontier),
               out_dev_frontier(out_dev_frontier) {}
 
-    inline ContextState init(sycl::nd_item<1>& item) const {
+    inline frontier_context_state init(sycl::nd_item<1>& item) const {
         return {
             item.get_group_linear_id(),
             static_cast<uint16_t>(item.get_local_range(0) / in_dev_frontier.get_element_bitsize()),
@@ -43,157 +40,196 @@ struct Context {
     }
 
     /// This method checks if there are more elements to process in the current group.
-    inline bool need_to_process(ContextState& state) const {
+    inline bool need_to_process(frontier_context_state& state) const {
         return (state.group_offset * state.coarsening_factor < state.offsets_size);
     }
 
     /// This method completes the current iteration by updating the group offset.
-    inline void complete_iteration(ContextState& state) const {
+    inline void complete_iteration(frontier_context_state& state) const {
         state.group_offset += state.item.get_group_range(0);
     }
 
     /// This method retrieves the assigned element for the current work item.
-    inline size_t get_assigned_element(const ContextState& state) const {
+    inline size_t get_assigned_element(const frontier_context_state& state) const {
         const uint16_t element_bitsize = in_dev_frontier.get_element_bitsize();
         const uint32_t acutal_id_offset = (state.group_offset * state.coarsening_factor) +
                                           (state.item.get_local_linear_id() / element_bitsize);
         const uint32_t* bitmap_offsets = in_dev_frontier.get_offsets();
+        ONEDAL_ASSERT(acutal_id_offset < in_dev_frontier.get_offsets_size()[0]);
         const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * element_bitsize) +
                                      (state.item.get_local_linear_id() % element_bitsize);
         return assigned_vertex;
     }
 
     /// This method checks if a vertex is in the input frontier.
-    inline bool check(const ContextState& state, size_t vertex) const {
+    inline bool check(const frontier_context_state& state, size_t vertex) const {
         return vertex < limit && in_dev_frontier.check(vertex);
     }
 
     /// This method inserts a vertex into the output frontier.
-    inline void insert(const ContextState& state, size_t vertex) const {
+    inline void insert(const frontier_context_state& state, size_t vertex) const {
         out_dev_frontier.insert(vertex);
     }
+
+    size_t limit;
+    InFrontierDevT in_dev_frontier;
+    OutFrontierDevT out_dev_frontier;
 };
 
 /// BitmapKernel is a template struct that defines the kernel to be executed on the device.
 /// It processes the input frontier and advances it based on the provided functor.
 template <typename T, typename ContextT, typename GraphDevT, typename LambdaT>
 struct BitmapKernel {
-    void operator()(sycl::nd_item<1> item) const {
-        const size_t lid = item.get_local_linear_id();
-        const auto wgroup = item.get_group();
+    template<typename VertexT>
+    inline void distribute_workload(frontier_context_state& state, const VertexT& vertex) const {
+        const size_t lid = state.item.get_local_linear_id();
+        const auto wgroup = state.item.get_group();
         const size_t wgroup_size = wgroup.get_local_range(0);
-        const auto sgroup = item.get_sub_group();
+        const auto sgroup = state.item.get_sub_group();
         const auto sgroup_id = sgroup.get_group_id();
         const size_t sgroup_size = sgroup.get_local_range()[0];
-        const size_t llid = sgroup.get_local_linear_id();
 
-        auto state = context.init(item);
+        if (sgroup.leader()) {
+            subgroup_reduce_tail[sgroup_id] = 0;
+            }
+        if (wgroup.leader()) {
+            workgroup_reduce_tail[0] = 0;
+        }
+        
+        sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group>
+            sg_tail{ subgroup_reduce_tail[sgroup_id] };
+        sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group>
+            wg_tail{ workgroup_reduce_tail[0] };
+        const uint32_t offset = sgroup_id * sgroup_size;
+
+        if (context.check(state, vertex)) {
+            uint32_t n_edges = graph_dev.get_degree(vertex);
+            if (n_edges >= wgroup_size * wgroup_size) { // if the number of edges is large enough, we can assign the vertex to the workgroup
+                uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
+                n_edges_wg[loc] = n_edges;
+                workgroup_reduce[loc] = vertex;
+                workgroup_ids[loc] = lid;
+            }
+            else if (n_edges >= sgroup_size) { // assign to the subgroup
+                uint32_t loc = sg_tail.fetch_add(static_cast<uint32_t>(1));
+                n_edges_sg[offset + loc] = n_edges;
+                subgroup_reduce[offset + loc] = vertex;
+                subgroup_ids[offset + loc] = lid;
+            }
+            visited[lid] = false;
+        }
+        else {
+            visited[lid] = true;
+        }
+    }
 
-        while (context.need_to_process(state)) {
-            const auto assigned_vertex = context.get_assigned_element(state);
+    inline void process_workgroup_reduction(frontier_context_state& state) const {
+        /// This function processes the vertices assigned to the workgroup.
+        sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group>
+            wg_tail{ workgroup_reduce_tail[0] };
+        
+        const auto wgroup = state.item.get_group();
+        const size_t lid = state.item.get_local_linear_id();
+        const size_t wgroup_size = wgroup.get_local_range(0);
 
-            if (sgroup.leader()) {
-                subgroup_reduce_tail[sgroup_id] = 0;
+        for (size_t i = 0; i < wg_tail.load(); i++) {
+            auto vertex = workgroup_reduce[i];
+            size_t n_edges = n_edges_wg[i];
+            auto start = graph_dev.begin(vertex);
+
+            for (auto j = lid; j < n_edges; j += wgroup_size) {
+                auto n = start + j;
+                auto edge = n.get_index();
+                auto weight = graph_dev.get_weight(edge);
+                auto neighbor = *n;
+                if (functor(vertex, neighbor, edge, weight)) {
+                    context.insert(state, neighbor);
+                }
             }
+
             if (wgroup.leader()) {
-                workgroup_reduce_tail[0] = 0;
+                visited[workgroup_ids[i]] = true;
             }
+        }
+    }
 
-            sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group>
-                sg_tail{ subgroup_reduce_tail[sgroup_id] };
-            sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group>
-                wg_tail{ workgroup_reduce_tail[0] };
-
-            // 1. distribute the workload based on the number of edges to the workgroup, subgroup or workitem
-            const uint32_t offset = sgroup_id * sgroup_size;
-            if (context.check(state, assigned_vertex)) {
-                uint32_t n_edges = graph_dev.get_degree(assigned_vertex);
-                if (n_edges >=
-                    wgroup_size *
-                        wgroup_size) { // if the number of edges is large enough, we can assign the vertex to the workgroup
-                    uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
-                    n_edges_wg[loc] = n_edges;
-                    workgroup_reduce[loc] = assigned_vertex;
-                    workgroup_ids[loc] = lid;
-                }
-                else if (n_edges >= sgroup_size) { // assign to the subgroup
-                    uint32_t loc = sg_tail.fetch_add(static_cast<uint32_t>(1));
-                    n_edges_sg[offset + loc] = n_edges;
-                    subgroup_reduce[offset + loc] = assigned_vertex;
-                    subgroup_ids[offset + loc] = lid;
+    inline void process_subgroup_reduction(frontier_context_state& state) const {
+        const auto sgroup = state.item.get_sub_group();
+        const auto sgroup_id = sgroup.get_group_id();
+        const size_t sgroup_size = sgroup.get_local_range()[0];
+        const size_t llid = sgroup.get_local_linear_id();
+        const uint32_t offset = sgroup_id * sgroup_size;
+
+        sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group>
+            sg_tail{ subgroup_reduce_tail[sgroup_id] };
+
+        for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) { 
+            // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
+            size_t vertex_id = offset + i;
+            auto vertex = subgroup_reduce[vertex_id];
+            size_t n_edges = n_edges_sg[vertex_id];
+
+            auto start = graph_dev.begin(vertex);
+
+            for (auto j = llid; j < n_edges; j += sgroup_size) {
+                auto n = start + j;
+                auto edge = n.get_index();
+                auto weight = graph_dev.get_weight(edge);
+                auto neighbor = *n;
+                if (functor(vertex, neighbor, edge, weight)) {
+                    context.insert(state, neighbor);
                 }
-                visited[lid] = false;
             }
-            else {
-                visited[lid] = true;
+
+            if (sgroup.leader()) {
+                visited[subgroup_ids[vertex_id]] = true;
             }
+        }
+    }
 
-            sycl::group_barrier(wgroup);
+    template<typename VertexT>
+    inline void process_workitem_reduction(frontier_context_state& state, const VertexT& vertex) const {
+        const size_t lid = state.item.get_local_linear_id();
 
-            // 2. process the the edge of one vertex at a time using the workgroup
-            for (size_t i = 0; i < wg_tail.load(); i++) {
-                auto vertex = workgroup_reduce[i];
-                size_t n_edges = n_edges_wg[i];
-                auto start = graph_dev.begin(vertex);
-
-                for (auto j = lid; j < n_edges; j += wgroup_size) {
-                    auto n = start + j;
-                    auto edge = n.get_index();
-                    auto weight = graph_dev.get_weight(edge);
-                    auto neighbor = *n;
-                    if (functor(vertex, neighbor, edge, weight)) {
-                        context.insert(state, neighbor);
-                    }
-                }
+        if (!visited[lid]) {
+            auto start = graph_dev.begin(vertex);
+            auto end = graph_dev.end(vertex);
 
-                if (wgroup.leader()) {
-                    visited[workgroup_ids[i]] = true;
+            for (auto n = start; n != end; ++n) {
+                auto edge = n.get_index();
+                auto weight = graph_dev.get_weight(edge);
+                auto neighbor = *n;
+                if (functor(vertex, neighbor, edge, weight)) {
+                    context.insert(state, neighbor);
                 }
             }
+        }
+    }
 
+    void operator()(sycl::nd_item<1> item) const {
+        auto state = context.init(item);
+        const auto wgroup = item.get_group();
+        const auto sgroup = item.get_sub_group();
+
+        while (context.need_to_process(state)) {
+            const auto assigned_vertex = context.get_assigned_element(state);
+
+            // 1. distribute the workload based on the number of edges to the workgroup, subgroup or workitem
+            distribute_workload(state, assigned_vertex);
+
+            sycl::group_barrier(wgroup);
+
+            // 2. process the the edge of one vertex at a time using the workgroup
+            process_workgroup_reduction(state);
             sycl::group_barrier(sgroup);
 
             // 3. process the edges of one vertex at a time using the subgroup
-            for (
-                size_t i = 0; i < subgroup_reduce_tail[sgroup_id];
-                i++) { // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
-                size_t vertex_id = offset + i;
-                auto vertex = subgroup_reduce[vertex_id];
-                size_t n_edges = n_edges_sg[vertex_id];
-
-                auto start = graph_dev.begin(vertex);
-
-                for (auto j = llid; j < n_edges; j += sgroup_size) {
-                    auto n = start + j;
-                    auto edge = n.get_index();
-                    auto weight = graph_dev.get_weight(edge);
-                    auto neighbor = *n;
-                    if (functor(vertex, neighbor, edge, weight)) {
-                        context.insert(state, neighbor);
-                    }
-                }
-
-                if (sgroup.leader()) {
-                    visited[subgroup_ids[vertex_id]] = true;
-                }
-            }
+            process_subgroup_reduction(state);
             sycl::group_barrier(sgroup);
 
             // 4. process the edges of the vertices that were not assigned to the workgroup or subgroup
-            if (!visited[lid]) {
-                auto vertex = assigned_vertex;
-                auto start = graph_dev.begin(vertex);
-                auto end = graph_dev.end(vertex);
-
-                for (auto n = start; n != end; ++n) {
-                    auto edge = n.get_index();
-                    auto weight = graph_dev.get_weight(edge);
-                    auto neighbor = *n;
-                    if (functor(vertex, neighbor, edge, weight)) {
-                        context.insert(state, neighbor);
-                    }
-                }
-            }
+            process_workitem_reduction(state, assigned_vertex);
+            
             context.complete_iteration(state); // complete the current iteration
         }
     }
@@ -249,7 +285,7 @@ sycl::event advance(const GraphT& graph,
                                      : global_size +
                                            (local_range[0] - global_size % local_range[0]) };
 
-    Context<decltype(in_dev_frontier), decltype(out_dev_frontier)> context{ num_nodes,
+    frontier_context<decltype(in_dev_frontier), decltype(out_dev_frontier)> context{ num_nodes,
                                                                             in_dev_frontier,
                                                                             out_dev_frontier };
     using bitmap_kernel_t =

From 2efbe84c7458c0a7c7e7d324a514053401b7db2c Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Fri, 19 Sep 2025 15:04:35 +0200
Subject: [PATCH 24/69] Remove performance testing scaffolding from frontier
 BFS test and rename test file

---
 .../test/{bfs_perf_dpc.cpp => bfs_dpc.cpp}    | 46 -------------------
 1 file changed, 46 deletions(-)
 rename cpp/oneapi/dal/backend/primitives/frontier/test/{bfs_perf_dpc.cpp => bfs_dpc.cpp} (82%)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
similarity index 82%
rename from cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
rename to cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
index 7b9c12b3ea8..b9e4b017d91 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_perf_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -12,45 +12,6 @@ namespace oneapi::dal::backend::primitives::test {
 
 namespace pr = dal::backend::primitives;
 
-class PerformanceTester {
-public:
-    void add(const std::string& name, const sycl::event& event) {
-        if (timings_.find(name) == timings_.end()) {
-            timings_[name] = std::vector<sycl::event>();
-        }
-        timings_[name].push_back(event);
-    }
-
-    void set_start() {
-        start_time_ = std::chrono::high_resolution_clock::now();
-    }
-
-    void set_end() {
-        auto end_time = std::chrono::high_resolution_clock::now();
-        auto duration =
-            std::chrono::duration_cast<std::chrono::milliseconds>(end_time - start_time_).count();
-        std::cout << "Total execution time: " << duration << " ms" << std::endl;
-    }
-
-    void print() const {
-        for (const auto& [name, events] : timings_) {
-            std::cout << "Performance for " << name << ": ";
-            for (const auto& event : events) {
-                auto duration =
-                    event.get_profiling_info<sycl::info::event_profiling::command_end>() -
-                    event.get_profiling_info<sycl::info::event_profiling::command_start>();
-                std::cout << duration / 1e6 << " ms ";
-            }
-            std::cout << std::endl;
-        }
-    }
-
-private:
-    // define start time
-    std::chrono::high_resolution_clock::time_point start_time_;
-    std::map<std::string, std::vector<sycl::event>> timings_;
-};
-
 void print_device_name(sycl::queue& queue) {
     const auto device = queue.get_device();
     const auto device_name = device.get_info<sycl::info::device::name>();
@@ -87,8 +48,6 @@ TEST("test advance operation", "[advance]") {
     auto& queue = policy.get_queue();
     print_device_name(queue);
 
-    PerformanceTester perf_tester;
-
     std::vector<std::uint32_t> row_ptr = {
         0,   2,   5,   9,   13,  17,  21,  25,  29,  33,  37,  41,  45,  49,  53,  57,  61,
         65,  69,  73,  77,  81,  85,  89,  93,  97,  101, 105, 109, 113, 117, 121, 125, 129,
@@ -156,7 +115,6 @@ TEST("test advance operation", "[advance]") {
     size_t iter = 0;
 
     /// Start BFS
-    perf_tester.set_start();
     while (!in_frontier.empty()) {
         auto e = pr::advance(graph,
                              in_frontier,
@@ -168,17 +126,13 @@ TEST("test advance operation", "[advance]") {
                                  }
                                  return !visited;
                              });
-        perf_tester.add("advance", e);
         e.wait_and_throw();
         iter++;
         pr::swap_frontiers(in_frontier, out_frontier);
         out_frontier.clear();
     }
-    perf_tester.set_end();
     /// End BFS
 
-    // perf_tester.print();
-
     auto expected_distances = host_bfs(row_ptr, col_indices, src);
     auto actual_distances = distance.to_host(queue).get_data();
     for (size_t i = 0; i < num_nodes; ++i) {

From 2b7b2c4670c52d149dde885be5dc9ad56b0eacae Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Fri, 19 Sep 2025 15:19:52 +0200
Subject: [PATCH 25/69] Enhance code readability by adding comments and using
 const for variable declarations in BitmapKernel and frontier_dpc
 implementations

---
 .../backend/primitives/frontier/advance.hpp   | 33 +++++++++++--------
 .../primitives/frontier/frontier_dpc.cpp      | 12 +++----
 2 files changed, 26 insertions(+), 19 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index b4e191ee34f..b2c8076719a 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -80,7 +80,8 @@ class frontier_context {
 /// It processes the input frontier and advances it based on the provided functor.
 template <typename T, typename ContextT, typename GraphDevT, typename LambdaT>
 struct BitmapKernel {
-    template<typename VertexT>
+    /// This function distributes the workload among the workgroup, subgroup, and individual work items
+    template <typename VertexT>
     inline void distribute_workload(frontier_context_state& state, const VertexT& vertex) const {
         const size_t lid = state.item.get_local_linear_id();
         const auto wgroup = state.item.get_group();
@@ -91,11 +92,11 @@ struct BitmapKernel {
 
         if (sgroup.leader()) {
             subgroup_reduce_tail[sgroup_id] = 0;
-            }
+        }
         if (wgroup.leader()) {
             workgroup_reduce_tail[0] = 0;
         }
-        
+
         sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group>
             sg_tail{ subgroup_reduce_tail[sgroup_id] };
         sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group>
@@ -104,7 +105,8 @@ struct BitmapKernel {
 
         if (context.check(state, vertex)) {
             uint32_t n_edges = graph_dev.get_degree(vertex);
-            if (n_edges >= wgroup_size * wgroup_size) { // if the number of edges is large enough, we can assign the vertex to the workgroup
+            // if the number of edges is large enough, we can assign the vertex to the workgroup
+            if (n_edges >= wgroup_size * wgroup_size) {
                 uint32_t loc = wg_tail.fetch_add(static_cast<uint32_t>(1));
                 n_edges_wg[loc] = n_edges;
                 workgroup_reduce[loc] = vertex;
@@ -123,11 +125,12 @@ struct BitmapKernel {
         }
     }
 
+    /// This function processes the vertices assigned to the workgroup.
     inline void process_workgroup_reduction(frontier_context_state& state) const {
         /// This function processes the vertices assigned to the workgroup.
         sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group>
             wg_tail{ workgroup_reduce_tail[0] };
-        
+
         const auto wgroup = state.item.get_group();
         const size_t lid = state.item.get_local_linear_id();
         const size_t wgroup_size = wgroup.get_local_range(0);
@@ -153,6 +156,7 @@ struct BitmapKernel {
         }
     }
 
+    /// This function processes the vertices assigned to the subgroup.
     inline void process_subgroup_reduction(frontier_context_state& state) const {
         const auto sgroup = state.item.get_sub_group();
         const auto sgroup_id = sgroup.get_group_id();
@@ -163,7 +167,7 @@ struct BitmapKernel {
         sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group>
             sg_tail{ subgroup_reduce_tail[sgroup_id] };
 
-        for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) { 
+        for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) {
             // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
             size_t vertex_id = offset + i;
             auto vertex = subgroup_reduce[vertex_id];
@@ -187,8 +191,10 @@ struct BitmapKernel {
         }
     }
 
-    template<typename VertexT>
-    inline void process_workitem_reduction(frontier_context_state& state, const VertexT& vertex) const {
+    /// This function processes the vertices that were not assigned to the workgroup or subgroup.
+    template <typename VertexT>
+    inline void process_workitem_reduction(frontier_context_state& state,
+                                           const VertexT& vertex) const {
         const size_t lid = state.item.get_local_linear_id();
 
         if (!visited[lid]) {
@@ -216,7 +222,6 @@ struct BitmapKernel {
 
             // 1. distribute the workload based on the number of edges to the workgroup, subgroup or workitem
             distribute_workload(state, assigned_vertex);
-
             sycl::group_barrier(wgroup);
 
             // 2. process the the edge of one vertex at a time using the workgroup
@@ -229,7 +234,7 @@ struct BitmapKernel {
 
             // 4. process the edges of the vertices that were not assigned to the workgroup or subgroup
             process_workitem_reduction(state, assigned_vertex);
-            
+
             context.complete_iteration(state); // complete the current iteration
         }
     }
@@ -285,9 +290,11 @@ sycl::event advance(const GraphT& graph,
                                      : global_size +
                                            (local_range[0] - global_size % local_range[0]) };
 
-    frontier_context<decltype(in_dev_frontier), decltype(out_dev_frontier)> context{ num_nodes,
-                                                                            in_dev_frontier,
-                                                                            out_dev_frontier };
+    frontier_context<decltype(in_dev_frontier), decltype(out_dev_frontier)> context{
+        num_nodes,
+        in_dev_frontier,
+        out_dev_frontier
+    };
     using bitmap_kernel_t =
         BitmapKernel<element_t, decltype(context), decltype(graph_dev), LambdaT>;
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index 4c142e2b83c..666d1cfb50d 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -87,12 +87,12 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
     auto offsets_size_pointer = _offsets.get_mutable_data();
     auto offsets_pointer = _offsets.get_mutable_data() + 1;
 
-    uint32_t element_bitsize = bitmap.get_element_bitsize();
-    size_t local_range = 256; // propose_wg_size(this->_queue);
-    size_t mlb_count = _mlb_layer.get_count();
-    size_t global_range = (mlb_count % local_range == 0)
-                              ? mlb_count
-                              : (mlb_count + local_range - (mlb_count % local_range));
+    const uint32_t element_bitsize = bitmap.get_element_bitsize();
+    const size_t local_range = 256; // propose_wg_size(this->_queue);
+    const size_t mlb_count = _mlb_layer.get_count();
+    const size_t global_range = (mlb_count % local_range == 0)
+                                    ? mlb_count
+                                    : (mlb_count + local_range - (mlb_count % local_range));
 
     // check if local memory is enough
     bool use_local_mem =

From 5dda7de993fe5a1737c52a45a93b1e540c727ab4 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Mon, 22 Sep 2025 11:27:18 +0200
Subject: [PATCH 26/69] Add copyright notices to header files in the frontier
 module

---
 .../backend/primitives/frontier/advance.hpp    | 18 ++++++++++++++++++
 .../dal/backend/primitives/frontier/bitset.hpp | 18 ++++++++++++++++++
 .../backend/primitives/frontier/frontier.hpp   | 18 ++++++++++++++++++
 .../primitives/frontier/frontier_dpc.cpp       | 18 ++++++++++++++++++
 .../dal/backend/primitives/frontier/graph.hpp  | 18 ++++++++++++++++++
 .../primitives/frontier/test/advance_dpc.cpp   | 18 ++++++++++++++++++
 .../primitives/frontier/test/bfs_dpc.cpp       | 18 ++++++++++++++++++
 .../primitives/frontier/test/frontier_dpc.cpp  | 18 ++++++++++++++++++
 8 files changed, 144 insertions(+)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index b2c8076719a..f7b42e6bc6a 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -1,3 +1,21 @@
+/*******************************************************************************
+* Copyright 2025 Intel Corporation
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #pragma once
 
 #include "oneapi/dal/backend/primitives/ndarray.hpp"
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index e554f11c1ee..5f944c01dc5 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -1,3 +1,21 @@
+/*******************************************************************************
+* Copyright 2025 Intel Corporation
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #pragma once
 
 #include "oneapi/dal/backend/memory.hpp"
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index 9efe5365792..21864ad3d98 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -1,3 +1,21 @@
+/*******************************************************************************
+* Copyright 2025 Intel Corporation
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #pragma once
 
 #include "oneapi/dal/common.hpp"
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index 666d1cfb50d..9b9b7e9118d 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -1,3 +1,21 @@
+/*******************************************************************************
+* Copyright 2025 Intel Corporation
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 
 namespace oneapi::dal::backend::primitives {
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index 11a9a529f8f..39dd86a4d06 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -1,3 +1,21 @@
+/*******************************************************************************
+* Copyright 2025 Intel Corporation
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #pragma once
 
 #include "oneapi/dal/common.hpp"
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index 7e35eeb7683..83fc94c6254 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -1,3 +1,21 @@
+/*******************************************************************************
+* Copyright 2025 Intel Corporation
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 #include "oneapi/dal/backend/primitives/frontier/advance.hpp"
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
index b9e4b017d91..f5258ba0e58 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -1,3 +1,21 @@
+/*******************************************************************************
+* Copyright 2025 Intel Corporation
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #include "oneapi/dal/backend/primitives/frontier.hpp"
 
 #include "oneapi/dal/test/engine/common.hpp"
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
index c3d089afb6d..7119905157e 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
@@ -1,3 +1,21 @@
+/*******************************************************************************
+* Copyright 2025 Intel Corporation
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 
 #include "oneapi/dal/test/engine/common.hpp"

From f2641e6811f745a24ae5274189fc3c6bd85c0b14 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Mon, 22 Sep 2025 11:40:08 +0200
Subject: [PATCH 27/69] Refactor frontier test files: change vector to set for
 frontier representation and update test case names for clarity

---
 .../primitives/frontier/test/advance_dpc.cpp  | 23 +++++++------------
 .../primitives/frontier/test/bfs_dpc.cpp      |  7 ++----
 2 files changed, 10 insertions(+), 20 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index 83fc94c6254..c9bdba2e67e 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -42,10 +42,10 @@ void print_frontier(const T* data, size_t count, size_t num_items) {
     }
 }
 
-std::vector<uint32_t> compute_next_frontier(std::vector<uint32_t>& row_ptr,
-                                            std::vector<uint32_t>& col_indices,
-                                            std::vector<uint32_t>& frontier) {
-    std::vector<uint32_t> next_frontier;
+std::set<uint32_t> compute_next_frontier(std::vector<uint32_t>& row_ptr,
+                                          std::vector<uint32_t>& col_indices,
+                                          std::set<uint32_t>& frontier) {
+    std::set<uint32_t> next_frontier;
 
     for (auto node : frontier) {
         auto start = row_ptr[node];
@@ -53,21 +53,17 @@ std::vector<uint32_t> compute_next_frontier(std::vector<uint32_t>& row_ptr,
 
         for (size_t i = start; i < end; ++i) {
             auto neighbor = col_indices[i];
-            next_frontier.push_back(neighbor);
+            next_frontier.insert(neighbor);
         }
     }
-    // Remove duplicates
-    std::sort(next_frontier.begin(), next_frontier.end());
-    next_frontier.erase(std::unique(next_frontier.begin(), next_frontier.end()),
-                        next_frontier.end());
     return next_frontier;
 }
 
 template <typename T>
-void compare_frontiers(T& device_frontier, std::vector<uint32_t>& host_frontier, size_t num_nodes) {
+void compare_frontiers(T& device_frontier, std::set<uint32_t>& host_frontier, size_t num_nodes) {
     for (size_t i = 0; i < num_nodes; ++i) {
         bool tmpd = device_frontier.check(i);
-        bool tmph = std::find(host_frontier.begin(), host_frontier.end(), i) != host_frontier.end();
+        bool tmph = host_frontier.find(i) != host_frontier.end();
         if (tmpd != tmph) {
             std::cout << "Mismatch at vertex " << i << ": device = " << tmpd << ", host = " << tmph
                       << std::endl;
@@ -81,9 +77,6 @@ TEST("test advance operation", "[advance]") {
     auto& queue = policy.get_queue();
     print_device_name(queue);
 
-    // std::vector<std::uint32_t> row_ptr = {0, 2, 4, 6};
-    // std::vector<std::uint32_t> col_indices = {1, 2, 0, 2, 0, 1};
-    // std::vector<std::uint32_t> weights = {1, 1, 1, 1, 1, 1};
     std::vector<std::uint32_t> row_ptr = {
         0,   2,   5,   9,   13,  17,  21,  25,  29,  33,  37,  41,  45,  49,  53,  57,  61,
         65,  69,  73,  77,  81,  85,  89,  93,  97,  101, 105, 109, 113, 117, 121, 125, 129,
@@ -138,7 +131,7 @@ TEST("test advance operation", "[advance]") {
     in_frontier.insert(4);
     in_frontier.insert(52);
     in_frontier.insert(100);
-    std::vector<std::uint32_t> host_frontier = { 3, 4, 52, 100 };
+    std::set<std::uint32_t> host_frontier = { 3, 4, 52, 100 };
 
     pr::advance(graph,
                 in_frontier,
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
index f5258ba0e58..25940923c23 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -17,14 +17,11 @@
 *******************************************************************************/
 
 #include "oneapi/dal/backend/primitives/frontier.hpp"
-
 #include "oneapi/dal/test/engine/common.hpp"
-#include "oneapi/dal/test/engine/fixtures.hpp"
-#include "oneapi/dal/test/engine/dataframe.hpp"
+
 #include <queue>
 #include <vector>
 #include <map>
-#include <chrono>
 
 namespace oneapi::dal::backend::primitives::test {
 
@@ -61,7 +58,7 @@ std::vector<std::uint32_t> host_bfs(std::vector<T>& row_offsets,
     return distances;
 }
 
-TEST("test advance operation", "[advance]") {
+TEST("test BFS", "[bfs]") {
     DECLARE_TEST_POLICY(policy);
     auto& queue = policy.get_queue();
     print_device_name(queue);

From 06265d4061fcd4200511ad78d44bc4d59483e84f Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Mon, 22 Sep 2025 11:53:00 +0200
Subject: [PATCH 28/69] Refactor compute_next_frontier to use vector<bool>
 instead of set<uint32_t> for improved performance and memory efficiency

---
 .../primitives/frontier/test/advance_dpc.cpp  | 24 ++++++++++++-------
 1 file changed, 15 insertions(+), 9 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index c9bdba2e67e..398c072ff85 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -42,28 +42,30 @@ void print_frontier(const T* data, size_t count, size_t num_items) {
     }
 }
 
-std::set<uint32_t> compute_next_frontier(std::vector<uint32_t>& row_ptr,
-                                          std::vector<uint32_t>& col_indices,
-                                          std::set<uint32_t>& frontier) {
-    std::set<uint32_t> next_frontier;
+std::vector<bool> compute_next_frontier(std::vector<uint32_t>& row_ptr,
+                                        std::vector<uint32_t>& col_indices,
+                                        std::vector<bool>& frontier) {
+    std::vector<bool> next_frontier(frontier.size(), false);
+
+    for (size_t node = 0; node < frontier.size(); ++node) {
+        if (!frontier[node]) continue;
 
-    for (auto node : frontier) {
         auto start = row_ptr[node];
         auto end = row_ptr[node + 1];
 
         for (size_t i = start; i < end; ++i) {
             auto neighbor = col_indices[i];
-            next_frontier.insert(neighbor);
+            next_frontier[neighbor] = true;
         }
     }
     return next_frontier;
 }
 
 template <typename T>
-void compare_frontiers(T& device_frontier, std::set<uint32_t>& host_frontier, size_t num_nodes) {
+void compare_frontiers(T& device_frontier, std::vector<bool>& host_frontier, size_t num_nodes) {
     for (size_t i = 0; i < num_nodes; ++i) {
         bool tmpd = device_frontier.check(i);
-        bool tmph = host_frontier.find(i) != host_frontier.end();
+        bool tmph = host_frontier[i];
         if (tmpd != tmph) {
             std::cout << "Mismatch at vertex " << i << ": device = " << tmpd << ", host = " << tmph
                       << std::endl;
@@ -131,7 +133,11 @@ TEST("test advance operation", "[advance]") {
     in_frontier.insert(4);
     in_frontier.insert(52);
     in_frontier.insert(100);
-    std::set<std::uint32_t> host_frontier = { 3, 4, 52, 100 };
+    std::vector<bool> host_frontier(num_nodes, false);
+    host_frontier[3] = true;
+    host_frontier[4] = true;
+    host_frontier[52] = true;
+    host_frontier[100] = true;
 
     pr::advance(graph,
                 in_frontier,

From df28d7a78e3287d62601e96411842438cd87992c Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Mon, 22 Sep 2025 14:04:47 +0200
Subject: [PATCH 29/69] tests(frontier): add shared test utilities and wire
 includes; expose header to BUILD

---
 .../dal/backend/primitives/frontier/BUILD     |  3 +
 .../primitives/frontier/test/advance_dpc.cpp  |  7 +--
 .../primitives/frontier/test/bfs_dpc.cpp      | 13 ++--
 .../primitives/frontier/test/frontier_dpc.cpp |  8 +--
 .../primitives/frontier/test/utils.hpp        | 62 +++++++++++++++++++
 5 files changed, 71 insertions(+), 22 deletions(-)
 create mode 100644 cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/BUILD b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
index 83d8a7dd277..3e2ab8a790c 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/BUILD
+++ b/cpp/oneapi/dal/backend/primitives/frontier/BUILD
@@ -17,6 +17,9 @@ dal_test_suite (
     framework = "catch2",
     compile_as = [ "dpc++" ],
     private = True,
+    hdrs = glob([
+        "test/*.hpp",
+    ]),
     srcs = glob([
         "test/*_dpc.cpp",
     ], exclude=[
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index 398c072ff85..bfc48c4ad3a 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -19,6 +19,7 @@
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 #include "oneapi/dal/backend/primitives/frontier/advance.hpp"
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"
+#include "oneapi/dal/backend/primitives/frontier/test/utils.hpp"
 
 #include "oneapi/dal/test/engine/common.hpp"
 
@@ -26,12 +27,6 @@ namespace oneapi::dal::backend::primitives::test {
 
 namespace pr = dal::backend::primitives;
 
-void print_device_name(sycl::queue& queue) {
-    const auto device = queue.get_device();
-    const auto device_name = device.get_info<sycl::info::device::name>();
-    std::cout << "Running on device: " << device_name << std::endl;
-}
-
 template <typename T>
 void print_frontier(const T* data, size_t count, size_t num_items) {
     size_t element_bitsize = sizeof(T) * 8;
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
index 25940923c23..b63d405cabb 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -17,6 +17,7 @@
 *******************************************************************************/
 
 #include "oneapi/dal/backend/primitives/frontier.hpp"
+#include "oneapi/dal/backend/primitives/frontier/test/utils.hpp"
 #include "oneapi/dal/test/engine/common.hpp"
 
 #include <queue>
@@ -27,16 +28,10 @@ namespace oneapi::dal::backend::primitives::test {
 
 namespace pr = dal::backend::primitives;
 
-void print_device_name(sycl::queue& queue) {
-    const auto device = queue.get_device();
-    const auto device_name = device.get_info<sycl::info::device::name>();
-    std::cout << "Running on device: " << device_name << std::endl;
-}
-
 template <typename T>
-std::vector<std::uint32_t> host_bfs(std::vector<T>& row_offsets,
-                                    std::vector<T>& col_indices,
-                                    T src) {
+std::vector<std::uint32_t> host_bfs(const std::vector<T>& row_offsets,
+                                    const std::vector<T>& col_indices,
+                                    const T src) {
     std::vector<std::uint32_t> distances(row_offsets.size() - 1,
                                          std::numeric_limits<std::uint32_t>::max());
     std::queue<T> q;
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
index 7119905157e..bb128870ae8 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
@@ -17,19 +17,13 @@
 *******************************************************************************/
 
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
-
+#include "oneapi/dal/backend/primitives/frontier/test/utils.hpp"
 #include "oneapi/dal/test/engine/common.hpp"
 
 namespace oneapi::dal::backend::primitives::test {
 
 namespace pr = dal::backend::primitives;
 
-void print_device_name(sycl::queue& queue) {
-    const auto device = queue.get_device();
-    const auto device_name = device.get_info<sycl::info::device::name>();
-    std::cout << "Running on device: " << device_name << std::endl;
-}
-
 template <typename T>
 void print_frontier(const T* data, size_t count, size_t num_items) {
     size_t element_bitsize = sizeof(T) * 8;
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
new file mode 100644
index 00000000000..dcecc208ffe
--- /dev/null
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
@@ -0,0 +1,62 @@
+#pragma once
+
+#include <random>
+#include <vector>
+
+
+void print_device_name(sycl::queue& queue) {
+    const auto device = queue.get_device();
+    const auto device_name = device.get_info<sycl::info::device::name>();
+    std::cout << "Running on device: " << device_name << std::endl;
+}
+
+namespace oneapi::dal::backend::primitives {
+  struct csr_graph_data {
+    std::vector<std::uint32_t> row_ptr;
+    std::vector<std::uint32_t> col_indices;
+    std::vector<std::uint32_t> weights;
+};
+
+csr_graph_data generate_random_graph(std::size_t vertex_count,
+                                     double edge_probability,
+                                     std::uint32_t seed) {
+    if (vertex_count == 0) {
+        return { std::vector<std::uint32_t>{ 0 }, {}, {} };
+    }
+
+    std::mt19937 rng(seed);
+    std::bernoulli_distribution edge_dist(edge_probability);
+    std::uniform_int_distribution<std::uint32_t> vertex_dist(0,
+                                                             static_cast<std::uint32_t>(vertex_count - 1));
+
+    std::vector<std::uint32_t> row_ptr(vertex_count + 1, 0);
+    std::vector<std::uint32_t> col_indices;
+    col_indices.reserve(vertex_count);
+
+    for (std::size_t src = 0; src < vertex_count; ++src) {
+        const auto edges_before = col_indices.size();
+        for (std::size_t dst = 0; dst < vertex_count; ++dst) {
+            if (src == dst) {
+                continue;
+            }
+            if (edge_dist(rng)) {
+                col_indices.push_back(static_cast<std::uint32_t>(dst));
+            }
+        }
+
+        if (col_indices.size() == edges_before && vertex_count > 1) {
+            std::uint32_t fallback = vertex_dist(rng);
+            if (fallback == src) {
+                fallback = (fallback + 1) % static_cast<std::uint32_t>(vertex_count);
+            }
+            col_indices.push_back(fallback);
+        }
+
+        row_ptr[src + 1] = static_cast<std::uint32_t>(col_indices.size());
+    }
+
+    std::vector<std::uint32_t> weights(col_indices.size(), 1);
+    return { std::move(row_ptr), std::move(col_indices), std::move(weights) };
+}
+
+} // namespace oneapi::dal::backend::primitives
\ No newline at end of file

From 225b1117d3c9823caf9911f9e37e960eb54618c3 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Mon, 22 Sep 2025 14:04:47 +0200
Subject: [PATCH 30/69] tests(frontier): switch tests to randomized graph
 generation and refine helper signatures

---
 .../primitives/frontier/test/advance_dpc.cpp  | 87 +++++++------------
 .../primitives/frontier/test/bfs_dpc.cpp      | 53 ++---------
 2 files changed, 36 insertions(+), 104 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index bfc48c4ad3a..990799febda 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -37,9 +37,9 @@ void print_frontier(const T* data, size_t count, size_t num_items) {
     }
 }
 
-std::vector<bool> compute_next_frontier(std::vector<uint32_t>& row_ptr,
-                                        std::vector<uint32_t>& col_indices,
-                                        std::vector<bool>& frontier) {
+std::vector<bool> compute_next_frontier(const std::vector<std::uint32_t>& row_ptr,
+                                        const std::vector<std::uint32_t>& col_indices,
+                                        const std::vector<bool>& frontier) {
     std::vector<bool> next_frontier(frontier.size(), false);
 
     for (size_t node = 0; node < frontier.size(); ++node) {
@@ -57,7 +57,9 @@ std::vector<bool> compute_next_frontier(std::vector<uint32_t>& row_ptr,
 }
 
 template <typename T>
-void compare_frontiers(T& device_frontier, std::vector<bool>& host_frontier, size_t num_nodes) {
+void compare_frontiers(T& device_frontier,
+                       const std::vector<bool>& host_frontier,
+                       size_t num_nodes) {
     for (size_t i = 0; i < num_nodes; ++i) {
         bool tmpd = device_frontier.check(i);
         bool tmph = host_frontier[i];
@@ -74,65 +76,34 @@ TEST("test advance operation", "[advance]") {
     auto& queue = policy.get_queue();
     print_device_name(queue);
 
-    std::vector<std::uint32_t> row_ptr = {
-        0,   2,   5,   9,   13,  17,  21,  25,  29,  33,  37,  41,  45,  49,  53,  57,  61,
-        65,  69,  73,  77,  81,  85,  89,  93,  97,  101, 105, 109, 113, 117, 121, 125, 129,
-        133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197,
-        201, 205, 209, 213, 217, 221, 225, 229, 233, 237, 241, 245, 249, 253, 257, 261, 265,
-        269, 273, 277, 281, 285, 289, 293, 297, 301, 305, 309, 313, 317, 321, 325, 329, 333,
-        337, 341, 345, 349, 353, 357, 361, 365, 369, 373, 377, 381, 385, 389, 393, 397, 401,
-        405, 409, 413, 417, 421, 425, 429, 433, 437, 441, 445, 449, 453, 457, 461, 465, 469,
-        473, 477, 481, 485, 489, 493, 497, 501, 504, 506
-    };
-    std::vector<std::uint32_t> col_indices = {
-        1,   2,   0,   2,   3,   0,   1,   3,   4,   1,   2,   4,   5,   2,   3,   5,   6,   3,
-        4,   6,   7,   4,   5,   7,   8,   5,   6,   8,   9,   6,   7,   9,   10,  7,   8,   10,
-        11,  8,   9,   11,  12,  9,   10,  12,  13,  10,  11,  13,  14,  11,  12,  14,  15,  12,
-        13,  15,  16,  13,  14,  16,  17,  14,  15,  17,  18,  15,  16,  18,  19,  16,  17,  19,
-        20,  17,  18,  20,  21,  18,  19,  21,  22,  19,  20,  22,  23,  20,  21,  23,  24,  21,
-        22,  24,  25,  22,  23,  25,  26,  23,  24,  26,  27,  24,  25,  27,  28,  25,  26,  28,
-        29,  26,  27,  29,  30,  27,  28,  30,  31,  28,  29,  31,  32,  29,  30,  32,  33,  30,
-        31,  33,  34,  31,  32,  34,  35,  32,  33,  35,  36,  33,  34,  36,  37,  34,  35,  37,
-        38,  35,  36,  38,  39,  36,  37,  39,  40,  37,  38,  40,  41,  38,  39,  41,  42,  39,
-        40,  42,  43,  40,  41,  43,  44,  41,  42,  44,  45,  42,  43,  45,  46,  43,  44,  46,
-        47,  44,  45,  47,  48,  45,  46,  48,  49,  46,  47,  49,  50,  47,  48,  50,  51,  48,
-        49,  51,  52,  49,  50,  52,  53,  50,  51,  53,  54,  51,  52,  54,  55,  52,  53,  55,
-        56,  53,  54,  56,  57,  54,  55,  57,  58,  55,  56,  58,  59,  56,  57,  59,  60,  57,
-        58,  60,  61,  58,  59,  61,  62,  59,  60,  62,  63,  60,  61,  63,  64,  61,  62,  64,
-        65,  62,  63,  65,  66,  63,  64,  66,  67,  64,  65,  67,  68,  65,  66,  68,  69,  66,
-        67,  69,  70,  67,  68,  70,  71,  68,  69,  71,  72,  69,  70,  72,  73,  70,  71,  73,
-        74,  71,  72,  74,  75,  72,  73,  75,  76,  73,  74,  76,  77,  74,  75,  77,  78,  75,
-        76,  78,  79,  76,  77,  79,  80,  77,  78,  80,  81,  78,  79,  81,  82,  79,  80,  82,
-        83,  80,  81,  83,  84,  81,  82,  84,  85,  82,  83,  85,  86,  83,  84,  86,  87,  84,
-        85,  87,  88,  85,  86,  88,  89,  86,  87,  89,  90,  87,  88,  90,  91,  88,  89,  91,
-        92,  89,  90,  92,  93,  90,  91,  93,  94,  91,  92,  94,  95,  92,  93,  95,  96,  93,
-        94,  96,  97,  94,  95,  97,  98,  95,  96,  98,  99,  96,  97,  99,  100, 97,  98,  100,
-        101, 98,  99,  101, 102, 99,  100, 102, 103, 100, 101, 103, 104, 101, 102, 104, 105, 102,
-        103, 105, 106, 103, 104, 106, 107, 104, 105, 107, 108, 105, 106, 108, 109, 106, 107, 109,
-        110, 107, 108, 110, 111, 108, 109, 111, 112, 109, 110, 112, 113, 110, 111, 113, 114, 111,
-        112, 114, 115, 112, 113, 115, 116, 113, 114, 116, 117, 114, 115, 117, 118, 115, 116, 118,
-        119, 116, 117, 119, 120, 117, 118, 120, 121, 118, 119, 121, 122, 119, 120, 122, 123, 120,
-        121, 123, 124, 121, 122, 124, 125, 122, 123, 125, 126, 123, 124, 126, 127, 124, 125, 127,
-        125, 126
-    };
-    std::vector<std::uint32_t> weights(col_indices.size(), 1);
-    size_t num_nodes = row_ptr.size() - 1;
-
-    auto graph = pr::csr_graph(queue, row_ptr, col_indices, weights);
+    const std::uint32_t seed = GENERATE(42u, 313u, 2025u);
+    const double edge_probability = GENERATE(0.05, 0.1, 0.2);
+    const std::size_t num_nodes = GENERATE(128, 512, 1024);
+
+    const auto graph_data = generate_random_graph(num_nodes, edge_probability, seed);
+    auto graph = pr::csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
     auto in_frontier =
         pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
     auto out_frontier =
         pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
 
-    in_frontier.insert(3);
-    in_frontier.insert(4);
-    in_frontier.insert(52);
-    in_frontier.insert(100);
     std::vector<bool> host_frontier(num_nodes, false);
-    host_frontier[3] = true;
-    host_frontier[4] = true;
-    host_frontier[52] = true;
-    host_frontier[100] = true;
+    std::mt19937 frontier_rng(seed ^ 0x9e3779b9u);
+    std::bernoulli_distribution frontier_dist(0.1);
+
+    for (std::size_t vertex = 0; vertex < num_nodes; ++vertex) {
+        if (frontier_dist(frontier_rng)) {
+            in_frontier.insert(static_cast<std::uint32_t>(vertex));
+            host_frontier[vertex] = true;
+        }
+    }
+
+    if (in_frontier.empty()) {
+        std::uniform_int_distribution<std::uint32_t> vertex_dist(0, static_cast<std::uint32_t>(num_nodes - 1));
+        const auto fallback_vertex = vertex_dist(frontier_rng);
+        in_frontier.insert(fallback_vertex);
+        host_frontier[fallback_vertex] = true;
+    }
 
     pr::advance(graph,
                 in_frontier,
@@ -142,7 +113,7 @@ TEST("test advance operation", "[advance]") {
                 })
         .wait_and_throw();
 
-    auto tmp_frontier = compute_next_frontier(row_ptr, col_indices, host_frontier);
+    auto tmp_frontier = compute_next_frontier(graph_data.row_ptr, graph_data.col_indices, host_frontier);
     compare_frontiers(out_frontier, tmp_frontier, num_nodes);
 } // TEST "test advance operation"
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
index b63d405cabb..7c0576ffc59 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -58,51 +58,12 @@ TEST("test BFS", "[bfs]") {
     auto& queue = policy.get_queue();
     print_device_name(queue);
 
-    std::vector<std::uint32_t> row_ptr = {
-        0,   2,   5,   9,   13,  17,  21,  25,  29,  33,  37,  41,  45,  49,  53,  57,  61,
-        65,  69,  73,  77,  81,  85,  89,  93,  97,  101, 105, 109, 113, 117, 121, 125, 129,
-        133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197,
-        201, 205, 209, 213, 217, 221, 225, 229, 233, 237, 241, 245, 249, 253, 257, 261, 265,
-        269, 273, 277, 281, 285, 289, 293, 297, 301, 305, 309, 313, 317, 321, 325, 329, 333,
-        337, 341, 345, 349, 353, 357, 361, 365, 369, 373, 377, 381, 385, 389, 393, 397, 401,
-        405, 409, 413, 417, 421, 425, 429, 433, 437, 441, 445, 449, 453, 457, 461, 465, 469,
-        473, 477, 481, 485, 489, 493, 497, 501, 504, 506
-    };
-    std::vector<std::uint32_t> col_indices = {
-        1,   2,   0,   2,   3,   0,   1,   3,   4,   1,   2,   4,   5,   2,   3,   5,   6,   3,
-        4,   6,   7,   4,   5,   7,   8,   5,   6,   8,   9,   6,   7,   9,   10,  7,   8,   10,
-        11,  8,   9,   11,  12,  9,   10,  12,  13,  10,  11,  13,  14,  11,  12,  14,  15,  12,
-        13,  15,  16,  13,  14,  16,  17,  14,  15,  17,  18,  15,  16,  18,  19,  16,  17,  19,
-        20,  17,  18,  20,  21,  18,  19,  21,  22,  19,  20,  22,  23,  20,  21,  23,  24,  21,
-        22,  24,  25,  22,  23,  25,  26,  23,  24,  26,  27,  24,  25,  27,  28,  25,  26,  28,
-        29,  26,  27,  29,  30,  27,  28,  30,  31,  28,  29,  31,  32,  29,  30,  32,  33,  30,
-        31,  33,  34,  31,  32,  34,  35,  32,  33,  35,  36,  33,  34,  36,  37,  34,  35,  37,
-        38,  35,  36,  38,  39,  36,  37,  39,  40,  37,  38,  40,  41,  38,  39,  41,  42,  39,
-        40,  42,  43,  40,  41,  43,  44,  41,  42,  44,  45,  42,  43,  45,  46,  43,  44,  46,
-        47,  44,  45,  47,  48,  45,  46,  48,  49,  46,  47,  49,  50,  47,  48,  50,  51,  48,
-        49,  51,  52,  49,  50,  52,  53,  50,  51,  53,  54,  51,  52,  54,  55,  52,  53,  55,
-        56,  53,  54,  56,  57,  54,  55,  57,  58,  55,  56,  58,  59,  56,  57,  59,  60,  57,
-        58,  60,  61,  58,  59,  61,  62,  59,  60,  62,  63,  60,  61,  63,  64,  61,  62,  64,
-        65,  62,  63,  65,  66,  63,  64,  66,  67,  64,  65,  67,  68,  65,  66,  68,  69,  66,
-        67,  69,  70,  67,  68,  70,  71,  68,  69,  71,  72,  69,  70,  72,  73,  70,  71,  73,
-        74,  71,  72,  74,  75,  72,  73,  75,  76,  73,  74,  76,  77,  74,  75,  77,  78,  75,
-        76,  78,  79,  76,  77,  79,  80,  77,  78,  80,  81,  78,  79,  81,  82,  79,  80,  82,
-        83,  80,  81,  83,  84,  81,  82,  84,  85,  82,  83,  85,  86,  83,  84,  86,  87,  84,
-        85,  87,  88,  85,  86,  88,  89,  86,  87,  89,  90,  87,  88,  90,  91,  88,  89,  91,
-        92,  89,  90,  92,  93,  90,  91,  93,  94,  91,  92,  94,  95,  92,  93,  95,  96,  93,
-        94,  96,  97,  94,  95,  97,  98,  95,  96,  98,  99,  96,  97,  99,  100, 97,  98,  100,
-        101, 98,  99,  101, 102, 99,  100, 102, 103, 100, 101, 103, 104, 101, 102, 104, 105, 102,
-        103, 105, 106, 103, 104, 106, 107, 104, 105, 107, 108, 105, 106, 108, 109, 106, 107, 109,
-        110, 107, 108, 110, 111, 108, 109, 111, 112, 109, 110, 112, 113, 110, 111, 113, 114, 111,
-        112, 114, 115, 112, 113, 115, 116, 113, 114, 116, 117, 114, 115, 117, 118, 115, 116, 118,
-        119, 116, 117, 119, 120, 117, 118, 120, 121, 118, 119, 121, 122, 119, 120, 122, 123, 120,
-        121, 123, 124, 121, 122, 124, 125, 122, 123, 125, 126, 123, 124, 126, 127, 124, 125, 127,
-        125, 126
-    };
-    std::vector<std::uint32_t> weights(col_indices.size(), 1);
-
-    auto graph = pr::csr_graph(queue, row_ptr, col_indices, weights);
-    size_t num_nodes = row_ptr.size() - 1;
+    const std::uint32_t seed = GENERATE(42u, 313u, 2025u);
+    const double edge_probability = GENERATE(0.05, 0.1, 0.2);
+    const std::size_t num_nodes = GENERATE(128, 512, 1024);
+
+    const auto graph_data = generate_random_graph(num_nodes, edge_probability, seed);
+    auto graph = pr::csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
     auto in_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
     auto out_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
     pr::ndarray<std::uint32_t, 1> distance =
@@ -143,7 +104,7 @@ TEST("test BFS", "[bfs]") {
     }
     /// End BFS
 
-    auto expected_distances = host_bfs(row_ptr, col_indices, src);
+    auto expected_distances = host_bfs<std::uint32_t>(graph_data.row_ptr, graph_data.col_indices, src);
     auto actual_distances = distance.to_host(queue).get_data();
     for (size_t i = 0; i < num_nodes; ++i) {
         REQUIRE(actual_distances[i] == expected_distances[i]);

From a9c67478f320c92ec22b60bb6421854b5f362e24 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Mon, 22 Sep 2025 14:06:44 +0200
Subject: [PATCH 31/69] applied clang-format to the new files

---
 .../primitives/frontier/test/advance_dpc.cpp        | 13 +++++++++----
 .../backend/primitives/frontier/test/bfs_dpc.cpp    |  6 ++++--
 .../dal/backend/primitives/frontier/test/utils.hpp  |  8 ++++----
 3 files changed, 17 insertions(+), 10 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index 990799febda..7496d46b460 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -43,7 +43,8 @@ std::vector<bool> compute_next_frontier(const std::vector<std::uint32_t>& row_pt
     std::vector<bool> next_frontier(frontier.size(), false);
 
     for (size_t node = 0; node < frontier.size(); ++node) {
-        if (!frontier[node]) continue;
+        if (!frontier[node])
+            continue;
 
         auto start = row_ptr[node];
         auto end = row_ptr[node + 1];
@@ -81,7 +82,8 @@ TEST("test advance operation", "[advance]") {
     const std::size_t num_nodes = GENERATE(128, 512, 1024);
 
     const auto graph_data = generate_random_graph(num_nodes, edge_probability, seed);
-    auto graph = pr::csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
+    auto graph =
+        pr::csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
     auto in_frontier =
         pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
     auto out_frontier =
@@ -99,7 +101,9 @@ TEST("test advance operation", "[advance]") {
     }
 
     if (in_frontier.empty()) {
-        std::uniform_int_distribution<std::uint32_t> vertex_dist(0, static_cast<std::uint32_t>(num_nodes - 1));
+        std::uniform_int_distribution<std::uint32_t> vertex_dist(
+            0,
+            static_cast<std::uint32_t>(num_nodes - 1));
         const auto fallback_vertex = vertex_dist(frontier_rng);
         in_frontier.insert(fallback_vertex);
         host_frontier[fallback_vertex] = true;
@@ -113,7 +117,8 @@ TEST("test advance operation", "[advance]") {
                 })
         .wait_and_throw();
 
-    auto tmp_frontier = compute_next_frontier(graph_data.row_ptr, graph_data.col_indices, host_frontier);
+    auto tmp_frontier =
+        compute_next_frontier(graph_data.row_ptr, graph_data.col_indices, host_frontier);
     compare_frontiers(out_frontier, tmp_frontier, num_nodes);
 } // TEST "test advance operation"
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
index 7c0576ffc59..eee1db7671d 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -63,7 +63,8 @@ TEST("test BFS", "[bfs]") {
     const std::size_t num_nodes = GENERATE(128, 512, 1024);
 
     const auto graph_data = generate_random_graph(num_nodes, edge_probability, seed);
-    auto graph = pr::csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
+    auto graph =
+        pr::csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
     auto in_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
     auto out_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
     pr::ndarray<std::uint32_t, 1> distance =
@@ -104,7 +105,8 @@ TEST("test BFS", "[bfs]") {
     }
     /// End BFS
 
-    auto expected_distances = host_bfs<std::uint32_t>(graph_data.row_ptr, graph_data.col_indices, src);
+    auto expected_distances =
+        host_bfs<std::uint32_t>(graph_data.row_ptr, graph_data.col_indices, src);
     auto actual_distances = distance.to_host(queue).get_data();
     for (size_t i = 0; i < num_nodes; ++i) {
         REQUIRE(actual_distances[i] == expected_distances[i]);
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
index dcecc208ffe..7ec59e59f1e 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
@@ -3,7 +3,6 @@
 #include <random>
 #include <vector>
 
-
 void print_device_name(sycl::queue& queue) {
     const auto device = queue.get_device();
     const auto device_name = device.get_info<sycl::info::device::name>();
@@ -11,7 +10,7 @@ void print_device_name(sycl::queue& queue) {
 }
 
 namespace oneapi::dal::backend::primitives {
-  struct csr_graph_data {
+struct csr_graph_data {
     std::vector<std::uint32_t> row_ptr;
     std::vector<std::uint32_t> col_indices;
     std::vector<std::uint32_t> weights;
@@ -26,8 +25,9 @@ csr_graph_data generate_random_graph(std::size_t vertex_count,
 
     std::mt19937 rng(seed);
     std::bernoulli_distribution edge_dist(edge_probability);
-    std::uniform_int_distribution<std::uint32_t> vertex_dist(0,
-                                                             static_cast<std::uint32_t>(vertex_count - 1));
+    std::uniform_int_distribution<std::uint32_t> vertex_dist(
+        0,
+        static_cast<std::uint32_t>(vertex_count - 1));
 
     std::vector<std::uint32_t> row_ptr(vertex_count + 1, 0);
     std::vector<std::uint32_t> col_indices;

From 67edbaf53608b1933765d6a64ba1e2f41f174ff5 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Mon, 22 Sep 2025 15:15:57 +0200
Subject: [PATCH 32/69] add trailing new line to comply with format checker

---
 cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
index 7ec59e59f1e..2ca64ac5b61 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
@@ -59,4 +59,4 @@ csr_graph_data generate_random_graph(std::size_t vertex_count,
     return { std::move(row_ptr), std::move(col_indices), std::move(weights) };
 }
 
-} // namespace oneapi::dal::backend::primitives
\ No newline at end of file
+} // namespace oneapi::dal::backend::primitives

From 4a169554dfedb3c66a5c4bf4a55f21a7eed18a9d Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 18:49:55 +0200
Subject: [PATCH 33/69] Update copyright notices

---
 .../dal/backend/primitives/frontier/advance.hpp |  1 -
 .../dal/backend/primitives/frontier/bitset.hpp  |  1 -
 .../backend/primitives/frontier/frontier.hpp    |  1 -
 .../primitives/frontier/frontier_dpc.cpp        |  1 -
 .../dal/backend/primitives/frontier/graph.hpp   |  1 -
 .../primitives/frontier/test/advance_dpc.cpp    |  1 -
 .../primitives/frontier/test/bfs_dpc.cpp        |  1 -
 .../primitives/frontier/test/frontier_dpc.cpp   |  1 -
 .../backend/primitives/frontier/test/utils.hpp  | 17 +++++++++++++++++
 9 files changed, 17 insertions(+), 8 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index f7b42e6bc6a..9a7e1cf18de 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -1,5 +1,4 @@
 /*******************************************************************************
-* Copyright 2025 Intel Corporation
 * Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
 *
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index 5f944c01dc5..f14fa7a2887 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -1,5 +1,4 @@
 /*******************************************************************************
-* Copyright 2025 Intel Corporation
 * Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
 *
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index 21864ad3d98..88bbbfd5931 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -1,5 +1,4 @@
 /*******************************************************************************
-* Copyright 2025 Intel Corporation
 * Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
 *
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index 9b9b7e9118d..ab1bfb9f301 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -1,5 +1,4 @@
 /*******************************************************************************
-* Copyright 2025 Intel Corporation
 * Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
 *
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index 39dd86a4d06..721c0c3d61a 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -1,5 +1,4 @@
 /*******************************************************************************
-* Copyright 2025 Intel Corporation
 * Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
 *
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index 7496d46b460..fffe7d34ab0 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -1,5 +1,4 @@
 /*******************************************************************************
-* Copyright 2025 Intel Corporation
 * Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
 *
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
index eee1db7671d..6508a3bd182 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -1,5 +1,4 @@
 /*******************************************************************************
-* Copyright 2025 Intel Corporation
 * Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
 *
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
index bb128870ae8..843d099d84f 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
@@ -1,5 +1,4 @@
 /*******************************************************************************
-* Copyright 2025 Intel Corporation
 * Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
 *
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
index 2ca64ac5b61..3fa3b83afe7 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
@@ -1,3 +1,20 @@
+/*******************************************************************************
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #pragma once
 
 #include <random>

From 44d96789cd31d0a903044f157c299e2f6b4ab085 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 18:50:29 +0200
Subject: [PATCH 34/69] update copyright notice and license information in
 frontier.hpp

---
 cpp/oneapi/dal/backend/primitives/frontier.hpp | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier.hpp
index 69fe3aab466..52adfcd2496 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier.hpp
@@ -1,3 +1,20 @@
+/*******************************************************************************
+* Copyright contributors to the oneDAL project
+* Copyright 2025 University of Salerno
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 #include "oneapi/dal/backend/primitives/frontier/advance.hpp"
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"

From 7bbaac7a30e5227fef8c70ceff9b5c5cfa0fa49c Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 19:11:39 +0200
Subject: [PATCH 35/69] =?UTF-8?q?frontier:=20refactor=20advance.hpp=20?=
 =?UTF-8?q?=E2=80=94=20use=20fixed-width=20integers=20and=20simplify=20fro?=
 =?UTF-8?q?ntier=5Fcontext=20API?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../backend/primitives/frontier/advance.hpp   | 74 ++++++++++---------
 1 file changed, 38 insertions(+), 36 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index 9a7e1cf18de..71d8c9e062d 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -27,9 +27,9 @@ namespace oneapi::dal::backend::primitives {
 /// It includes the group offset, coarsening factor, offsets size, and the SYCL
 /// nd_item for the current work item.
 struct frontier_context_state {
-    size_t group_offset;
-    const uint16_t coarsening_factor;
-    const uint32_t offsets_size;
+    std::uint64_t group_offset; // Offset of the current group being processed
+    const uint16_t coarsening_factor; // Number of integers a single work-group should handle
+    const uint32_t offsets_size; // Size of the offsets buffer array
     const sycl::nd_item<1> item;
 };
 
@@ -39,10 +39,12 @@ struct frontier_context_state {
 /// the context state, check if there are more elements to process, get the
 /// assigned element, check if a vertex is in the frontier, and insert a vertex
 /// into the output frontier.
+/// \tparam InFrontierDevT input frontier device view type. Inferred from the input frontier.
+/// \tparam OutFrontierDevT output frontier device view type. Inferred from the output frontier.
 template <typename InFrontierDevT, typename OutFrontierDevT>
 class frontier_context {
 public:
-    frontier_context(size_t limit, InFrontierDevT in_dev_frontier, OutFrontierDevT out_dev_frontier)
+    frontier_context(std::uint64_t limit, InFrontierDevT in_dev_frontier, OutFrontierDevT out_dev_frontier)
             : limit(limit),
               in_dev_frontier(in_dev_frontier),
               out_dev_frontier(out_dev_frontier) {}
@@ -56,39 +58,39 @@ class frontier_context {
         };
     }
 
-    /// This method checks if there are more elements to process in the current group.
+    /// checks if there are more elements to process in the current group.
     inline bool need_to_process(frontier_context_state& state) const {
         return (state.group_offset * state.coarsening_factor < state.offsets_size);
     }
 
-    /// This method completes the current iteration by updating the group offset.
+    /// completes the current iteration by updating the group offset.
     inline void complete_iteration(frontier_context_state& state) const {
         state.group_offset += state.item.get_group_range(0);
     }
 
-    /// This method retrieves the assigned element for the current work item.
+    /// retrieves the assigned element for the current work item.
     inline size_t get_assigned_element(const frontier_context_state& state) const {
         const uint16_t element_bitsize = in_dev_frontier.get_element_bitsize();
-        const uint32_t acutal_id_offset = (state.group_offset * state.coarsening_factor) +
+        const uint32_t actual_id_offset = (state.group_offset * state.coarsening_factor) +
                                           (state.item.get_local_linear_id() / element_bitsize);
+        ONEDAL_ASSERT(actual_id_offset < in_dev_frontier.get_offsets_size()[0]);
         const uint32_t* bitmap_offsets = in_dev_frontier.get_offsets();
-        ONEDAL_ASSERT(acutal_id_offset < in_dev_frontier.get_offsets_size()[0]);
-        const auto assigned_vertex = (bitmap_offsets[acutal_id_offset] * element_bitsize) +
+        const auto assigned_vertex = (bitmap_offsets[actual_id_offset] * element_bitsize) +
                                      (state.item.get_local_linear_id() % element_bitsize);
         return assigned_vertex;
     }
 
-    /// This method checks if a vertex is in the input frontier.
-    inline bool check(const frontier_context_state& state, size_t vertex) const {
+    /// checks if a vertex is in the input frontier.
+    inline bool check(std::uint64_t vertex) const {
         return vertex < limit && in_dev_frontier.check(vertex);
     }
 
-    /// This method inserts a vertex into the output frontier.
-    inline void insert(const frontier_context_state& state, size_t vertex) const {
+    /// inserts a vertex into the output frontier.
+    inline void insert(std::uint64_t vertex) const {
         out_dev_frontier.insert(vertex);
     }
 
-    size_t limit;
+    std::uint64_t limit;
     InFrontierDevT in_dev_frontier;
     OutFrontierDevT out_dev_frontier;
 };
@@ -100,12 +102,12 @@ struct BitmapKernel {
     /// This function distributes the workload among the workgroup, subgroup, and individual work items
     template <typename VertexT>
     inline void distribute_workload(frontier_context_state& state, const VertexT& vertex) const {
-        const size_t lid = state.item.get_local_linear_id();
+        const std::uint64_t lid = state.item.get_local_linear_id();
         const auto wgroup = state.item.get_group();
-        const size_t wgroup_size = wgroup.get_local_range(0);
+        const std::uint64_t wgroup_size = wgroup.get_local_range(0);
         const auto sgroup = state.item.get_sub_group();
         const auto sgroup_id = sgroup.get_group_id();
-        const size_t sgroup_size = sgroup.get_local_range()[0];
+        const std::uint64_t sgroup_size = sgroup.get_local_range()[0];
 
         if (sgroup.leader()) {
             subgroup_reduce_tail[sgroup_id] = 0;
@@ -120,7 +122,7 @@ struct BitmapKernel {
             wg_tail{ workgroup_reduce_tail[0] };
         const uint32_t offset = sgroup_id * sgroup_size;
 
-        if (context.check(state, vertex)) {
+        if (context.check(vertex)) {
             uint32_t n_edges = graph_dev.get_degree(vertex);
             // if the number of edges is large enough, we can assign the vertex to the workgroup
             if (n_edges >= wgroup_size * wgroup_size) {
@@ -149,12 +151,12 @@ struct BitmapKernel {
             wg_tail{ workgroup_reduce_tail[0] };
 
         const auto wgroup = state.item.get_group();
-        const size_t lid = state.item.get_local_linear_id();
-        const size_t wgroup_size = wgroup.get_local_range(0);
+        const std::uint64_t lid = state.item.get_local_linear_id();
+        const std::uint64_t wgroup_size = wgroup.get_local_range(0);
 
-        for (size_t i = 0; i < wg_tail.load(); i++) {
+        for (std::uint64_t i = 0; i < wg_tail.load(); i++) {
             auto vertex = workgroup_reduce[i];
-            size_t n_edges = n_edges_wg[i];
+            std::uint64_t n_edges = n_edges_wg[i];
             auto start = graph_dev.begin(vertex);
 
             for (auto j = lid; j < n_edges; j += wgroup_size) {
@@ -163,7 +165,7 @@ struct BitmapKernel {
                 auto weight = graph_dev.get_weight(edge);
                 auto neighbor = *n;
                 if (functor(vertex, neighbor, edge, weight)) {
-                    context.insert(state, neighbor);
+                    context.insert(neighbor);
                 }
             }
 
@@ -177,18 +179,18 @@ struct BitmapKernel {
     inline void process_subgroup_reduction(frontier_context_state& state) const {
         const auto sgroup = state.item.get_sub_group();
         const auto sgroup_id = sgroup.get_group_id();
-        const size_t sgroup_size = sgroup.get_local_range()[0];
-        const size_t llid = sgroup.get_local_linear_id();
+        const std::uint64_t sgroup_size = sgroup.get_local_range()[0];
+        const std::uint64_t llid = sgroup.get_local_linear_id();
         const uint32_t offset = sgroup_id * sgroup_size;
 
         sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::sub_group>
             sg_tail{ subgroup_reduce_tail[sgroup_id] };
 
-        for (size_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) {
+        for (std::uint64_t i = 0; i < subgroup_reduce_tail[sgroup_id]; i++) {
             // active_elements_tail[subgroup_id] is always less or equal than subgroup_size
-            size_t vertex_id = offset + i;
+            std::uint64_t vertex_id = offset + i;
             auto vertex = subgroup_reduce[vertex_id];
-            size_t n_edges = n_edges_sg[vertex_id];
+            std::uint64_t n_edges = n_edges_sg[vertex_id];
 
             auto start = graph_dev.begin(vertex);
 
@@ -198,7 +200,7 @@ struct BitmapKernel {
                 auto weight = graph_dev.get_weight(edge);
                 auto neighbor = *n;
                 if (functor(vertex, neighbor, edge, weight)) {
-                    context.insert(state, neighbor);
+                    context.insert(neighbor);
                 }
             }
 
@@ -212,7 +214,7 @@ struct BitmapKernel {
     template <typename VertexT>
     inline void process_workitem_reduction(frontier_context_state& state,
                                            const VertexT& vertex) const {
-        const size_t lid = state.item.get_local_linear_id();
+        const std::uint64_t lid = state.item.get_local_linear_id();
 
         if (!visited[lid]) {
             auto start = graph_dev.begin(vertex);
@@ -223,7 +225,7 @@ struct BitmapKernel {
                 auto weight = graph_dev.get_weight(edge);
                 auto neighbor = *n;
                 if (functor(vertex, neighbor, edge, weight)) {
-                    context.insert(state, neighbor);
+                    context.insert(neighbor);
                 }
             }
         }
@@ -284,18 +286,18 @@ sycl::event advance(const GraphT& graph,
 
     sycl::queue& q = graph.get_queue();
 
-    size_t num_nodes = graph.get_vertex_count();
+    std::uint64_t num_nodes = graph.get_vertex_count();
 
     auto in_dev_frontier = in.get_device_view();
     auto out_dev_frontier = out.get_device_view();
     auto graph_dev = graph.get_device_view();
 
     /// The coarsening factor represents the number of integers a single work-group should handle.
-    size_t coarsening_factor = 1; // it should be Compute Unit Size / num subgroups;
+    std::uint64_t coarsening_factor = 1; // it should be Compute Unit Size / num subgroups;
 
-    size_t element_bitsize = in_dev_frontier.get_element_bitsize(); // in bits
+    std::uint64_t element_bitsize = in_dev_frontier.get_element_bitsize(); // in bits
     sycl::range<1> local_range = { element_bitsize * coarsening_factor };
-    size_t global_size;
+    std::uint64_t global_size;
 
     sycl::event to_wait =
         in.compute_active_frontier(); // kernel launch to compute active bitmap regions

From 13673837f54ab4ebcd7b02bdaee43ba7b4eda41b Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 19:11:39 +0200
Subject: [PATCH 36/69] frontier: use std::uint64_t for sizes in bitset,
 frontier and frontier_dpc.cpp

---
 .../backend/primitives/frontier/bitset.hpp    |  4 +--
 .../backend/primitives/frontier/frontier.hpp  | 26 +++++++++----------
 .../primitives/frontier/frontier_dpc.cpp      | 16 ++++++------
 3 files changed, 23 insertions(+), 23 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index f14fa7a2887..b55a64a8515 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -28,7 +28,7 @@ template <typename ElementType = std::uint32_t>
 class bitset {
 public:
     using element_t = ElementType;
-    static constexpr size_t element_bitsize = sizeof(element_t) * 8; // Number of bits in an element
+    static constexpr std::uint64_t element_bitsize = sizeof(element_t) * 8; // Number of bits in an element
 
     bitset(element_t* data) : _data(data) {}
 
@@ -98,7 +98,7 @@ class bitset {
     }
 
     /// override operator []
-    inline element_t& operator[](std::size_t index) {
+    inline element_t& operator[](std::uint64_t index) {
         return _data[index];
     }
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index 88bbbfd5931..4468371a09f 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -29,14 +29,14 @@ template <typename ElementType>
 class frontier_view {
 public:
     using bitmap_t = ElementType;
-    static constexpr std::size_t divide_factor = bitset<bitmap_t>::element_bitsize;
+    static constexpr std::uint64_t divide_factor = bitset<bitmap_t>::element_bitsize;
 
     frontier_view() = default;
-    frontier_view(bitmap_t* data_layer,
-                  bitmap_t* mlb_layer,
-                  std::uint32_t* offsets,
-                  std::uint32_t* offsets_size,
-                  size_t num_items)
+    frontier_view(bitmap_t* data_layer, // First layer (tracks vertices in the frontier)
+                  bitmap_t* mlb_layer, // Second layer (to track non-zero elements in the first layer)
+                  std::uint32_t* offsets, // Array to store the indices of the non-zero elements
+                  std::uint32_t* offsets_size, // Pointer to store the size of the offsets array
+                  std::uint64_t num_items) // Maximum number of items that can be stored in the frontier
             : _num_items(num_items),
               _data_layer(bitset<bitmap_t>{ data_layer }),
               _mlb_layer(bitset<bitmap_t>{ mlb_layer }),
@@ -60,7 +60,7 @@ class frontier_view {
         return _data_layer.atomic_test(idx);
     }
 
-    inline size_t get_element_bitsize() const {
+    inline std::uint64_t get_element_bitsize() const {
         return bitset<bitmap_t>::element_bitsize;
     }
 
@@ -73,7 +73,7 @@ class frontier_view {
     }
 
 private:
-    size_t _num_items;
+    std::uint64_t _num_items;
 
     bitset<bitmap_t> _data_layer;
     bitset<bitmap_t> _mlb_layer;
@@ -89,7 +89,7 @@ class frontier {
 
 public:
     frontier(sycl::queue& queue,
-             std::size_t num_items,
+             std::uint64_t num_items,
              sycl::usm::alloc alloc = sycl::usm::alloc::shared);
 
     const frontier_view<ElementType> get_device_view() const {
@@ -100,7 +100,7 @@ class frontier {
                  _mlb_layer.get_mutable_data(),
                  offsets_pointer,
                  offsets_size_pointer,
-                 static_cast<std::size_t>(_data_layer.get_count()) };
+                 static_cast<std::uint64_t>(_data_layer.get_count()) };
     }
 
     inline ndview<ElementType, 1> get_data() const {
@@ -144,14 +144,14 @@ class frontier {
 
 private:
     sycl::queue& _queue;
-    size_t _num_items;
+    std::uint64_t _num_items;
 
     ndarray<ElementType, 1> _data_layer;
     ndarray<ElementType, 1> _mlb_layer;
     ndarray<std::uint32_t, 1> _offsets;
     ndarray<buffer_t, 1> _buffer;
-    const size_t _TMP_VAR = 0;
-    const size_t _CAF_FLAG = 1; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
+    const std::uint64_t _TMP_VAR = 0;
+    const std::uint64_t _CAF_FLAG = 1; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
 };
 
 template <typename ElementType>
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index ab1bfb9f301..0cae68f326e 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -22,7 +22,7 @@ namespace oneapi::dal::backend::primitives {
 #ifdef ONEDAL_DATA_PARALLEL
 
 template <typename ElementType>
-frontier<ElementType>::frontier(sycl::queue& queue, std::size_t num_items, sycl::usm::alloc alloc)
+frontier<ElementType>::frontier(sycl::queue& queue, std::uint64_t num_items, sycl::usm::alloc alloc)
         : _queue(queue),
           _num_items(num_items) {
     std::int64_t array_size = (num_items + bitset<ElementType>::element_bitsize - 1) /
@@ -105,9 +105,9 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
     auto offsets_pointer = _offsets.get_mutable_data() + 1;
 
     const uint32_t element_bitsize = bitmap.get_element_bitsize();
-    const size_t local_range = 256; // propose_wg_size(this->_queue);
-    const size_t mlb_count = _mlb_layer.get_count();
-    const size_t global_range = (mlb_count % local_range == 0)
+    const std::uint64_t local_range = 256; // propose_wg_size(this->_queue);
+    const std::uint64_t mlb_count = _mlb_layer.get_count();
+    const std::uint64_t global_range = (mlb_count % local_range == 0)
                                     ? mlb_count
                                     : (mlb_count + local_range - (mlb_count % local_range));
 
@@ -145,7 +145,7 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
                                      offsets_size_ref{ offsets_size[0] };
 
                                  ElementType data = data_layer[idx];
-                                 for (size_t i = 0; i < element_bitsize; i++) {
+                                 for (std::uint64_t i = 0; i < element_bitsize; i++) {
                                      if (data & (static_cast<ElementType>(1) << i)) {
                                          offsets[offsets_size_ref++] = i + idx * element_bitsize;
                                      }
@@ -185,7 +185,7 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
                     for (uint32_t gid = item.get_global_linear_id(); gid < size;
                          gid += item.get_global_range(0)) {
                         ElementType data = data_layer[gid];
-                        for (size_t i = 0; i < element_bitsize; i++) {
+                        for (std::uint64_t i = 0; i < element_bitsize; i++) {
                             if (data & (static_cast<ElementType>(1) << i)) {
                                 local_offsets[local_size_ref++] = i + gid * element_bitsize;
                             }
@@ -194,12 +194,12 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
 
                     sycl::group_barrier(group);
 
-                    size_t data_offset = 0;
+                    std::uint64_t data_offset = 0;
                     if (group.leader()) {
                         data_offset = offsets_size_ref.fetch_add(local_size_ref.load());
                     }
                     data_offset = sycl::group_broadcast(group, data_offset, 0);
-                    for (size_t i = item.get_local_linear_id(); i < local_size_ref.load();
+                    for (std::uint64_t i = item.get_local_linear_id(); i < local_size_ref.load();
                          i += item.get_local_range(0)) {
                         offsets[data_offset + i] = local_offsets[i];
                     }

From 7b39e37d17a6a053f4db4722e0ed84d0f303b128 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 19:11:39 +0200
Subject: [PATCH 37/69] graph: use std::uint64_t for number of nodes in
 csr_graph_view

---
 cpp/oneapi/dal/backend/primitives/frontier/graph.hpp | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index 721c0c3d61a..78208029312 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -70,7 +70,7 @@ class csr_graph_view {
     };
 
 public:
-    csr_graph_view(std::size_t num_nodes, vertex_t* row_ptr, edge_t* col_indices, weight_t* weights)
+    csr_graph_view(std::uint64_t num_nodes, vertex_t* row_ptr, edge_t* col_indices, weight_t* weights)
             : _num_nodes(num_nodes),
               _row_ptr(row_ptr),
               _col_indices(col_indices),
@@ -100,7 +100,7 @@ class csr_graph_view {
     }
 
 private:
-    std::size_t _num_nodes;
+    std::uint64_t _num_nodes;
     vertex_t* _row_ptr;
     edge_t* _col_indices;
     weight_t* _weights;
@@ -162,13 +162,13 @@ class csr_graph {
         return _queue;
     }
 
-    std::size_t get_vertex_count() const {
+    std::uint64_t get_vertex_count() const {
         return _num_nodes;
     }
 
 private:
     sycl::queue& _queue;
-    std::size_t _num_nodes;
+    std::uint64_t _num_nodes;
     ndarray<vertex_t, 1> _row_ptr;
     ndarray<edge_t, 1> _col_indices;
     ndarray<weight_t, 1> _weights;

From 12c499768998f069f81392a4a50580643d113edf Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 19:11:39 +0200
Subject: [PATCH 38/69] tests: adapt frontier and BFS tests to use
 std::uint64_t for counts and loops

---
 .../primitives/frontier/test/advance_dpc.cpp  | 20 +++++++++----------
 .../primitives/frontier/test/bfs_dpc.cpp      |  8 ++++----
 .../primitives/frontier/test/frontier_dpc.cpp | 10 +++++-----
 .../primitives/frontier/test/utils.hpp        |  6 +++---
 4 files changed, 22 insertions(+), 22 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index fffe7d34ab0..89681e8c6c2 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -27,10 +27,10 @@ namespace oneapi::dal::backend::primitives::test {
 namespace pr = dal::backend::primitives;
 
 template <typename T>
-void print_frontier(const T* data, size_t count, size_t num_items) {
-    size_t element_bitsize = sizeof(T) * 8;
-    for (size_t i = 0; i < count; ++i) {
-        for (size_t j = 0; j < element_bitsize; ++j) {
+void print_frontier(const T* data, std::uint64_t count, std::uint64_t num_items) {
+    std::uint64_t element_bitsize = sizeof(T) * 8;
+    for (std::uint64_t i = 0; i < count; ++i) {
+        for (std::uint64_t j = 0; j < element_bitsize; ++j) {
             std::cout << ((data[i] & (static_cast<T>(1) << j)) ? "1" : "0");
         }
     }
@@ -41,14 +41,14 @@ std::vector<bool> compute_next_frontier(const std::vector<std::uint32_t>& row_pt
                                         const std::vector<bool>& frontier) {
     std::vector<bool> next_frontier(frontier.size(), false);
 
-    for (size_t node = 0; node < frontier.size(); ++node) {
+    for (std::uint64_t node = 0; node < frontier.size(); ++node) {
         if (!frontier[node])
             continue;
 
         auto start = row_ptr[node];
         auto end = row_ptr[node + 1];
 
-        for (size_t i = start; i < end; ++i) {
+        for (std::uint64_t i = start; i < end; ++i) {
             auto neighbor = col_indices[i];
             next_frontier[neighbor] = true;
         }
@@ -59,8 +59,8 @@ std::vector<bool> compute_next_frontier(const std::vector<std::uint32_t>& row_pt
 template <typename T>
 void compare_frontiers(T& device_frontier,
                        const std::vector<bool>& host_frontier,
-                       size_t num_nodes) {
-    for (size_t i = 0; i < num_nodes; ++i) {
+                       std::uint64_t num_nodes) {
+    for (std::uint64_t i = 0; i < num_nodes; ++i) {
         bool tmpd = device_frontier.check(i);
         bool tmph = host_frontier[i];
         if (tmpd != tmph) {
@@ -78,7 +78,7 @@ TEST("test advance operation", "[advance]") {
 
     const std::uint32_t seed = GENERATE(42u, 313u, 2025u);
     const double edge_probability = GENERATE(0.05, 0.1, 0.2);
-    const std::size_t num_nodes = GENERATE(128, 512, 1024);
+    const std::uint64_t num_nodes = GENERATE(128, 512, 1024);
 
     const auto graph_data = generate_random_graph(num_nodes, edge_probability, seed);
     auto graph =
@@ -92,7 +92,7 @@ TEST("test advance operation", "[advance]") {
     std::mt19937 frontier_rng(seed ^ 0x9e3779b9u);
     std::bernoulli_distribution frontier_dist(0.1);
 
-    for (std::size_t vertex = 0; vertex < num_nodes; ++vertex) {
+    for (std::uint64_t vertex = 0; vertex < num_nodes; ++vertex) {
         if (frontier_dist(frontier_rng)) {
             in_frontier.insert(static_cast<std::uint32_t>(vertex));
             host_frontier[vertex] = true;
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
index 6508a3bd182..49ca07095ad 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -41,7 +41,7 @@ std::vector<std::uint32_t> host_bfs(const std::vector<T>& row_offsets,
         T node = q.front();
         q.pop();
 
-        for (size_t i = row_offsets[node]; i < row_offsets[node + 1]; ++i) {
+        for (std::uint64_t i = row_offsets[node]; i < row_offsets[node + 1]; ++i) {
             auto neighbor = col_indices[i];
             if (distances[neighbor] == std::numeric_limits<std::uint32_t>::max()) {
                 distances[neighbor] = distances[node] + 1;
@@ -59,7 +59,7 @@ TEST("test BFS", "[bfs]") {
 
     const std::uint32_t seed = GENERATE(42u, 313u, 2025u);
     const double edge_probability = GENERATE(0.05, 0.1, 0.2);
-    const std::size_t num_nodes = GENERATE(128, 512, 1024);
+    const std::uint64_t num_nodes = GENERATE(128, 512, 1024);
 
     const auto graph_data = generate_random_graph(num_nodes, edge_probability, seed);
     auto graph =
@@ -83,7 +83,7 @@ TEST("test BFS", "[bfs]") {
         .wait_and_throw();
 
     in_frontier.insert(src);
-    size_t iter = 0;
+    std::uint64_t iter = 0;
 
     /// Start BFS
     while (!in_frontier.empty()) {
@@ -107,7 +107,7 @@ TEST("test BFS", "[bfs]") {
     auto expected_distances =
         host_bfs<std::uint32_t>(graph_data.row_ptr, graph_data.col_indices, src);
     auto actual_distances = distance.to_host(queue).get_data();
-    for (size_t i = 0; i < num_nodes; ++i) {
+    for (std::uint64_t i = 0; i < num_nodes; ++i) {
         REQUIRE(actual_distances[i] == expected_distances[i]);
     }
 } // TEST "test advance operation"
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
index 843d099d84f..3abce2a0b09 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
@@ -24,10 +24,10 @@ namespace oneapi::dal::backend::primitives::test {
 namespace pr = dal::backend::primitives;
 
 template <typename T>
-void print_frontier(const T* data, size_t count, size_t num_items) {
-    size_t element_bitsize = sizeof(T) * 8;
-    for (size_t i = 0; i < count; ++i) {
-        for (size_t j = 0; j < element_bitsize; ++j) {
+void print_frontier(const T* data, std::uint64_t count, std::uint64_t num_items) {
+    std::uint64_t element_bitsize = sizeof(T) * 8;
+    for (std::uint64_t i = 0; i < count; ++i) {
+        for (std::uint64_t j = 0; j < element_bitsize; ++j) {
             std::cout << ((data[i] & (static_cast<T>(1) << j)) ? "1" : "0");
         }
     }
@@ -38,7 +38,7 @@ TEST("frontier queue basic operations", "[frontier]") {
     auto& queue = policy.get_queue();
     print_device_name(queue);
 
-    const std::size_t num_items = 100;
+    const std::uint64_t num_items = 100;
     auto f = pr::frontier<std::uint32_t>(queue, num_items, sycl::usm::alloc::shared);
 
     REQUIRE(f.empty() == true);
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
index 3fa3b83afe7..1d822aec69b 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
@@ -33,7 +33,7 @@ struct csr_graph_data {
     std::vector<std::uint32_t> weights;
 };
 
-csr_graph_data generate_random_graph(std::size_t vertex_count,
+csr_graph_data generate_random_graph(std::uint64_t vertex_count,
                                      double edge_probability,
                                      std::uint32_t seed) {
     if (vertex_count == 0) {
@@ -50,9 +50,9 @@ csr_graph_data generate_random_graph(std::size_t vertex_count,
     std::vector<std::uint32_t> col_indices;
     col_indices.reserve(vertex_count);
 
-    for (std::size_t src = 0; src < vertex_count; ++src) {
+    for (std::uint64_t src = 0; src < vertex_count; ++src) {
         const auto edges_before = col_indices.size();
-        for (std::size_t dst = 0; dst < vertex_count; ++dst) {
+        for (std::uint64_t dst = 0; dst < vertex_count; ++dst) {
             if (src == dst) {
                 continue;
             }

From a85aa7ebe2f0a114974a8aa4a6c62bd9f2b01e59 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 19:29:23 +0200
Subject: [PATCH 39/69] frontier: add element count to bitset constructor and
 store size

---
 cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index b55a64a8515..72d888c5642 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -30,7 +30,7 @@ class bitset {
     using element_t = ElementType;
     static constexpr std::uint64_t element_bitsize = sizeof(element_t) * 8; // Number of bits in an element
 
-    bitset(element_t* data) : _data(data) {}
+    bitset(element_t* data, const size_t num_items) : _data(data), _num_items(num_items) {}
 
     /// Sets the bit at the specified index to 1.
     inline void set(std::uint32_t index) const {
@@ -104,6 +104,7 @@ class bitset {
 
 private:
     element_t* _data;
+    std::uint64_t _num_items;
 };
 
 } // namespace oneapi::dal::backend::primitives

From 838e25a9e34584e9f9bc659ad2aac7c3ce6cc62f Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 19:29:23 +0200
Subject: [PATCH 40/69] frontier: propagate sizes and add docs and swap helper

---
 cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index 4468371a09f..b9f966c4972 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -25,6 +25,7 @@
 namespace oneapi::dal::backend::primitives {
 
 /// @brief A view of a frontier that provides an interface for the kernel to interact with the frontier data structure.
+/// \tparam ElementType the type of the elements in the frontier (e.g., std::uint32_t).
 template <typename ElementType>
 class frontier_view {
 public:
@@ -38,8 +39,8 @@ class frontier_view {
                   std::uint32_t* offsets_size, // Pointer to store the size of the offsets array
                   std::uint64_t num_items) // Maximum number of items that can be stored in the frontier
             : _num_items(num_items),
-              _data_layer(bitset<bitmap_t>{ data_layer }),
-              _mlb_layer(bitset<bitmap_t>{ mlb_layer }),
+              _data_layer(bitset<bitmap_t>{ data_layer, num_items }), // first layer size is num_items
+              _mlb_layer(bitset<bitmap_t>{ mlb_layer, num_items / divide_factor }), // second layer size is (num_items / divide_factor) because each bit in the second layer represents an element in the first layer
               _offsets(offsets),
               _offsets_size(offsets_size) {}
 
@@ -83,6 +84,7 @@ class frontier_view {
 };
 
 /// @brief The Two-Layer bitmap frontier class
+/// \tparam ElementType the type that describes the bitmap integers type (e.g., std::uint32_t).
 template <typename ElementType>
 class frontier {
     using buffer_t = std::uint32_t;
@@ -154,6 +156,8 @@ class frontier {
     const std::uint64_t _CAF_FLAG = 1; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
 };
 
+/// Swaps the contents of two frontiers.
+/// \tparam ElementType the type that describes the bitmap integers type (e.g., std::uint32_t). Inferred from the frontier.
 template <typename ElementType>
 void swap_frontiers(frontier<ElementType>& f1, frontier<ElementType>& f2) {
     frontier<ElementType>::swap(f1, f2);

From 5a7ee624d5620f7ad07e6cb09d87bbb5bb7fe112 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 19:29:23 +0200
Subject: [PATCH 41/69] frontier: remove unnecessary bitset include from graph
 header

---
 cpp/oneapi/dal/backend/primitives/frontier/graph.hpp | 1 -
 1 file changed, 1 deletion(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index 78208029312..43e1e5b839c 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -20,7 +20,6 @@
 #include "oneapi/dal/common.hpp"
 #include "oneapi/dal/graph/detail/common.hpp"
 #include "oneapi/dal/graph/detail/container.hpp"
-#include "oneapi/dal/backend/primitives/frontier/bitset.hpp"
 #include "oneapi/dal/backend/primitives/ndarray.hpp"
 
 namespace oneapi::dal::backend::primitives {

From 5088c49161efc976ca56c0d00fc6074c4b51590f Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 19:29:23 +0200
Subject: [PATCH 42/69] frontier/advance: rename kernel, tighten types, and
 polish docs/formatting

---
 .../backend/primitives/frontier/advance.hpp   | 95 +++++++------------
 1 file changed, 34 insertions(+), 61 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index 71d8c9e062d..acc6b852d42 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -58,18 +58,18 @@ class frontier_context {
         };
     }
 
-    /// checks if there are more elements to process in the current group.
+    /// Checks if there are more elements to process in the current group.
     inline bool need_to_process(frontier_context_state& state) const {
         return (state.group_offset * state.coarsening_factor < state.offsets_size);
     }
 
-    /// completes the current iteration by updating the group offset.
+    /// Completes the current iteration by updating the group offset.
     inline void complete_iteration(frontier_context_state& state) const {
         state.group_offset += state.item.get_group_range(0);
     }
 
-    /// retrieves the assigned element for the current work item.
-    inline size_t get_assigned_element(const frontier_context_state& state) const {
+    /// Retrieves the assigned element for the current work item.
+    inline std::uint64_t get_assigned_element(const frontier_context_state& state) const {
         const uint16_t element_bitsize = in_dev_frontier.get_element_bitsize();
         const uint32_t actual_id_offset = (state.group_offset * state.coarsening_factor) +
                                           (state.item.get_local_linear_id() / element_bitsize);
@@ -80,12 +80,12 @@ class frontier_context {
         return assigned_vertex;
     }
 
-    /// checks if a vertex is in the input frontier.
+    /// Checks if a vertex is in the input frontier.
     inline bool check(std::uint64_t vertex) const {
         return vertex < limit && in_dev_frontier.check(vertex);
     }
 
-    /// inserts a vertex into the output frontier.
+    /// Inserts a vertex into the output frontier.
     inline void insert(std::uint64_t vertex) const {
         out_dev_frontier.insert(vertex);
     }
@@ -95,11 +95,15 @@ class frontier_context {
     OutFrontierDevT out_dev_frontier;
 };
 
-/// BitmapKernel is a template struct that defines the kernel to be executed on the device.
+/// bitmap_kernel is a template struct that defines the kernel to be executed on the device.
 /// It processes the input frontier and advances it based on the provided functor.
+/// \tparam T the type of the elements in the frontier (e.g., std::uint32_t).
+/// \tparam ContextT the type of the frontier context. Inferred from the frontier_context.
+/// \tparam GraphDevT the type of the graph device view. Inferred from the graph.
+/// \tparam LambdaT the type of the functor to be applied to each edge.
 template <typename T, typename ContextT, typename GraphDevT, typename LambdaT>
-struct BitmapKernel {
-    /// This function distributes the workload among the workgroup, subgroup, and individual work items
+struct bitmap_kernel {
+    /// Distributes the workload among the workgroup, subgroup, and individual work items
     template <typename VertexT>
     inline void distribute_workload(frontier_context_state& state, const VertexT& vertex) const {
         const std::uint64_t lid = state.item.get_local_linear_id();
@@ -144,9 +148,8 @@ struct BitmapKernel {
         }
     }
 
-    /// This function processes the vertices assigned to the workgroup.
+    /// Processes the vertices assigned to the workgroup.
     inline void process_workgroup_reduction(frontier_context_state& state) const {
-        /// This function processes the vertices assigned to the workgroup.
         sycl::atomic_ref<uint32_t, sycl::memory_order::relaxed, sycl::memory_scope::work_group>
             wg_tail{ workgroup_reduce_tail[0] };
 
@@ -175,7 +178,7 @@ struct BitmapKernel {
         }
     }
 
-    /// This function processes the vertices assigned to the subgroup.
+    /// Processes the vertices assigned to the subgroup.
     inline void process_subgroup_reduction(frontier_context_state& state) const {
         const auto sgroup = state.item.get_sub_group();
         const auto sgroup_id = sgroup.get_group_id();
@@ -210,7 +213,8 @@ struct BitmapKernel {
         }
     }
 
-    /// This function processes the vertices that were not assigned to the workgroup or subgroup.
+    /// Processes the vertices that were not assigned to the workgroup or subgroup.
+    /// \tparam VertexT the type of the vertex. Inferred from the graph.
     template <typename VertexT>
     inline void process_workitem_reduction(frontier_context_state& state,
                                            const VertexT& vertex) const {
@@ -231,6 +235,7 @@ struct BitmapKernel {
         }
     }
 
+    /// The main operator that executes the kernel logic.
     void operator()(sycl::nd_item<1> item) const {
         auto state = context.init(item);
         const auto wgroup = item.get_group();
@@ -272,11 +277,12 @@ struct BitmapKernel {
     const LambdaT functor;
 };
 
-/// advance is a function that launches the BitmapKernel on the device to advance the frontier.
+/// Advance is a function that launches the bitmap_kernel on the device to advance the frontier.
 /// It takes the graph, input frontier, output frontier, and the functor.
-/// The expected_size parameter is used to specify the expected size of the input frontier, in order
-/// to optimize the kernel launch parameters. If expected_size is zero, a default size is used.
 /// It returns a sycl::event that can be used to synchronize the execution.
+/// \tparam FrontierSizeT the type of the elements in the frontier (e.g., std::uint32_t).
+/// \tparam GraphT the type of the graph. Inferred from the csr_graph.
+/// \tparam LambdaT the type of the functor to be applied to each edge.
 template <typename FrontierSizeT, typename GraphT, typename LambdaT>
 sycl::event advance(const GraphT& graph,
                     frontier<FrontierSizeT>& in,
@@ -315,56 +321,23 @@ sycl::event advance(const GraphT& graph,
         out_dev_frontier
     };
     using bitmap_kernel_t =
-        BitmapKernel<element_t, decltype(context), decltype(graph_dev), LambdaT>;
+        bitmap_kernel<element_t, decltype(context), decltype(graph_dev), LambdaT>;
 
     const uint32_t max_num_subgroups = device_max_sg_count(q);
 
     auto e = q.submit([&](sycl::handler& cgh) {
         cgh.depends_on(to_wait);
-        sycl::local_accessor<uint32_t, 1> n_edges_wg{
-            local_range,
-            cgh
-        }; // number of edges of vertices to process at work-group granularity
-        sycl::local_accessor<uint32_t, 1> n_edges_sg{
-            local_range,
-            cgh
-        }; // number of edges of vertices to process at sub-group granularity
-        sycl::local_accessor<bool, 1> visited{
-            local_range,
-            cgh
-        }; // tracks the vertices already visited at work-group and sub-group granularity
-        sycl::local_accessor<element_t, 1> subgroup_reduce{
-            local_range,
-            cgh
-        }; // stores the vertices to process at sub-group granularity
-        sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail{
-            max_num_subgroups,
-            cgh
-        }; // stores the tail of the subgroup reduction
-        sycl::local_accessor<uint32_t, 1> subgroup_ids{
-            local_range,
-            cgh
-        }; // stores the thread id that found the vertex to process at sub-group level
-        sycl::local_accessor<element_t, 1> workgroup_reduce{
-            local_range,
-            cgh
-        }; // stores the vertices to process at work-group granularity
-        sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail{
-            1,
-            cgh
-        }; // stores the tail of the work-group reduction
-        sycl::local_accessor<uint32_t, 1> workgroup_ids{
-            local_range,
-            cgh
-        }; // stores the thread id that found the vertex to process at work-group level
-        sycl::local_accessor<element_t, 1> individual_reduce{
-            local_range,
-            cgh
-        }; // stores the vertices to process at individual thread granularity
-        sycl::local_accessor<uint32_t, 1> individual_reduce_tail{
-            1,
-            cgh
-        }; // stores the tail of the individual thread reduction
+        sycl::local_accessor<uint32_t, 1> n_edges_wg{local_range, cgh}; // number of edges of vertices to process at work-group granularity
+        sycl::local_accessor<uint32_t, 1> n_edges_sg{local_range, cgh}; // number of edges of vertices to process at sub-group granularity
+        sycl::local_accessor<bool, 1> visited{local_range, cgh}; // tracks the vertices already visited at work-group and sub-group granularity
+        sycl::local_accessor<element_t, 1> subgroup_reduce{local_range, cgh}; // stores the vertices to process at sub-group granularity
+        sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail{max_num_subgroups, cgh}; // stores the tail of the subgroup reduction
+        sycl::local_accessor<uint32_t, 1> subgroup_ids{local_range, cgh}; // stores the thread id that found the vertex to process at sub-group level
+        sycl::local_accessor<element_t, 1> workgroup_reduce{local_range, cgh}; // stores the vertices to process at work-group granularity
+        sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail{1, cgh}; // stores the tail of the work-group reduction
+        sycl::local_accessor<uint32_t, 1> workgroup_ids{local_range, cgh}; // stores the thread id that found the vertex to process at work-group level
+        sycl::local_accessor<element_t, 1> individual_reduce{local_range, cgh}; // stores the vertices to process at individual thread granularity
+        sycl::local_accessor<uint32_t, 1> individual_reduce_tail{1, cgh}; // stores the tail of the individual thread reduction
 
         cgh.parallel_for(sycl::nd_range<1>{ global_range, local_range },
                          bitmap_kernel_t{ context,

From daf56a1f865304b07f610115a076bb85a8301337 Mon Sep 17 00:00:00 2001
From: Antonio De Caro <antonio.decaro99@outlook.it>
Date: Wed, 15 Oct 2025 19:39:22 +0200
Subject: [PATCH 43/69] refactor: improve bitset layer size calculation for
 frontier initialization

---
 .../dal/backend/primitives/frontier/bitset.hpp  | 17 +++++++++++++----
 .../backend/primitives/frontier/frontier.hpp    |  2 +-
 2 files changed, 14 insertions(+), 5 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index 72d888c5642..6f54bcad949 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -21,21 +21,24 @@
 
 namespace oneapi::dal::backend::primitives {
 
-/**
- * @brief A bitset class that provides a set of operations on a bitset.
- */
+/// A bitset class that provides a set of operations on a bitset implemented using an array of integers.
+/// \tparam ElementType the type of the elements in the bitset (e.g., std::uint32_t).
 template <typename ElementType = std::uint32_t>
 class bitset {
 public:
     using element_t = ElementType;
     static constexpr std::uint64_t element_bitsize = sizeof(element_t) * 8; // Number of bits in an element
 
-    bitset(element_t* data, const size_t num_items) : _data(data), _num_items(num_items) {}
+    /// Constructs a bitset with the given data pointer and number of items.
+    /// \param data pointer to the underlying data.
+    /// \param num_items number of items in the bitset.
+    bitset(element_t* data, const size_t num_items) : _data(data), _num_items((num_items + element_bitsize - 1) / element_bitsize) {}
 
     /// Sets the bit at the specified index to 1.
     inline void set(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+        ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
         _data[element_index] |= (element_t(1) << bit_index);
     }
 
@@ -43,6 +46,7 @@ class bitset {
     inline void unset(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+        ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
         _data[element_index] &= ~(element_t(1) << bit_index);
     }
 
@@ -50,6 +54,7 @@ class bitset {
     inline bool test(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+        ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
         return (_data[element_index] & (element_t(1) << bit_index)) != 0;
     }
 
@@ -59,6 +64,7 @@ class bitset {
     inline void atomic_set(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+        ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
         sycl::atomic_ref<element_t, mem_order, mem_scope> atomic_element(_data[element_index]);
         atomic_element |= (element_t(1) << bit_index);
     }
@@ -69,6 +75,7 @@ class bitset {
     inline void atomic_unset(std::uint32_t index) {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+        ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
         sycl::atomic_ref<element_t, mem_order, mem_scope> atomic_element(_data[element_index]);
         atomic_element &= ~(element_t(1) << bit_index);
     }
@@ -79,6 +86,7 @@ class bitset {
     inline bool atomic_test(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+        ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
         sycl::atomic_ref<element_t, mem_order, mem_scope> atomic_element(_data[element_index]);
         return (atomic_element.load() & (element_t(1) << bit_index)) != 0;
     }
@@ -99,6 +107,7 @@ class bitset {
 
     /// override operator []
     inline element_t& operator[](std::uint64_t index) {
+        ONEDAL_ASSERT(index < _num_items, "Index out of bounds");
         return _data[index];
     }
 
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index b9f966c4972..47b6235d969 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -40,7 +40,7 @@ class frontier_view {
                   std::uint64_t num_items) // Maximum number of items that can be stored in the frontier
             : _num_items(num_items),
               _data_layer(bitset<bitmap_t>{ data_layer, num_items }), // first layer size is num_items
-              _mlb_layer(bitset<bitmap_t>{ mlb_layer, num_items / divide_factor }), // second layer size is (num_items / divide_factor) because each bit in the second layer represents an element in the first layer
+              _mlb_layer(bitset<bitmap_t>{ mlb_layer, (num_items + divide_factor - 1) / divide_factor }), // second layer size is ceil(num_items / divide_factor) because each bit in the second layer represents an element in the first layer
               _offsets(offsets),
               _offsets_size(offsets_size) {}
 

From 53b9f79b82e917f5bff4690dfff4f45b286ec4b8 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Fri, 16 Jan 2026 10:12:03 -0800
Subject: [PATCH 44/69] clang-format fix

---
 .../backend/primitives/frontier/advance.hpp   | 59 +++++++++++++++----
 .../backend/primitives/frontier/bitset.hpp    |  7 ++-
 .../backend/primitives/frontier/frontier.hpp  | 22 ++++---
 .../primitives/frontier/frontier_dpc.cpp      |  4 +-
 .../dal/backend/primitives/frontier/graph.hpp |  5 +-
 5 files changed, 72 insertions(+), 25 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index acc6b852d42..e1168364956 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -44,7 +44,9 @@ struct frontier_context_state {
 template <typename InFrontierDevT, typename OutFrontierDevT>
 class frontier_context {
 public:
-    frontier_context(std::uint64_t limit, InFrontierDevT in_dev_frontier, OutFrontierDevT out_dev_frontier)
+    frontier_context(std::uint64_t limit,
+                     InFrontierDevT in_dev_frontier,
+                     OutFrontierDevT out_dev_frontier)
             : limit(limit),
               in_dev_frontier(in_dev_frontier),
               out_dev_frontier(out_dev_frontier) {}
@@ -327,17 +329,50 @@ sycl::event advance(const GraphT& graph,
 
     auto e = q.submit([&](sycl::handler& cgh) {
         cgh.depends_on(to_wait);
-        sycl::local_accessor<uint32_t, 1> n_edges_wg{local_range, cgh}; // number of edges of vertices to process at work-group granularity
-        sycl::local_accessor<uint32_t, 1> n_edges_sg{local_range, cgh}; // number of edges of vertices to process at sub-group granularity
-        sycl::local_accessor<bool, 1> visited{local_range, cgh}; // tracks the vertices already visited at work-group and sub-group granularity
-        sycl::local_accessor<element_t, 1> subgroup_reduce{local_range, cgh}; // stores the vertices to process at sub-group granularity
-        sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail{max_num_subgroups, cgh}; // stores the tail of the subgroup reduction
-        sycl::local_accessor<uint32_t, 1> subgroup_ids{local_range, cgh}; // stores the thread id that found the vertex to process at sub-group level
-        sycl::local_accessor<element_t, 1> workgroup_reduce{local_range, cgh}; // stores the vertices to process at work-group granularity
-        sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail{1, cgh}; // stores the tail of the work-group reduction
-        sycl::local_accessor<uint32_t, 1> workgroup_ids{local_range, cgh}; // stores the thread id that found the vertex to process at work-group level
-        sycl::local_accessor<element_t, 1> individual_reduce{local_range, cgh}; // stores the vertices to process at individual thread granularity
-        sycl::local_accessor<uint32_t, 1> individual_reduce_tail{1, cgh}; // stores the tail of the individual thread reduction
+        sycl::local_accessor<uint32_t, 1> n_edges_wg{
+            local_range,
+            cgh
+        }; // number of edges of vertices to process at work-group granularity
+        sycl::local_accessor<uint32_t, 1> n_edges_sg{
+            local_range,
+            cgh
+        }; // number of edges of vertices to process at sub-group granularity
+        sycl::local_accessor<bool, 1> visited{
+            local_range,
+            cgh
+        }; // tracks the vertices already visited at work-group and sub-group granularity
+        sycl::local_accessor<element_t, 1> subgroup_reduce{
+            local_range,
+            cgh
+        }; // stores the vertices to process at sub-group granularity
+        sycl::local_accessor<uint32_t, 1> subgroup_reduce_tail{
+            max_num_subgroups,
+            cgh
+        }; // stores the tail of the subgroup reduction
+        sycl::local_accessor<uint32_t, 1> subgroup_ids{
+            local_range,
+            cgh
+        }; // stores the thread id that found the vertex to process at sub-group level
+        sycl::local_accessor<element_t, 1> workgroup_reduce{
+            local_range,
+            cgh
+        }; // stores the vertices to process at work-group granularity
+        sycl::local_accessor<uint32_t, 1> workgroup_reduce_tail{
+            1,
+            cgh
+        }; // stores the tail of the work-group reduction
+        sycl::local_accessor<uint32_t, 1> workgroup_ids{
+            local_range,
+            cgh
+        }; // stores the thread id that found the vertex to process at work-group level
+        sycl::local_accessor<element_t, 1> individual_reduce{
+            local_range,
+            cgh
+        }; // stores the vertices to process at individual thread granularity
+        sycl::local_accessor<uint32_t, 1> individual_reduce_tail{
+            1,
+            cgh
+        }; // stores the tail of the individual thread reduction
 
         cgh.parallel_for(sycl::nd_range<1>{ global_range, local_range },
                          bitmap_kernel_t{ context,
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index 6f54bcad949..618bacbd37a 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -27,12 +27,15 @@ template <typename ElementType = std::uint32_t>
 class bitset {
 public:
     using element_t = ElementType;
-    static constexpr std::uint64_t element_bitsize = sizeof(element_t) * 8; // Number of bits in an element
+    static constexpr std::uint64_t element_bitsize =
+        sizeof(element_t) * 8; // Number of bits in an element
 
     /// Constructs a bitset with the given data pointer and number of items.
     /// \param data pointer to the underlying data.
     /// \param num_items number of items in the bitset.
-    bitset(element_t* data, const size_t num_items) : _data(data), _num_items((num_items + element_bitsize - 1) / element_bitsize) {}
+    bitset(element_t* data, const size_t num_items)
+            : _data(data),
+              _num_items((num_items + element_bitsize - 1) / element_bitsize) {}
 
     /// Sets the bit at the specified index to 1.
     inline void set(std::uint32_t index) const {
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index 47b6235d969..85ac5a2cd1f 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -33,14 +33,19 @@ class frontier_view {
     static constexpr std::uint64_t divide_factor = bitset<bitmap_t>::element_bitsize;
 
     frontier_view() = default;
-    frontier_view(bitmap_t* data_layer, // First layer (tracks vertices in the frontier)
-                  bitmap_t* mlb_layer, // Second layer (to track non-zero elements in the first layer)
-                  std::uint32_t* offsets, // Array to store the indices of the non-zero elements
-                  std::uint32_t* offsets_size, // Pointer to store the size of the offsets array
-                  std::uint64_t num_items) // Maximum number of items that can be stored in the frontier
+    frontier_view(
+        bitmap_t* data_layer, // First layer (tracks vertices in the frontier)
+        bitmap_t* mlb_layer, // Second layer (to track non-zero elements in the first layer)
+        std::uint32_t* offsets, // Array to store the indices of the non-zero elements
+        std::uint32_t* offsets_size, // Pointer to store the size of the offsets array
+        std::uint64_t num_items) // Maximum number of items that can be stored in the frontier
             : _num_items(num_items),
-              _data_layer(bitset<bitmap_t>{ data_layer, num_items }), // first layer size is num_items
-              _mlb_layer(bitset<bitmap_t>{ mlb_layer, (num_items + divide_factor - 1) / divide_factor }), // second layer size is ceil(num_items / divide_factor) because each bit in the second layer represents an element in the first layer
+              _data_layer(
+                  bitset<bitmap_t>{ data_layer, num_items }), // first layer size is num_items
+              _mlb_layer(bitset<bitmap_t>{
+                  mlb_layer,
+                  (num_items + divide_factor - 1) /
+                      divide_factor }), // second layer size is ceil(num_items / divide_factor) because each bit in the second layer represents an element in the first layer
               _offsets(offsets),
               _offsets_size(offsets_size) {}
 
@@ -153,7 +158,8 @@ class frontier {
     ndarray<std::uint32_t, 1> _offsets;
     ndarray<buffer_t, 1> _buffer;
     const std::uint64_t _TMP_VAR = 0;
-    const std::uint64_t _CAF_FLAG = 1; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
+    const std::uint64_t _CAF_FLAG =
+        1; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
 };
 
 /// Swaps the contents of two frontiers.
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index 0cae68f326e..2f35fa25210 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -108,8 +108,8 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
     const std::uint64_t local_range = 256; // propose_wg_size(this->_queue);
     const std::uint64_t mlb_count = _mlb_layer.get_count();
     const std::uint64_t global_range = (mlb_count % local_range == 0)
-                                    ? mlb_count
-                                    : (mlb_count + local_range - (mlb_count % local_range));
+                                           ? mlb_count
+                                           : (mlb_count + local_range - (mlb_count % local_range));
 
     // check if local memory is enough
     bool use_local_mem =
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index 43e1e5b839c..681e2d52023 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -69,7 +69,10 @@ class csr_graph_view {
     };
 
 public:
-    csr_graph_view(std::uint64_t num_nodes, vertex_t* row_ptr, edge_t* col_indices, weight_t* weights)
+    csr_graph_view(std::uint64_t num_nodes,
+                   vertex_t* row_ptr,
+                   edge_t* col_indices,
+                   weight_t* weights)
             : _num_nodes(num_nodes),
               _row_ptr(row_ptr),
               _col_indices(col_indices),

From e7feaece7f0c8eadf8c4530228ec314a203a7131 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Mon, 19 Jan 2026 17:21:58 -0800
Subject: [PATCH 45/69] Change license yaml to be able to add possible
 additional copyright

---
 .github/.licenserc.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index cf9e7d1a4fe..e4d950d7485 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -19,7 +19,7 @@ header:
     spdx-id: Apache-2.0
     copyright-owner: contributors to the oneDAL project
     pattern: |
-      (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project)
+      (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project(?:\nCopyright[^\n]+)?)
 
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.

From dc4f81d74857b034b4583b0b4a5fb3034fcd2501 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Mon, 19 Jan 2026 17:48:56 -0800
Subject: [PATCH 46/69] fix?

---
 .github/.licenserc.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index e4d950d7485..ccd5ae4d4db 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -19,7 +19,7 @@ header:
     spdx-id: Apache-2.0
     copyright-owner: contributors to the oneDAL project
     pattern: |
-      (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project(?:\nCopyright[^\n]+)?)
+      (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project(?:\n(?:\s*\*\s*)?Copyright[^\n]+)?
 
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.

From 862feda5ee8f6bbbf5e79d0bc55c74a3bf123f88 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Mon, 19 Jan 2026 18:02:53 -0800
Subject: [PATCH 47/69] fix?

---
 .github/.licenserc.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index ccd5ae4d4db..7a1cec790cb 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -19,7 +19,7 @@ header:
     spdx-id: Apache-2.0
     copyright-owner: contributors to the oneDAL project
     pattern: |
-      (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project(?:\n(?:\s*\*\s*)?Copyright[^\n]+)?
+      (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project(?:\n(?:\s*\*\s*)?Copyright[^\n]+)?)
 
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.

From 8e758c90e79558669dacd3e018872d55bbd1e460 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 20 Jan 2026 05:27:22 -0800
Subject: [PATCH 48/69] fix?

---
 .github/.licenserc.yaml                                | 4 ++--
 cpp/oneapi/dal/backend/primitives/frontier/advance.hpp | 1 -
 2 files changed, 2 insertions(+), 3 deletions(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index 7a1cec790cb..fbbefdf3334 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -19,8 +19,8 @@ header:
     spdx-id: Apache-2.0
     copyright-owner: contributors to the oneDAL project
     pattern: |
-      (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project(?:\n(?:\s*\*\s*)?Copyright[^\n]+)?)
-
+      (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project)
+      (Copyright .*|)
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.
       You may obtain a copy of the License at
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index e1168364956..2432faaeafd 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -1,7 +1,6 @@
 /*******************************************************************************
 * Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
-*
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at

From a7806e2108da78fa184629f1e204ee288ee49e9c Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 20 Jan 2026 05:37:37 -0800
Subject: [PATCH 49/69] fix?

---
 .github/.licenserc.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index fbbefdf3334..e898308a2c9 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -20,7 +20,7 @@ header:
     copyright-owner: contributors to the oneDAL project
     pattern: |
       (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project)
-      (Copyright .*|)
+      (|Copyright .*)
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.
       You may obtain a copy of the License at

From b40d6db9bde990949eca9ed82f93950d6cb3b289 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 20 Jan 2026 05:42:13 -0800
Subject: [PATCH 50/69] fix?

---
 .github/.licenserc.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index e898308a2c9..1baff789167 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -20,7 +20,7 @@ header:
     copyright-owner: contributors to the oneDAL project
     pattern: |
       (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project)
-      (|Copyright .*)
+      (\s*|Copyright .*)
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.
       You may obtain a copy of the License at

From d0de4ec461ca77a879986e22ea08f642a51538dc Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 20 Jan 2026 05:49:32 -0800
Subject: [PATCH 51/69] fix?

---
 .github/.licenserc.yaml                                | 3 +--
 cpp/oneapi/dal/backend/primitives/frontier/advance.hpp | 2 +-
 2 files changed, 2 insertions(+), 3 deletions(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index 1baff789167..4ee1f8adc27 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -19,8 +19,7 @@ header:
     spdx-id: Apache-2.0
     copyright-owner: contributors to the oneDAL project
     pattern: |
-      (Copyright \d{4} Intel Corporation|Copyright contributors to the oneDAL project)
-      (\s*|Copyright .*)
+      Copyright .*
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.
       You may obtain a copy of the License at
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index 2432faaeafd..7dc3fbe5688 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -1,6 +1,6 @@
 /*******************************************************************************
-* Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
+*
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at

From ca9b27e6032c8fdb1b4a9566dd2f1ddf24818254 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 20 Jan 2026 06:02:29 -0800
Subject: [PATCH 52/69] fix?

---
 .github/.licenserc.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index 4ee1f8adc27..2268d49877b 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -19,7 +19,7 @@ header:
     spdx-id: Apache-2.0
     copyright-owner: contributors to the oneDAL project
     pattern: |
-      Copyright .*
+      Copyright ^[\n]+
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.
       You may obtain a copy of the License at

From f6c80b0b2205b5357b7a887f12e486df6341df93 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 20 Jan 2026 06:54:07 -0800
Subject: [PATCH 53/69] fix?

---
 .github/.licenserc.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index 2268d49877b..2989b7798ff 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -19,7 +19,7 @@ header:
     spdx-id: Apache-2.0
     copyright-owner: contributors to the oneDAL project
     pattern: |
-      Copyright ^[\n]+
+      Copyright [^\n]+
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.
       You may obtain a copy of the License at

From 6797388dc5d34e224f7a480975111f7ac1b74fbe Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 20 Jan 2026 07:02:41 -0800
Subject: [PATCH 54/69] fix?

---
 .github/.licenserc.yaml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index 2989b7798ff..986ea3e7e8a 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -20,6 +20,7 @@ header:
     copyright-owner: contributors to the oneDAL project
     pattern: |
       Copyright [^\n]+
+      
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.
       You may obtain a copy of the License at

From 649f16ff0a8b0b0707e25bc66fc41353d2d89d7a Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 20 Jan 2026 07:17:47 -0800
Subject: [PATCH 55/69] test

---
 cpp/oneapi/dal/backend/primitives/frontier/advance.hpp | 1 +
 1 file changed, 1 insertion(+)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index 7dc3fbe5688..09d2302b41f 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -1,5 +1,6 @@
 /*******************************************************************************
 * Copyright 2025 University of Salerno
+* testtesttest
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.

From 3859a984ebb0ebb4f6d8ae3a972da0bb308cf5e6 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 27 Jan 2026 06:08:39 -0800
Subject: [PATCH 56/69] fix

---
 .github/.licenserc.yaml                                | 2 +-
 cpp/oneapi/dal/backend/primitives/frontier/advance.hpp | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index 986ea3e7e8a..490219d8227 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -19,7 +19,7 @@ header:
     spdx-id: Apache-2.0
     copyright-owner: contributors to the oneDAL project
     pattern: |
-      Copyright [^\n]+
+      Copyright .*
       
       Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index 09d2302b41f..e1168364956 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -1,6 +1,6 @@
 /*******************************************************************************
+* Copyright contributors to the oneDAL project
 * Copyright 2025 University of Salerno
-* testtesttest
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.

From 22378f30068bf93813e4bd2c92f571f07a66bc22 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Thu, 29 Jan 2026 13:07:06 -0800
Subject: [PATCH 57/69] Make license checker strict

---
 .github/.licenserc.yaml | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/.github/.licenserc.yaml b/.github/.licenserc.yaml
index 490219d8227..2d7d9e9ae37 100644
--- a/.github/.licenserc.yaml
+++ b/.github/.licenserc.yaml
@@ -1,5 +1,5 @@
 #===============================================================================
-# Copyright Contributors to the oneDAL Project
+# Copyright contributors to the oneDAL Project
 #
 # Licensed under the Apache License, Version 2.0 (the "License");
 # you may not use this file except in compliance with the License.
@@ -19,9 +19,10 @@ header:
     spdx-id: Apache-2.0
     copyright-owner: contributors to the oneDAL project
     pattern: |
-      Copyright .*
-      
-      Licensed under the Apache License, Version 2\.0 \(the "License"\);
+      (?:Copyright \d{4} Intel Corporation
+      |Copyright contributors to the oneDAL project
+      |Copyright \d{4} University of Salerno
+      )+Licensed under the Apache License, Version 2\.0 \(the "License"\);
       you may not use this file except in compliance with the License\.
       You may obtain a copy of the License at
 

From a654178ee292899f457384b614741dc44bdf67ac Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Fri, 30 Jan 2026 15:08:30 -0800
Subject: [PATCH 58/69] Add preview namespace

---
 .../backend/primitives/frontier/advance.hpp   |  6 ++--
 .../backend/primitives/frontier/bitset.hpp    |  4 +--
 .../backend/primitives/frontier/frontier.hpp  | 21 ++++++------
 .../primitives/frontier/frontier_dpc.cpp      | 22 ++++++-------
 .../dal/backend/primitives/frontier/graph.hpp | 16 ++++-----
 .../primitives/frontier/test/advance_dpc.cpp  | 23 +++++++------
 .../primitives/frontier/test/bfs_dpc.cpp      | 33 +++++++++----------
 .../primitives/frontier/test/frontier_dpc.cpp |  6 ++--
 .../primitives/frontier/test/utils.hpp        |  4 +--
 9 files changed, 67 insertions(+), 68 deletions(-)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
index e1168364956..00820e51391 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/advance.hpp
@@ -21,7 +21,7 @@
 #include "oneapi/dal/backend/primitives/frontier/graph.hpp"
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 
-namespace oneapi::dal::backend::primitives {
+namespace oneapi::dal::preview::backend::primitives {
 
 /// frontier_context_state holds the state of the current processing group in the kernel
 /// It includes the group offset, coarsening factor, offsets size, and the SYCL
@@ -325,7 +325,7 @@ sycl::event advance(const GraphT& graph,
     using bitmap_kernel_t =
         bitmap_kernel<element_t, decltype(context), decltype(graph_dev), LambdaT>;
 
-    const uint32_t max_num_subgroups = device_max_sg_count(q);
+    const uint32_t max_num_subgroups = oneapi::dal::backend::device_max_sg_count(q);
 
     auto e = q.submit([&](sycl::handler& cgh) {
         cgh.depends_on(to_wait);
@@ -391,4 +391,4 @@ sycl::event advance(const GraphT& graph,
     return { e };
 }
 
-} // namespace oneapi::dal::backend::primitives
+} // namespace oneapi::dal::preview::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index 618bacbd37a..bf5e97dece5 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -19,7 +19,7 @@
 
 #include "oneapi/dal/backend/memory.hpp"
 
-namespace oneapi::dal::backend::primitives {
+namespace oneapi::dal::preview::backend::primitives {
 
 /// A bitset class that provides a set of operations on a bitset implemented using an array of integers.
 /// \tparam ElementType the type of the elements in the bitset (e.g., std::uint32_t).
@@ -119,4 +119,4 @@ class bitset {
     std::uint64_t _num_items;
 };
 
-} // namespace oneapi::dal::backend::primitives
+} // namespace oneapi::dal::preview::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
index 85ac5a2cd1f..886bb92b242 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier.hpp
@@ -22,7 +22,8 @@
 #include "oneapi/dal/backend/primitives/frontier/bitset.hpp"
 #include "oneapi/dal/backend/primitives/ndarray.hpp"
 
-namespace oneapi::dal::backend::primitives {
+namespace oneapi::dal::preview::backend::primitives {
+namespace pr = dal::backend::primitives;
 
 /// @brief A view of a frontier that provides an interface for the kernel to interact with the frontier data structure.
 /// \tparam ElementType the type of the elements in the frontier (e.g., std::uint32_t).
@@ -110,19 +111,19 @@ class frontier {
                  static_cast<std::uint64_t>(_data_layer.get_count()) };
     }
 
-    inline ndview<ElementType, 1> get_data() const {
+    inline pr::ndview<ElementType, 1> get_data() const {
         return _data_layer;
     }
 
-    inline ndview<ElementType, 1> get_mlb() const {
+    inline pr::ndview<ElementType, 1> get_mlb() const {
         return _mlb_layer;
     }
 
-    inline ndview<std::uint32_t, 1> get_offsets() const {
+    inline pr::ndview<std::uint32_t, 1> get_offsets() const {
         return _offsets.slice(1, _offsets.get_count());
     }
 
-    inline ndview<std::uint32_t, 1> get_offsets_size() const {
+    inline pr::ndview<std::uint32_t, 1> get_offsets_size() const {
         return _offsets.slice(0, 1);
     }
 
@@ -153,10 +154,10 @@ class frontier {
     sycl::queue& _queue;
     std::uint64_t _num_items;
 
-    ndarray<ElementType, 1> _data_layer;
-    ndarray<ElementType, 1> _mlb_layer;
-    ndarray<std::uint32_t, 1> _offsets;
-    ndarray<buffer_t, 1> _buffer;
+    pr::ndarray<ElementType, 1> _data_layer;
+    pr::ndarray<ElementType, 1> _mlb_layer;
+    pr::ndarray<std::uint32_t, 1> _offsets;
+    pr::ndarray<buffer_t, 1> _buffer;
     const std::uint64_t _TMP_VAR = 0;
     const std::uint64_t _CAF_FLAG =
         1; // Compute Active Frontier Flag (1 if already computed, 0 otherwise)
@@ -169,4 +170,4 @@ void swap_frontiers(frontier<ElementType>& f1, frontier<ElementType>& f2) {
     frontier<ElementType>::swap(f1, f2);
 }
 
-} // namespace oneapi::dal::backend::primitives
+} // namespace oneapi::dal::preview::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
index 2f35fa25210..80aa6edf272 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/frontier_dpc.cpp
@@ -17,7 +17,7 @@
 
 #include "oneapi/dal/backend/primitives/frontier/frontier.hpp"
 
-namespace oneapi::dal::backend::primitives {
+namespace oneapi::dal::preview::backend::primitives {
 
 #ifdef ONEDAL_DATA_PARALLEL
 
@@ -29,13 +29,13 @@ frontier<ElementType>::frontier(sycl::queue& queue, std::uint64_t num_items, syc
                               bitset<ElementType>::element_bitsize;
     std::int64_t mlb_size = (array_size + bitset<ElementType>::element_bitsize - 1) /
                             bitset<ElementType>::element_bitsize;
-    _data_layer = ndarray<ElementType, 1>::empty(_queue, { array_size }, alloc);
-    _mlb_layer = ndarray<ElementType, 1>::empty(_queue, { mlb_size }, alloc);
-    _offsets = ndarray<std::uint32_t, 1>::empty(
+    _data_layer = pr::ndarray<ElementType, 1>::empty(_queue, { array_size }, alloc);
+    _mlb_layer = pr::ndarray<ElementType, 1>::empty(_queue, { mlb_size }, alloc);
+    _offsets = pr::ndarray<std::uint32_t, 1>::empty(
         _queue,
         { array_size + 1 },
         alloc); /// First offset is to keep the size of the frontier
-    _buffer = ndarray<std::uint32_t, 1>::empty(_queue, { 10 }, alloc);
+    _buffer = pr::ndarray<std::uint32_t, 1>::empty(_queue, { 10 }, alloc);
 
     sycl::event e1, e2, e3;
     e1 = _data_layer.fill(_queue, ElementType(0));
@@ -49,13 +49,13 @@ frontier<ElementType>::frontier(sycl::queue& queue, std::uint64_t num_items, syc
 
 template <typename ElementType>
 bool frontier<ElementType>::empty() {
-    ndview<std::uint32_t, 1> empty_buff = _buffer.slice(0, 1);
+    pr::ndview<std::uint32_t, 1> empty_buff = _buffer.slice(0, 1);
     auto copy_e = fill(_queue, empty_buff, buffer_t(0));
     auto* const empty_buff_ptr = empty_buff.get_mutable_data();
 
     auto e = _queue.submit([&](sycl::handler& cgh) {
         cgh.depends_on(copy_e);
-        const auto range = make_range_1d(_mlb_layer.get_count());
+        const auto range = oneapi::dal::backend::make_range_1d(_mlb_layer.get_count());
         auto sum_reduction = sycl::reduction(empty_buff_ptr, sycl::plus<>());
         auto* const f_ptr = _mlb_layer.get_mutable_data();
 
@@ -113,7 +113,7 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
 
     // check if local memory is enough
     bool use_local_mem =
-        device_local_mem_size(this->_queue) >=
+        oneapi::dal::backend::device_local_mem_size(this->_queue) >=
         static_cast<std::int64_t>(local_range * element_bitsize * sizeof(uint32_t));
 
     auto e0 = _queue.submit([&](sycl::handler& cgh) {
@@ -129,7 +129,7 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
         cgh.depends_on(e0);
 
         if (!use_local_mem) {
-            cgh.parallel_for(make_range_1d(_mlb_layer.get_count()),
+            cgh.parallel_for(oneapi::dal::backend::make_range_1d(_mlb_layer.get_count()),
                              [=,
                               offsets = offsets_pointer,
                               offsets_size = offsets_size_pointer,
@@ -157,7 +157,7 @@ inline sycl::event frontier<ElementType>::compute_active_frontier() {
             sycl::local_accessor<uint32_t, 1> local_size(1, cgh);
 
             cgh.parallel_for(
-                make_multiple_nd_range_1d(global_range, local_range),
+                oneapi::dal::backend::make_multiple_nd_range_1d(global_range, local_range),
                 [=,
                  offsets = offsets_pointer,
                  offsets_size = offsets_size_pointer,
@@ -216,4 +216,4 @@ INSTANTIATE(std::uint32_t)
 
 #endif
 
-} // namespace oneapi::dal::backend::primitives
+} // namespace oneapi::dal::preview::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
index 681e2d52023..0c1f045d79c 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/graph.hpp
@@ -22,7 +22,7 @@
 #include "oneapi/dal/graph/detail/container.hpp"
 #include "oneapi/dal/backend/primitives/ndarray.hpp"
 
-namespace oneapi::dal::backend::primitives {
+namespace oneapi::dal::preview::backend::primitives {
 
 template <typename VertexT = std::uint32_t,
           typename EdgeT = std::uint32_t,
@@ -129,9 +129,9 @@ class csr_graph {
         std::int64_t col_indices_size = static_cast<std::int64_t>(col_indices.size());
         std::int64_t weights_size = static_cast<std::int64_t>(weights.size());
 
-        _row_ptr = ndarray<vertex_t, 1>::empty(_queue, { row_ptr_size }, alloc);
-        _col_indices = ndarray<edge_t, 1>::empty(_queue, { col_indices_size }, alloc);
-        _weights = ndarray<weight_t, 1>::empty(_queue, { weights_size }, alloc);
+        _row_ptr = pr::ndarray<vertex_t, 1>::empty(_queue, { row_ptr_size }, alloc);
+        _col_indices = pr::ndarray<edge_t, 1>::empty(_queue, { col_indices_size }, alloc);
+        _weights = pr::ndarray<weight_t, 1>::empty(_queue, { weights_size }, alloc);
 
         auto e1 = dal::backend::copy_host2usm(_queue,
                                               _row_ptr.get_mutable_data(),
@@ -171,9 +171,9 @@ class csr_graph {
 private:
     sycl::queue& _queue;
     std::uint64_t _num_nodes;
-    ndarray<vertex_t, 1> _row_ptr;
-    ndarray<edge_t, 1> _col_indices;
-    ndarray<weight_t, 1> _weights;
+    pr::ndarray<vertex_t, 1> _row_ptr;
+    pr::ndarray<edge_t, 1> _col_indices;
+    pr::ndarray<weight_t, 1> _weights;
 };
 
-} // namespace oneapi::dal::backend::primitives
+} // namespace oneapi::dal::preview::backend::primitives
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
index 89681e8c6c2..bc746e76dc0 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/advance_dpc.cpp
@@ -22,7 +22,7 @@
 
 #include "oneapi/dal/test/engine/common.hpp"
 
-namespace oneapi::dal::backend::primitives::test {
+namespace oneapi::dal::preview::backend::primitives::test {
 
 namespace pr = dal::backend::primitives;
 
@@ -81,12 +81,11 @@ TEST("test advance operation", "[advance]") {
     const std::uint64_t num_nodes = GENERATE(128, 512, 1024);
 
     const auto graph_data = generate_random_graph(num_nodes, edge_probability, seed);
-    auto graph =
-        pr::csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
+    auto graph = csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
     auto in_frontier =
-        pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+        frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
     auto out_frontier =
-        pr::frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
+        frontier<std::uint32_t>(queue, graph.get_vertex_count(), sycl::usm::alloc::device);
 
     std::vector<bool> host_frontier(num_nodes, false);
     std::mt19937 frontier_rng(seed ^ 0x9e3779b9u);
@@ -108,12 +107,12 @@ TEST("test advance operation", "[advance]") {
         host_frontier[fallback_vertex] = true;
     }
 
-    pr::advance(graph,
-                in_frontier,
-                out_frontier,
-                [=](auto vertex, auto neighbor, auto edge, auto weight) {
-                    return true; // Always advance
-                })
+    advance(graph,
+            in_frontier,
+            out_frontier,
+            [=](auto vertex, auto neighbor, auto edge, auto weight) {
+                return true; // Always advance
+            })
         .wait_and_throw();
 
     auto tmp_frontier =
@@ -121,4 +120,4 @@ TEST("test advance operation", "[advance]") {
     compare_frontiers(out_frontier, tmp_frontier, num_nodes);
 } // TEST "test advance operation"
 
-} // namespace oneapi::dal::backend::primitives::test
+} // namespace oneapi::dal::preview::backend::primitives::test
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
index 49ca07095ad..69ee98b9542 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/bfs_dpc.cpp
@@ -23,7 +23,7 @@
 #include <vector>
 #include <map>
 
-namespace oneapi::dal::backend::primitives::test {
+namespace oneapi::dal::preview::backend::primitives::test {
 
 namespace pr = dal::backend::primitives;
 
@@ -62,10 +62,9 @@ TEST("test BFS", "[bfs]") {
     const std::uint64_t num_nodes = GENERATE(128, 512, 1024);
 
     const auto graph_data = generate_random_graph(num_nodes, edge_probability, seed);
-    auto graph =
-        pr::csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
-    auto in_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
-    auto out_frontier = pr::frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
+    auto graph = csr_graph(queue, graph_data.row_ptr, graph_data.col_indices, graph_data.weights);
+    auto in_frontier = frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
+    auto out_frontier = frontier<std::uint32_t>(queue, num_nodes, sycl::usm::alloc::device);
     pr::ndarray<std::uint32_t, 1> distance =
         pr::ndarray<std::uint32_t, 1>::empty(queue,
                                              { static_cast<std::int64_t>(num_nodes) },
@@ -87,19 +86,19 @@ TEST("test BFS", "[bfs]") {
 
     /// Start BFS
     while (!in_frontier.empty()) {
-        auto e = pr::advance(graph,
-                             in_frontier,
-                             out_frontier,
-                             [=](auto vertex, auto neighbor, auto edge, auto weight) {
-                                 bool visited = distance_ptr[neighbor] < num_nodes + 1;
-                                 if (!visited) {
-                                     distance_ptr[neighbor] = iter + 1;
-                                 }
-                                 return !visited;
-                             });
+        auto e = advance(graph,
+                         in_frontier,
+                         out_frontier,
+                         [=](auto vertex, auto neighbor, auto edge, auto weight) {
+                             bool visited = distance_ptr[neighbor] < num_nodes + 1;
+                             if (!visited) {
+                                 distance_ptr[neighbor] = iter + 1;
+                             }
+                             return !visited;
+                         });
         e.wait_and_throw();
         iter++;
-        pr::swap_frontiers(in_frontier, out_frontier);
+        swap_frontiers(in_frontier, out_frontier);
         out_frontier.clear();
     }
     /// End BFS
@@ -112,4 +111,4 @@ TEST("test BFS", "[bfs]") {
     }
 } // TEST "test advance operation"
 
-} // namespace oneapi::dal::backend::primitives::test
+} // namespace oneapi::dal::preview::backend::primitives::test
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
index 3abce2a0b09..9dcc156c83c 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/frontier_dpc.cpp
@@ -19,7 +19,7 @@
 #include "oneapi/dal/backend/primitives/frontier/test/utils.hpp"
 #include "oneapi/dal/test/engine/common.hpp"
 
-namespace oneapi::dal::backend::primitives::test {
+namespace oneapi::dal::preview::backend::primitives::test {
 
 namespace pr = dal::backend::primitives;
 
@@ -39,7 +39,7 @@ TEST("frontier queue basic operations", "[frontier]") {
     print_device_name(queue);
 
     const std::uint64_t num_items = 100;
-    auto f = pr::frontier<std::uint32_t>(queue, num_items, sycl::usm::alloc::shared);
+    auto f = frontier<std::uint32_t>(queue, num_items, sycl::usm::alloc::shared);
 
     REQUIRE(f.empty() == true);
     f.insert(0);
@@ -71,4 +71,4 @@ TEST("frontier queue basic operations", "[frontier]") {
     REQUIRE(f.empty() == true);
 } // TEST "frontier queue operations"
 
-} // namespace oneapi::dal::backend::primitives::test
+} // namespace oneapi::dal::preview::backend::primitives::test
diff --git a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
index 1d822aec69b..93911e05dd3 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/test/utils.hpp
@@ -26,7 +26,7 @@ void print_device_name(sycl::queue& queue) {
     std::cout << "Running on device: " << device_name << std::endl;
 }
 
-namespace oneapi::dal::backend::primitives {
+namespace oneapi::dal::preview::backend::primitives {
 struct csr_graph_data {
     std::vector<std::uint32_t> row_ptr;
     std::vector<std::uint32_t> col_indices;
@@ -76,4 +76,4 @@ csr_graph_data generate_random_graph(std::uint64_t vertex_count,
     return { std::move(row_ptr), std::move(col_indices), std::move(weights) };
 }
 
-} // namespace oneapi::dal::backend::primitives
+} // namespace oneapi::dal::preview::backend::primitives

From 8947a095627f5b953aa2a3d5582696a5a43851bb Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Mon, 11 May 2026 06:15:10 -0700
Subject: [PATCH 59/69] check

---
 .github/workflows/ci.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index e4a82d13e98..7db6156f0bd 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -75,7 +75,7 @@ jobs:
           source /opt/intel/oneapi/setvars.sh
           .ci/scripts/build.sh --compiler icx  --optimizations ${{ matrix.ISA }} --target oneapi_c --debug symbols --jobs 20
           rm -rf __work
-          .ci/scripts/build.sh --compiler icx  --optimizations ${{ matrix.ISA }} --target oneapi_dpc --debug symbols --jobs 20
+          .ci/scripts/build.sh --compiler icx  --optimizations ${{ matrix.ISA }} --target oneapi_dpc --jobs 20
           # clean up build directory due to space limitations
           rm -rf __work
           echo "key=__release_lnx-$(git rev-parse HEAD)" >> "$GITHUB_OUTPUT"

From 7b6c44916af446b652c08820204a73295b193741 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 12 May 2026 09:33:49 -0700
Subject: [PATCH 60/69] check

---
 .github/workflows/ci.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 7db6156f0bd..e4a82d13e98 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -75,7 +75,7 @@ jobs:
           source /opt/intel/oneapi/setvars.sh
           .ci/scripts/build.sh --compiler icx  --optimizations ${{ matrix.ISA }} --target oneapi_c --debug symbols --jobs 20
           rm -rf __work
-          .ci/scripts/build.sh --compiler icx  --optimizations ${{ matrix.ISA }} --target oneapi_dpc --jobs 20
+          .ci/scripts/build.sh --compiler icx  --optimizations ${{ matrix.ISA }} --target oneapi_dpc --debug symbols --jobs 20
           # clean up build directory due to space limitations
           rm -rf __work
           echo "key=__release_lnx-$(git rev-parse HEAD)" >> "$GITHUB_OUTPUT"

From db05f457832eae3e2523b9a42afbdb9fdd843994 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 12 May 2026 11:11:19 -0700
Subject: [PATCH 61/69] Fix dbg

---
 .../dal/backend/primitives/frontier/bitset.hpp     | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
index bf5e97dece5..82f75f31e0c 100644
--- a/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
+++ b/cpp/oneapi/dal/backend/primitives/frontier/bitset.hpp
@@ -41,7 +41,9 @@ class bitset {
     inline void set(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+#ifndef __SYCL_DEVICE_ONLY__
         ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
+#endif
         _data[element_index] |= (element_t(1) << bit_index);
     }
 
@@ -49,7 +51,9 @@ class bitset {
     inline void unset(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+#ifndef __SYCL_DEVICE_ONLY__
         ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
+#endif
         _data[element_index] &= ~(element_t(1) << bit_index);
     }
 
@@ -57,7 +61,9 @@ class bitset {
     inline bool test(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+#ifndef __SYCL_DEVICE_ONLY__
         ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
+#endif
         return (_data[element_index] & (element_t(1) << bit_index)) != 0;
     }
 
@@ -67,7 +73,9 @@ class bitset {
     inline void atomic_set(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+#ifndef __SYCL_DEVICE_ONLY__
         ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
+#endif
         sycl::atomic_ref<element_t, mem_order, mem_scope> atomic_element(_data[element_index]);
         atomic_element |= (element_t(1) << bit_index);
     }
@@ -78,7 +86,9 @@ class bitset {
     inline void atomic_unset(std::uint32_t index) {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+#ifndef __SYCL_DEVICE_ONLY__
         ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
+#endif
         sycl::atomic_ref<element_t, mem_order, mem_scope> atomic_element(_data[element_index]);
         atomic_element &= ~(element_t(1) << bit_index);
     }
@@ -89,7 +99,9 @@ class bitset {
     inline bool atomic_test(std::uint32_t index) const {
         element_t element_index = index / element_bitsize;
         element_t bit_index = index % element_bitsize;
+#ifndef __SYCL_DEVICE_ONLY__
         ONEDAL_ASSERT(element_index < _num_items, "Index out of bounds");
+#endif
         sycl::atomic_ref<element_t, mem_order, mem_scope> atomic_element(_data[element_index]);
         return (atomic_element.load() & (element_t(1) << bit_index)) != 0;
     }
@@ -110,7 +122,9 @@ class bitset {
 
     /// override operator []
     inline element_t& operator[](std::uint64_t index) {
+#ifndef __SYCL_DEVICE_ONLY__
         ONEDAL_ASSERT(index < _num_items, "Index out of bounds");
+#endif
         return _data[index];
     }
 

From 87c706a5832e305b89eba2df8eba7d9c0e6beddb Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 5 May 2026 07:12:33 -0700
Subject: [PATCH 62/69] tc gpu

---
 cpp/oneapi/dal/algo/triangle_counting/BUILD   |  17 +-
 .../backend/gpu/CMakeLists.txt                |   5 +
 .../backend/gpu/triangle_counting.hpp         |  16 +
 .../vertex_ranking_default_kernel_gpu_dpc.cpp | 258 +++++++++++
 .../backend/gpu/vertex_ranking_kernel.hpp     |  36 ++
 .../dal/algo/triangle_counting/common.hpp     |  20 +
 .../detail/select_kernel.hpp                  |  26 ++
 .../detail/select_kernel_dpc.cpp              | 122 +++++
 .../detail/vertex_ranking_ops.hpp             |  19 +-
 .../test/triangle_counting_gpu_test.cpp       | 426 ++++++++++++++++++
 cpp/oneapi/dal/detail/vertex_ranking_ops.hpp  |  22 +
 cpp/oneapi/dal/graph/detail/csr_topology.hpp  |  54 ++-
 .../dal/graph/detail/device_csr_topology.hpp  | 265 +++++++++++
 ...undirected_adjacency_vector_graph_impl.hpp |  37 ++
 .../undirected_adjacency_vector_graph.hpp     |   7 +
 cpp/oneapi/dal/vertex_ranking.hpp             |  12 +
 .../triangle_counting_batch.cpp               |   5 +
 examples/oneapi/dpc/BUILD                     |   1 +
 .../triangle_counting_batch.cpp               |  67 +++
 19 files changed, 1410 insertions(+), 5 deletions(-)
 create mode 100644 cpp/oneapi/dal/algo/triangle_counting/backend/gpu/CMakeLists.txt
 create mode 100644 cpp/oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp
 create mode 100644 cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_default_kernel_gpu_dpc.cpp
 create mode 100644 cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp
 create mode 100644 cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel_dpc.cpp
 create mode 100644 cpp/oneapi/dal/algo/triangle_counting/test/triangle_counting_gpu_test.cpp
 create mode 100644 cpp/oneapi/dal/graph/detail/device_csr_topology.hpp
 create mode 100644 examples/oneapi/dpc/source/triangle_counting/triangle_counting_batch.cpp

diff --git a/cpp/oneapi/dal/algo/triangle_counting/BUILD b/cpp/oneapi/dal/algo/triangle_counting/BUILD
index ec0af5a5613..ab503dec297 100755
--- a/cpp/oneapi/dal/algo/triangle_counting/BUILD
+++ b/cpp/oneapi/dal/algo/triangle_counting/BUILD
@@ -10,7 +10,7 @@ dal_module(
     dal_deps = [
         "@onedal//cpp/oneapi/dal:core",
         "@onedal//cpp/oneapi/dal/backend/primitives:intersection",
-    ]
+    ],
 )
 
 dal_test_suite(
@@ -19,6 +19,21 @@ dal_test_suite(
     framework = "catch2",
     srcs = glob([
         "test/*.cpp",
+    ],
+    exclude = [
+        "test/*_gpu_test.cpp",
+    ]),
+    dal_deps = [
+        ":triangle_counting",
+    ],
+)
+
+dal_test_suite(
+    name = "gpu_tests",
+    framework = "catch2",
+    compile_as = [ "dpc++" ],
+    srcs = glob([
+        "test/*_gpu_test.cpp",
     ]),
     dal_deps = [
         ":triangle_counting",
diff --git a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/CMakeLists.txt b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/CMakeLists.txt
new file mode 100644
index 00000000000..a7f81fe3901
--- /dev/null
+++ b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/CMakeLists.txt
@@ -0,0 +1,5 @@
+set(ONEDAL_TRIANGLE_COUNTING_BACKEND_GPU_HEADERS
+    ${CMAKE_CURRENT_LIST_DIR}/triangle_counting.hpp
+    ${CMAKE_CURRENT_LIST_DIR}/vertex_ranking_kernel.hpp
+    PARENT_SCOPE
+)
diff --git a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp
new file mode 100644
index 00000000000..a6c9dae0b66
--- /dev/null
+++ b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp
@@ -0,0 +1,16 @@
+#pragma once
+
+#include "oneapi/dal/algo/triangle_counting/common.hpp"
+#include "oneapi/dal/algo/triangle_counting/vertex_ranking_types.hpp"
+#include "oneapi/dal/backend/dispatcher.hpp"
+
+namespace oneapi::dal::preview::triangle_counting::backend {
+
+template <typename Float, typename Task, typename Topology>
+struct vertex_ranking_kernel_gpu {
+    vertex_ranking_result<Task> operator()(const dal::backend::context_gpu& ctx,
+                                           const detail::descriptor_base<Task>& desc,
+                                           const Topology& topology) const;
+};
+
+} // namespace oneapi::dal::preview::triangle_counting::backend
diff --git a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_default_kernel_gpu_dpc.cpp b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_default_kernel_gpu_dpc.cpp
new file mode 100644
index 00000000000..51dda423f24
--- /dev/null
+++ b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_default_kernel_gpu_dpc.cpp
@@ -0,0 +1,258 @@
+/*******************************************************************************
+* Copyright 2020 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#include <sycl/sycl.hpp>
+
+#include "oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp"
+#include "oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp"
+#include "oneapi/dal/backend/dispatcher.hpp"
+#include "oneapi/dal/table/detail/table_builder.hpp"
+
+namespace oneapi::dal::preview::triangle_counting::backend {
+
+namespace detail_gpu {
+
+/// Counts triangles for each vertex in a CSR graph on the GPU using a
+/// binary-search intersection approach.
+///
+/// @tparam Index  The index type used for vertex/edge indexing
+/// @param[in]  queue         SYCL queue for device execution
+/// @param[in]  rows          CSR row-offset array (vertex_count + 1 entries)
+/// @param[in]  cols          CSR column-index array (2 * edge_count entries)
+/// @param[in]  vertex_count  Number of vertices in the graph
+/// @param[in]  edge_count    Number of undirected edges
+/// @return     A USM-allocated array of per-vertex triangle counts
+template <typename Index>
+std::int64_t* count_triangles_gpu(sycl::queue& queue,
+                                  const std::int64_t* rows,
+                                  const Index* cols,
+                                  std::int64_t vertex_count,
+                                  std::int64_t edge_count) {
+    auto* local_triangles =
+        sycl::malloc_shared<std::int64_t>(vertex_count, queue);
+    queue.memset(local_triangles, 0, vertex_count * sizeof(std::int64_t)).wait_and_throw();
+
+    // Parallel kernel: each work-item processes one vertex
+    queue.submit([&](sycl::handler& cgh) {
+        const std::int64_t* d_rows = rows;
+        const Index* d_cols = cols;
+        std::int64_t* d_triangles = local_triangles;
+        const std::int64_t vc = vertex_count;
+
+        cgh.parallel_for(sycl::range<1>(vc), [=](sycl::id<1> idx) {
+            const std::int64_t u = idx[0];
+            const std::int64_t u_start = d_rows[u];
+            const std::int64_t u_end = d_rows[u + 1];
+
+            std::int64_t count = 0;
+
+            // Iterate over each neighbor v of u where v > u
+            for (std::int64_t i = u_start; i < u_end; ++i) {
+                const std::int64_t v = d_cols[i];
+                if (v <= u) continue;
+
+                const std::int64_t v_start = d_rows[v];
+                const std::int64_t v_end = d_rows[v + 1];
+
+                // Merge-based intersection of neighbors of u and v
+                std::int64_t ui = u_start;
+                std::int64_t vi = v_start;
+                while (ui < u_end && vi < v_end) {
+                    const std::int64_t nu = d_cols[ui];
+                    const std::int64_t nv = d_cols[vi];
+                    if (nu == nv) {
+                        // Only count if common neighbor w > v to avoid
+                        // triple-counting the same triangle
+                        if (nu > v) {
+                            // Found a triangle (u, v, nu) with u < v < nu
+                            count++;
+                            // Atomically increment counts for v and the common neighbor
+                            sycl::atomic_ref<std::int64_t,
+                                             sycl::memory_order::relaxed,
+                                             sycl::memory_scope::device,
+                                             sycl::access::address_space::global_space>(
+                                d_triangles[v])
+                                .fetch_add(1);
+                            sycl::atomic_ref<std::int64_t,
+                                             sycl::memory_order::relaxed,
+                                             sycl::memory_scope::device,
+                                             sycl::access::address_space::global_space>(
+                                d_triangles[nu])
+                                .fetch_add(1);
+                        }
+                        ++ui;
+                        ++vi;
+                    }
+                    else if (nu < nv) {
+                        ++ui;
+                    }
+                    else {
+                        ++vi;
+                    }
+                }
+            }
+            // Add the count for vertex u
+            sycl::atomic_ref<std::int64_t,
+                             sycl::memory_order::relaxed,
+                             sycl::memory_scope::device,
+                             sycl::access::address_space::global_space>(d_triangles[u])
+                .fetch_add(count);
+        });
+    }).wait_and_throw();
+
+    return local_triangles;
+}
+
+/// Sums per-vertex triangle counts and divides by 3 to get the global count.
+///
+/// @param[in]  queue           SYCL queue for device execution
+/// @param[in]  local_triangles Per-vertex triangle count array
+/// @param[in]  vertex_count    Number of vertices
+/// @return     The global (total) triangle count
+std::int64_t sum_triangles_gpu(sycl::queue& queue,
+                               const std::int64_t* local_triangles,
+                               std::int64_t vertex_count) {
+    auto* sum_buf = sycl::malloc_shared<std::int64_t>(1, queue);
+    sum_buf[0] = 0;
+
+    queue.submit([&](sycl::handler& cgh) {
+        const std::int64_t* d_triangles = local_triangles;
+        std::int64_t* d_sum = sum_buf;
+        const std::int64_t vc = vertex_count;
+
+        cgh.parallel_for(sycl::range<1>(vc), [=](sycl::id<1> idx) {
+            sycl::atomic_ref<std::int64_t,
+                             sycl::memory_order::relaxed,
+                             sycl::memory_scope::device,
+                             sycl::access::address_space::global_space>(d_sum[0])
+                .fetch_add(d_triangles[idx[0]]);
+        });
+    }).wait_and_throw();
+
+    // Each triangle is counted 3 times (once per vertex)
+    const std::int64_t result = sum_buf[0] / 3;
+    sycl::free(sum_buf, queue);
+    return result;
+}
+
+} // namespace detail_gpu
+
+template <typename Float, typename Task, typename Index>
+vertex_ranking_result<Task> run_vertex_ranking_gpu(const dal::backend::context_gpu& ctx,
+                                                   const detail::descriptor_base<Task>& desc,
+                                                   const csr_topology_gpu_view<Index>& topology) {
+    auto& queue = ctx.get_queue();
+
+    const auto vertex_count = topology.vertex_count;
+    const auto edge_count = topology.edge_count;
+
+    if (vertex_count == 0) {
+        return vertex_ranking_result<Task>();
+    }
+
+    auto* local_triangles =
+        detail_gpu::count_triangles_gpu(queue, topology.rows, topology.cols,
+                                        vertex_count, edge_count);
+
+    vertex_ranking_result<Task> result;
+
+    if constexpr (std::is_same_v<Task, task::local> ||
+                  std::is_same_v<Task, task::local_and_global>) {
+        auto arr = array<std::int64_t>(queue, local_triangles, vertex_count,
+                                       [queue](std::int64_t* ptr) mutable {
+                                           sycl::free(ptr, queue);
+                                       });
+        result.set_ranks(dal::detail::homogen_table_builder{}
+                             .reset(arr, vertex_count, 1)
+                             .build());
+    }
+
+    if constexpr (std::is_same_v<Task, task::global> ||
+                  std::is_same_v<Task, task::local_and_global>) {
+        std::int64_t global_count =
+            detail_gpu::sum_triangles_gpu(queue, local_triangles, vertex_count);
+        result.set_global_rank(global_count);
+    }
+
+    // Free local_triangles only if not wrapped into the result table
+    if constexpr (std::is_same_v<Task, task::global>) {
+        sycl::free(local_triangles, queue);
+    }
+
+    return result;
+}
+
+template <typename Float, typename Task, typename Topology>
+vertex_ranking_result<Task> vertex_ranking_kernel_gpu<Float, Task, Topology>::operator()(
+    const dal::backend::context_gpu& ctx,
+    const detail::descriptor_base<Task>& desc,
+    const Topology& topology) const {
+    auto& queue = ctx.get_queue();
+    const auto vertex_count = topology.get_vertex_count();
+
+    if (vertex_count == 0) {
+        return vertex_ranking_result<Task>();
+    }
+
+    using namespace dal::preview::detail;
+
+    const auto* rows_ptr = topology._rows.get_data();
+    const auto alloc_type = sycl::get_pointer_type(rows_ptr, queue.get_context());
+
+    if (alloc_type == sycl::usm::alloc::device || alloc_type == sycl::usm::alloc::shared) {
+        csr_topology_gpu_view<std::int32_t> gpu_view;
+        gpu_view.rows = rows_ptr;
+        gpu_view.cols = topology._cols.get_data();
+        gpu_view.vertex_count = vertex_count;
+        gpu_view.edge_count = topology.get_edge_count();
+        return run_vertex_ranking_gpu<Float, Task, std::int32_t>(ctx, desc, gpu_view);
+    }
+
+    auto device_topo = topology_to_device<std::int32_t>(queue, topology);
+    const auto gpu_view = make_gpu_view(device_topo);
+    return run_vertex_ranking_gpu<Float, Task, std::int32_t>(ctx, desc, gpu_view);
+}
+
+// Explicit template instantiations
+template struct vertex_ranking_kernel_gpu<float,
+                                          task::local,
+                                          dal::preview::detail::topology<std::int32_t>>;
+template struct vertex_ranking_kernel_gpu<float,
+                                          task::global,
+                                          dal::preview::detail::topology<std::int32_t>>;
+template struct vertex_ranking_kernel_gpu<float,
+                                          task::local_and_global,
+                                          dal::preview::detail::topology<std::int32_t>>;
+
+template vertex_ranking_result<task::local>
+run_vertex_ranking_gpu<float, task::local, std::int32_t>(
+    const dal::backend::context_gpu&,
+    const detail::descriptor_base<task::local>&,
+    const csr_topology_gpu_view<std::int32_t>&);
+
+template vertex_ranking_result<task::global>
+run_vertex_ranking_gpu<float, task::global, std::int32_t>(
+    const dal::backend::context_gpu&,
+    const detail::descriptor_base<task::global>&,
+    const csr_topology_gpu_view<std::int32_t>&);
+
+template vertex_ranking_result<task::local_and_global>
+run_vertex_ranking_gpu<float, task::local_and_global, std::int32_t>(
+    const dal::backend::context_gpu&,
+    const detail::descriptor_base<task::local_and_global>&,
+    const csr_topology_gpu_view<std::int32_t>&);
+
+} // namespace oneapi::dal::preview::triangle_counting::backend
diff --git a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp
new file mode 100644
index 00000000000..e3e0b15da03
--- /dev/null
+++ b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp
@@ -0,0 +1,36 @@
+#pragma once
+
+#include <cstdint>
+
+#include "oneapi/dal/algo/triangle_counting/vertex_ranking_types.hpp"
+#include "oneapi/dal/backend/dispatcher.hpp"
+#include "oneapi/dal/graph/detail/device_csr_topology.hpp"
+
+namespace oneapi::dal::preview::triangle_counting::backend {
+
+template <typename Index = std::int32_t>
+struct csr_topology_gpu_view {
+    const std::int64_t* rows = nullptr;
+    const Index* cols = nullptr;
+    std::int64_t vertex_count = 0;
+    std::int64_t edge_count = 0;
+};
+
+/// Creates a GPU view from a device_csr_topology (zero-copy, just extracts pointers).
+template <typename Index = std::int32_t>
+csr_topology_gpu_view<Index> make_gpu_view(
+        const dal::preview::detail::device_csr_topology<Index>& device_topo) {
+    csr_topology_gpu_view<Index> view;
+    view.rows = device_topo.get_rows();
+    view.cols = device_topo.get_cols();
+    view.vertex_count = device_topo.get_vertex_count();
+    view.edge_count = device_topo.get_edge_count();
+    return view;
+}
+
+template <typename Float, typename Task, typename Index = std::int32_t>
+vertex_ranking_result<Task> run_vertex_ranking_gpu(const dal::backend::context_gpu& ctx,
+                                                   const detail::descriptor_base<Task>& desc,
+                                                   const csr_topology_gpu_view<Index>& topology);
+
+} // namespace oneapi::dal::preview::triangle_counting::backend
diff --git a/cpp/oneapi/dal/algo/triangle_counting/common.hpp b/cpp/oneapi/dal/algo/triangle_counting/common.hpp
index cb5ed359c56..2db9f54c9c6 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/common.hpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/common.hpp
@@ -17,6 +17,7 @@
 #pragma once
 #include "oneapi/dal/detail/common.hpp"
 #include "oneapi/dal/graph/undirected_adjacency_vector_graph.hpp"
+#include "oneapi/dal/graph/detail/device_csr_topology.hpp"
 #include "oneapi/dal/table/common.hpp"
 
 namespace oneapi::dal::preview::triangle_counting {
@@ -139,6 +140,24 @@ class descriptor : public detail::descriptor_base<Task> {
 
 namespace detail {
 
+#ifdef ONEDAL_DATA_PARALLEL
+template <typename T>
+struct is_device_csr_topology : std::false_type {};
+
+template <typename Index, typename Weight>
+struct is_device_csr_topology<dal::preview::detail::device_csr_topology<Index, Weight>>
+    : std::true_type {};
+
+template <typename Graph>
+constexpr bool is_valid_graph =
+    is_device_csr_topology<Graph>::value ||
+    dal::detail::is_one_of_v<Graph,
+                             undirected_adjacency_vector_graph<vertex_user_value_type<Graph>,
+                                                               edge_user_value_type<Graph>,
+                                                               graph_user_value_type<Graph>,
+                                                               vertex_type<Graph>,
+                                                               graph_allocator<Graph>>>;
+#else
 template <typename Graph>
 constexpr bool is_valid_graph =
     dal::detail::is_one_of_v<Graph,
@@ -147,6 +166,7 @@ constexpr bool is_valid_graph =
                                                                graph_user_value_type<Graph>,
                                                                vertex_type<Graph>,
                                                                graph_allocator<Graph>>>;
+#endif
 
 } // namespace detail
 } // namespace oneapi::dal::preview::triangle_counting
diff --git a/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel.hpp b/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel.hpp
index cf0b2f7acc7..84ed6c67fe8 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel.hpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel.hpp
@@ -21,6 +21,10 @@
 #include "oneapi/dal/algo/triangle_counting/vertex_ranking_types.hpp"
 #include "oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp"
 
+#ifdef ONEDAL_DATA_PARALLEL
+#include "oneapi/dal/detail/policy.hpp"
+#endif
+
 namespace oneapi::dal::preview::triangle_counting::detail {
 
 template <typename Policy, typename Descriptor, typename Topology>
@@ -57,6 +61,28 @@ struct backend_default : public backend_base<Policy, Descriptor, Topology> {
     }
 };
 
+#ifdef ONEDAL_DATA_PARALLEL
+/// GPU dispatch specialization.
+///
+/// The actual GPU kernel implementation is resolved at link time via the
+/// pre-compiled oneDAL DPC++ library. Only a forward declaration of the
+/// kernel struct is needed here, avoiding backend header dependencies
+/// that are not part of the public/detail header set.
+template <typename Descriptor, typename Topology>
+struct backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>
+        : public backend_base<dal::detail::data_parallel_policy, Descriptor, Topology> {
+    using float_t = typename Descriptor::float_t;
+    using task_t = typename Descriptor::task_t;
+    using method_t = typename Descriptor::method_t;
+    using allocator_t = typename Descriptor::allocator_t;
+
+    virtual vertex_ranking_result<task_t> operator()(
+        const dal::detail::data_parallel_policy& ctx,
+        const Descriptor& descriptor,
+        const Topology& t);
+};
+#endif
+
 template <typename Policy, typename Descriptor, typename Topology>
 dal::detail::shared<backend_base<Policy, Descriptor, Topology>> get_backend(const Descriptor& desc,
                                                                             const Topology& t) {
diff --git a/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel_dpc.cpp b/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel_dpc.cpp
new file mode 100644
index 00000000000..170e5ae41ec
--- /dev/null
+++ b/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel_dpc.cpp
@@ -0,0 +1,122 @@
+/*******************************************************************************
+* Copyright 2020 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#include "oneapi/dal/algo/triangle_counting/detail/select_kernel.hpp"
+#include "oneapi/dal/algo/triangle_counting/detail/vertex_ranking_ops.hpp"
+#include "oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp"
+#include "oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp"
+#include "oneapi/dal/backend/dispatcher.hpp"
+#include "oneapi/dal/graph/detail/device_csr_topology.hpp"
+
+namespace oneapi::dal::preview::triangle_counting::detail {
+
+template <typename Descriptor, typename Topology>
+vertex_ranking_result<typename Descriptor::task_t>
+backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>::operator()(
+    const dal::detail::data_parallel_policy& ctx,
+    const Descriptor& descriptor,
+    const Topology& t) {
+    using float_t = typename Descriptor::float_t;
+    using task_t = typename Descriptor::task_t;
+    using method_t = typename Descriptor::method_t;
+    using allocator_t = typename Descriptor::allocator_t;
+
+    return dal::backend::dispatch_by_device(
+        ctx,
+        [&]() {
+            // CPU path: delegate to host policy kernel
+            return vertex_ranking_kernel_cpu<method_t, task_t, allocator_t, Topology>()(
+                dal::detail::host_policy::get_default(),
+                descriptor,
+                descriptor.get_allocator(),
+                t);
+        },
+        [&]() {
+            // GPU path: delegate to GPU kernel
+            dal::backend::context_gpu gpu_ctx{ ctx };
+            return backend::vertex_ranking_kernel_gpu<float_t, task_t, Topology>()(
+                gpu_ctx,
+                descriptor,
+                t);
+        });
+}
+
+/// Specialization for device_csr_topology: GPU-only path (no CPU fallback).
+/// Handled directly in vertex_ranking_ops_dispatcher.
+
+template <typename Descriptor, typename Index>
+vertex_ranking_result<typename Descriptor::task_t>
+vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy, Descriptor,
+                              dal::preview::detail::device_csr_topology<Index>>::operator()(
+    const dal::detail::data_parallel_policy &policy,
+    const Descriptor &descriptor,
+    input_t &input) const {
+    using float_t = typename Descriptor::float_t;
+    using task_t = typename Descriptor::task_t;
+
+    const auto &device_topo = input.get_graph();
+    if (device_topo.get_vertex_count() == 0) {
+        return vertex_ranking_result<task_t>();
+    }
+    dal::backend::context_gpu gpu_ctx{ policy };
+    const auto gpu_view = backend::make_gpu_view(device_topo);
+    return backend::run_vertex_ranking_gpu<float_t, task_t, Index>(gpu_ctx, descriptor, gpu_view);
+}
+
+// Explicit instantiations for supported descriptor/topology combinations
+using default_descriptor_local = descriptor<
+    float,
+    method::ordered_count,
+    task::local,
+    std::allocator<char>>;
+
+using default_descriptor_global = descriptor<
+    float,
+    method::ordered_count,
+    task::global,
+    std::allocator<char>>;
+
+using default_descriptor_local_and_global = descriptor<
+    float,
+    method::ordered_count,
+    task::local_and_global,
+    std::allocator<char>>;
+
+using default_topology = dal::preview::detail::topology<std::int32_t>;
+using device_topology = dal::preview::detail::device_csr_topology<std::int32_t>;
+
+template struct ONEDAL_EXPORT backend_default<dal::detail::data_parallel_policy,
+                                              default_descriptor_local,
+                                              default_topology>;
+template struct ONEDAL_EXPORT backend_default<dal::detail::data_parallel_policy,
+                                              default_descriptor_global,
+                                              default_topology>;
+template struct ONEDAL_EXPORT backend_default<dal::detail::data_parallel_policy,
+                                              default_descriptor_local_and_global,
+                                              default_topology>;
+
+// Explicit instantiations for device_csr_topology dispatcher
+template struct vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy,
+                                              default_descriptor_local,
+                                              device_topology>;
+template struct vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy,
+                                              default_descriptor_global,
+                                              device_topology>;
+template struct vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy,
+                                              default_descriptor_local_and_global,
+                                              device_topology>;
+
+} // namespace oneapi::dal::preview::triangle_counting::detail
diff --git a/cpp/oneapi/dal/algo/triangle_counting/detail/vertex_ranking_ops.hpp b/cpp/oneapi/dal/algo/triangle_counting/detail/vertex_ranking_ops.hpp
index e69b822283b..cef64393fb2 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/detail/vertex_ranking_ops.hpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/detail/vertex_ranking_ops.hpp
@@ -23,6 +23,7 @@
 #include "oneapi/dal/detail/policy.hpp"
 #include "oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp"
 #include "oneapi/dal/graph/detail/undirected_adjacency_vector_graph_topology_builder.hpp"
+#include "oneapi/dal/graph/detail/device_csr_topology.hpp"
 
 namespace oneapi::dal::preview::triangle_counting::detail {
 
@@ -36,7 +37,7 @@ struct vertex_ranking_ops_dispatcher {
 
         const auto &t = topology_builder(input.get_graph());
 
-        static auto impl = get_backend<Policy, Descriptor>(descriptor, t);
+        auto impl = get_backend<Policy, Descriptor>(descriptor, t);
 
         return (*impl)(policy, descriptor, t);
     }
@@ -58,4 +59,20 @@ struct vertex_ranking_ops {
     }
 };
 
+#ifdef ONEDAL_DATA_PARALLEL
+/// Specialization for device_csr_topology: skips host-to-device transfer
+/// since the graph data is already on the device.
+template <typename Descriptor, typename Index>
+struct vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy, Descriptor,
+                                     dal::preview::detail::device_csr_topology<Index>> {
+    using task_t = typename Descriptor::task_t;
+    using input_t = vertex_ranking_input<dal::preview::detail::device_csr_topology<Index>, task_t>;
+
+    vertex_ranking_result<task_t> operator()(
+        const dal::detail::data_parallel_policy &policy,
+        const Descriptor &descriptor,
+        input_t &input) const;
+};
+#endif
+
 } // namespace oneapi::dal::preview::triangle_counting::detail
diff --git a/cpp/oneapi/dal/algo/triangle_counting/test/triangle_counting_gpu_test.cpp b/cpp/oneapi/dal/algo/triangle_counting/test/triangle_counting_gpu_test.cpp
new file mode 100644
index 00000000000..c28cc2f0517
--- /dev/null
+++ b/cpp/oneapi/dal/algo/triangle_counting/test/triangle_counting_gpu_test.cpp
@@ -0,0 +1,426 @@
+/*******************************************************************************
+* Copyright 2020 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#include <array>
+
+#ifndef ONEDAL_DATA_PARALLEL
+#define ONEDAL_DATA_PARALLEL
+#endif
+
+#include <sycl/sycl.hpp>
+
+#include "oneapi/dal/algo/triangle_counting/vertex_ranking.hpp"
+#include "oneapi/dal/graph/detail/device_csr_topology.hpp"
+
+#include "oneapi/dal/test/engine/common.hpp"
+
+namespace oneapi::dal::algo::triangle_counting::gpu::test {
+
+class graph_base_data {
+public:
+    graph_base_data() = default;
+
+    std::int64_t get_vertex_count() const {
+        return vertex_count;
+    }
+
+    std::int64_t get_edge_count() const {
+        return edge_count;
+    }
+
+    std::int64_t get_global_triangle_count() const {
+        return global_triangle_count;
+    }
+
+    std::int64_t get_cols_count() const {
+        return cols_count;
+    }
+
+    std::int64_t get_rows_count() const {
+        return rows_count;
+    }
+
+protected:
+    std::int64_t vertex_count;
+    std::int64_t edge_count;
+    std::int64_t cols_count;
+    std::int64_t rows_count;
+    std::int64_t global_triangle_count;
+};
+
+class complete_graph_5_type : public graph_base_data {
+public:
+    complete_graph_5_type() {
+        vertex_count = 5;
+        edge_count = 10;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        global_triangle_count = 10;
+    }
+
+    std::array<std::int32_t, 5> degrees = { 4, 4, 4, 4, 4 };
+    std::array<std::int32_t, 20> cols = {
+        1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3
+    };
+    std::array<std::int64_t, 6> rows = { 0, 4, 8, 12, 16, 20 };
+    std::array<std::int64_t, 5> local_triangles = { 6, 6, 6, 6, 6 };
+};
+
+class complete_graph_9_type : public graph_base_data {
+public:
+    complete_graph_9_type() {
+        vertex_count = 9;
+        edge_count = 36;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        global_triangle_count = 84;
+    }
+
+    std::array<std::int32_t, 9> degrees = { 8, 8, 8, 8, 8, 8, 8, 8, 8 };
+    std::array<std::int32_t, 72> cols = { 1, 2, 3, 4, 5, 6, 7, 8, 0, 2, 3, 4, 5, 6, 7, 8, 0, 1,
+                                          3, 4, 5, 6, 7, 8, 0, 1, 2, 4, 5, 6, 7, 8, 0, 1, 2, 3,
+                                          5, 6, 7, 8, 0, 1, 2, 3, 4, 6, 7, 8, 0, 1, 2, 3, 4, 5,
+                                          7, 8, 0, 1, 2, 3, 4, 5, 6, 8, 0, 1, 2, 3, 4, 5, 6, 7 };
+    std::array<std::int64_t, 10> rows = { 0, 8, 16, 24, 32, 40, 48, 56, 64, 72 };
+    std::array<std::int64_t, 9> local_triangles = { 28, 28, 28, 28, 28, 28, 28, 28, 28 };
+};
+
+class triangle_graph_type : public graph_base_data {
+public:
+    triangle_graph_type() {
+        vertex_count = 3;
+        edge_count = 3;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        global_triangle_count = 1;
+    }
+
+    std::array<std::int32_t, 3> degrees = { 2, 2, 2 };
+    std::array<std::int32_t, 6> cols = { 1, 2, 0, 2, 0, 1 };
+    std::array<std::int64_t, 4> rows = { 0, 2, 4, 6 };
+    std::array<std::int64_t, 3> local_triangles = { 1, 1, 1 };
+};
+
+class two_vertices_graph_type : public graph_base_data {
+public:
+    two_vertices_graph_type() {
+        vertex_count = 2;
+        edge_count = 1;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        global_triangle_count = 0;
+    }
+
+    std::array<std::int32_t, 2> degrees = { 1, 1 };
+    std::array<std::int32_t, 2> cols = { 1, 0 };
+    std::array<std::int64_t, 3> rows = { 0, 1, 2 };
+    std::array<std::int64_t, 2> local_triangles = { 0, 0 };
+};
+
+class wheel_graph_6_type : public graph_base_data {
+public:
+    wheel_graph_6_type() {
+        vertex_count = 6;
+        edge_count = 10;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        global_triangle_count = 5;
+    }
+
+    std::array<std::int32_t, 6> degrees = { 5, 3, 3, 3, 3, 3 };
+    std::array<std::int32_t, 20> cols = {
+        1, 2, 3, 4, 5, 0, 2, 5, 0, 1, 3, 0, 2, 4, 0, 3, 5, 0, 1, 4
+    };
+    std::array<std::int64_t, 7> rows = { 0, 5, 8, 11, 14, 17, 20 };
+    std::array<std::int64_t, 6> local_triangles = { 5, 2, 2, 2, 2, 2 };
+};
+
+class graph_with_isolated_vertices_10_type : public graph_base_data {
+public:
+    graph_with_isolated_vertices_10_type() {
+        vertex_count = 10;
+        edge_count = 11;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        global_triangle_count = 5;
+    }
+
+    std::array<std::int32_t, 10> degrees = { 5, 3, 2, 0, 3, 4, 0, 2, 0, 3 };
+    std::array<std::int32_t, 22> cols = { 1, 2, 4, 5, 7, 0, 5, 9, 0, 7, 0,
+                                          5, 9, 0, 1, 4, 9, 0, 2, 1, 4, 5 };
+    std::array<std::int64_t, 11> rows = { 0, 5, 8, 10, 10, 13, 17, 17, 19, 19, 22 };
+    std::array<std::int64_t, 10> local_triangles = { 3, 2, 1, 0, 2, 4, 0, 1, 0, 2 };
+};
+
+class triangle_counting_gpu_test {
+public:
+    template <typename GraphType>
+    auto create_graph() {
+        GraphType graph_data;
+        dal::preview::undirected_adjacency_vector_graph<> g;
+        auto& graph_impl = oneapi::dal::detail::get_impl(g);
+        auto& vertex_allocator = graph_impl._vertex_allocator;
+        auto& edge_allocator = graph_impl._edge_allocator;
+
+        const std::int64_t vertex_count = graph_data.get_vertex_count();
+        const std::int64_t edge_count = graph_data.get_edge_count();
+        const std::int64_t cols_count = graph_data.get_cols_count();
+        const std::int64_t rows_count = graph_data.get_rows_count();
+
+        std::int32_t* degrees =
+            oneapi::dal::preview::detail::allocate(vertex_allocator, vertex_count);
+        std::int32_t* cols = oneapi::dal::preview::detail::allocate(vertex_allocator, cols_count);
+        std::int64_t* rows = oneapi::dal::preview::detail::allocate(edge_allocator, rows_count);
+        std::int32_t* rows_vertex =
+            oneapi::dal::preview::detail::allocate(vertex_allocator, rows_count);
+
+        for (int i = 0; i < vertex_count; i++) {
+            degrees[i] = graph_data.degrees[i];
+        }
+
+        for (int i = 0; i < cols_count; i++) {
+            cols[i] = graph_data.cols[i];
+        }
+        for (int i = 0; i < rows_count; i++) {
+            rows[i] = graph_data.rows[i];
+            rows_vertex[i] = graph_data.rows[i];
+        }
+        graph_impl.set_topology(vertex_count, edge_count, rows, cols, cols_count, degrees);
+        graph_impl.get_topology()._rows_vertex =
+            oneapi::dal::preview::detail::container<std::int32_t>::wrap(rows_vertex, rows_count);
+        return g;
+    }
+
+    sycl::queue get_queue() {
+        return sycl::queue{ sycl::default_selector_v };
+    }
+
+    template <typename GraphType>
+    void check_local_task() {
+        GraphType graph_data;
+        const auto g = create_graph<GraphType>();
+        std::int64_t vertex_count = graph_data.get_vertex_count();
+
+        auto q = get_queue();
+
+        std::allocator<char> alloc;
+        const auto tc_desc = dal::preview::triangle_counting::descriptor<
+            float,
+            dal::preview::triangle_counting::method::ordered_count,
+            dal::preview::triangle_counting::task::local,
+            std::allocator<char>>(alloc);
+
+        const auto result = dal::preview::vertex_ranking(q, tc_desc, g);
+
+        const auto local_triangles_table = result.get_ranks();
+        const auto& local_triangles =
+            static_cast<const dal::homogen_table&>(local_triangles_table);
+        const auto local_triangles_data = local_triangles.get_data<std::int64_t>();
+
+        REQUIRE(local_triangles_table.get_row_count() == vertex_count);
+
+        int correct_local_triangle_count = 0;
+        for (std::int64_t i = 0; i < vertex_count; i++) {
+            if (local_triangles_data[i] == graph_data.local_triangles[i]) {
+                correct_local_triangle_count++;
+            }
+        }
+        REQUIRE(correct_local_triangle_count == vertex_count);
+    }
+
+    template <typename GraphType>
+    void check_local_and_global_task() {
+        GraphType graph_data;
+        const auto g = create_graph<GraphType>();
+        std::int64_t vertex_count = graph_data.get_vertex_count();
+        std::int64_t global_triangle_count = graph_data.get_global_triangle_count();
+
+        auto q = get_queue();
+
+        std::allocator<char> alloc;
+        const auto tc_desc = dal::preview::triangle_counting::descriptor<
+            float,
+            dal::preview::triangle_counting::method::ordered_count,
+            dal::preview::triangle_counting::task::local_and_global,
+            std::allocator<char>>(alloc);
+
+        const auto result = dal::preview::vertex_ranking(q, tc_desc, g);
+
+        const auto local_triangles_table = result.get_ranks();
+        const auto& local_triangles =
+            static_cast<const dal::homogen_table&>(local_triangles_table);
+        const auto local_triangles_data = local_triangles.get_data<std::int64_t>();
+
+        REQUIRE(result.get_global_rank() == global_triangle_count);
+        REQUIRE(local_triangles_table.get_row_count() == vertex_count);
+
+        int correct_local_triangle_count = 0;
+        for (std::int64_t i = 0; i < vertex_count; i++) {
+            if (local_triangles_data[i] == graph_data.local_triangles[i]) {
+                correct_local_triangle_count++;
+            }
+        }
+        REQUIRE(correct_local_triangle_count == vertex_count);
+    }
+
+    template <typename GraphType>
+    void check_global_task() {
+        GraphType graph_data;
+        const auto g = create_graph<GraphType>();
+        std::int64_t global_triangle_count = graph_data.get_global_triangle_count();
+
+        auto q = get_queue();
+
+        std::allocator<char> alloc;
+        const auto tc_desc = dal::preview::triangle_counting::descriptor<
+            float,
+            dal::preview::triangle_counting::method::ordered_count,
+            dal::preview::triangle_counting::task::global,
+            std::allocator<char>>(alloc);
+
+        const auto result = dal::preview::vertex_ranking(q, tc_desc, g);
+        REQUIRE(result.get_global_rank() == global_triangle_count);
+    }
+};
+
+TEST_M(triangle_counting_gpu_test, "GPU: Local task") {
+    this->check_local_task<complete_graph_5_type>();
+    this->check_local_task<complete_graph_9_type>();
+    this->check_local_task<triangle_graph_type>();
+    this->check_local_task<two_vertices_graph_type>();
+    this->check_local_task<wheel_graph_6_type>();
+    this->check_local_task<graph_with_isolated_vertices_10_type>();
+}
+
+TEST_M(triangle_counting_gpu_test, "GPU: Local and global task") {
+    this->check_local_and_global_task<complete_graph_5_type>();
+    this->check_local_and_global_task<complete_graph_9_type>();
+    this->check_local_and_global_task<triangle_graph_type>();
+    this->check_local_and_global_task<two_vertices_graph_type>();
+    this->check_local_and_global_task<wheel_graph_6_type>();
+    this->check_local_and_global_task<graph_with_isolated_vertices_10_type>();
+}
+
+TEST_M(triangle_counting_gpu_test, "GPU: Global task") {
+    this->check_global_task<complete_graph_5_type>();
+    this->check_global_task<complete_graph_9_type>();
+    this->check_global_task<triangle_graph_type>();
+    this->check_global_task<two_vertices_graph_type>();
+    this->check_global_task<wheel_graph_6_type>();
+    this->check_global_task<graph_with_isolated_vertices_10_type>();
+}
+
+TEST_M(triangle_counting_gpu_test, "GPU: Null graph - local task") {
+    dal::preview::undirected_adjacency_vector_graph<> null_graph;
+    auto q = get_queue();
+
+    std::allocator<char> alloc;
+    const auto tc_desc = dal::preview::triangle_counting::descriptor<
+        float,
+        dal::preview::triangle_counting::method::ordered_count,
+        dal::preview::triangle_counting::task::local,
+        std::allocator<char>>(alloc);
+
+    const auto result = dal::preview::vertex_ranking(q, tc_desc, null_graph);
+    const auto& local_triangles =
+        static_cast<const dal::homogen_table&>(result.get_ranks());
+    REQUIRE(local_triangles.has_data() == false);
+}
+
+TEST_M(triangle_counting_gpu_test, "GPU: Null graph - global task") {
+    dal::preview::undirected_adjacency_vector_graph<> null_graph;
+    auto q = get_queue();
+
+    std::allocator<char> alloc;
+    const auto tc_desc = dal::preview::triangle_counting::descriptor<
+        float,
+        dal::preview::triangle_counting::method::ordered_count,
+        dal::preview::triangle_counting::task::global,
+        std::allocator<char>>(alloc);
+
+    const auto result = dal::preview::vertex_ranking(q, tc_desc, null_graph);
+    REQUIRE(result.get_global_rank() == 0);
+}
+
+TEST_M(triangle_counting_gpu_test, "GPU: Null graph - local_and_global task") {
+    dal::preview::undirected_adjacency_vector_graph<> null_graph;
+    auto q = get_queue();
+
+    std::allocator<char> alloc;
+    const auto tc_desc = dal::preview::triangle_counting::descriptor<
+        float,
+        dal::preview::triangle_counting::method::ordered_count,
+        dal::preview::triangle_counting::task::local_and_global,
+        std::allocator<char>>(alloc);
+
+    const auto result = dal::preview::vertex_ranking(q, tc_desc, null_graph);
+    const auto& local_triangles =
+        static_cast<const dal::homogen_table&>(result.get_ranks());
+    REQUIRE(local_triangles.has_data() == false);
+    REQUIRE(result.get_global_rank() == 0);
+}
+
+TEST_M(triangle_counting_gpu_test, "GPU: topology_to_device round-trip") {
+    const auto g = create_graph<complete_graph_5_type>();
+    auto q = get_queue();
+
+    // Access the internal topology
+    const auto& topo = oneapi::dal::detail::get_impl(g).get_topology();
+
+    // Transfer topology to device
+    auto device_topo =
+        dal::preview::detail::topology_to_device<std::int32_t>(q, topo);
+
+    REQUIRE(device_topo.get_vertex_count() == 5);
+    REQUIRE(device_topo.get_edge_count() == 10);
+    REQUIRE(device_topo.get_rows() != nullptr);
+    REQUIRE(device_topo.get_cols() != nullptr);
+
+    // Transfer back to host and verify
+    auto host_topo = dal::preview::detail::topology_to_host(device_topo);
+
+    REQUIRE(host_topo.get_vertex_count() == 5);
+    REQUIRE(host_topo.get_edge_count() == 10);
+
+    // Verify row offsets match original
+    for (std::int64_t i = 0; i <= 5; ++i) {
+        REQUIRE(host_topo._rows[i] == topo._rows[i]);
+    }
+
+    // Verify column indices match original
+    for (std::int64_t i = 0; i < 20; ++i) {
+        REQUIRE(host_topo._cols[i] == topo._cols[i]);
+    }
+}
+
+TEST_M(triangle_counting_gpu_test, "GPU: Empty topology round-trip") {
+    auto q = get_queue();
+
+    dal::preview::detail::topology<std::int32_t> empty_topo;
+
+    auto device_topo =
+        dal::preview::detail::topology_to_device<std::int32_t>(q, empty_topo);
+
+    REQUIRE(device_topo.get_vertex_count() == 0);
+    REQUIRE(device_topo.get_edge_count() == 0);
+
+    auto host_topo = dal::preview::detail::topology_to_host(device_topo);
+
+    REQUIRE(host_topo.get_vertex_count() == 0);
+    REQUIRE(host_topo.get_edge_count() == 0);
+}
+
+} // namespace oneapi::dal::algo::triangle_counting::gpu::test
diff --git a/cpp/oneapi/dal/detail/vertex_ranking_ops.hpp b/cpp/oneapi/dal/detail/vertex_ranking_ops.hpp
index d034d9c08e8..9c30b50e886 100644
--- a/cpp/oneapi/dal/detail/vertex_ranking_ops.hpp
+++ b/cpp/oneapi/dal/detail/vertex_ranking_ops.hpp
@@ -34,10 +34,32 @@ auto vertex_ranking_dispatch_by_input(const Descriptor &desc, Head &&head, Tail
     return ops_t()(dal::detail::host_policy::get_default(), desc, input);
 }
 
+#ifdef ONEDAL_DATA_PARALLEL
+template <typename Descriptor, typename Head, typename... Tail>
+auto vertex_ranking_dispatch_by_input(const dal::detail::data_parallel_policy &policy,
+                                      const Descriptor &desc,
+                                      Head &&head,
+                                      Tail &&...tail) {
+    using tag_t = typename Descriptor::tag_t;
+    using ops_t = vertex_ranking_ops<Descriptor, std::decay_t<Head>, tag_t>;
+    using input_t = typename ops_t::input_t;
+
+    auto input = input_t{ std::forward<Head>(head), std::forward<Tail>(tail)... };
+    return ops_t()(policy, desc, input);
+}
+#endif
+
 template <typename Head, typename... Tail>
 auto vertex_ranking_dispatch(Head &&head, Tail &&...tail) {
     return vertex_ranking_dispatch_by_input(std::forward<Head>(head), std::forward<Tail>(tail)...);
 }
 
+#ifdef ONEDAL_DATA_PARALLEL
+template <typename... Tail>
+auto vertex_ranking_dispatch(const dal::detail::data_parallel_policy &policy, Tail &&...tail) {
+    return vertex_ranking_dispatch_by_input(policy, std::forward<Tail>(tail)...);
+}
+#endif
+
 } // namespace detail
 } // namespace oneapi::dal::preview
diff --git a/cpp/oneapi/dal/graph/detail/csr_topology.hpp b/cpp/oneapi/dal/graph/detail/csr_topology.hpp
index 169635fc675..8606a9963ed 100755
--- a/cpp/oneapi/dal/graph/detail/csr_topology.hpp
+++ b/cpp/oneapi/dal/graph/detail/csr_topology.hpp
@@ -21,6 +21,10 @@
 #include "oneapi/dal/graph/common.hpp"
 #include "oneapi/dal/graph/detail/container.hpp"
 
+#ifdef ONEDAL_DATA_PARALLEL
+#include <sycl/sycl.hpp>
+#endif
+
 namespace oneapi::dal::preview::detail {
 
 template <typename IndexType>
@@ -124,14 +128,58 @@ class topology {
         -> const_vertex_edge_iterator {
         return _cols_ptr + _rows[vertex + 1];
     }
+
+#ifdef ONEDAL_DATA_PARALLEL
+    inline void set_topology(const sycl::queue& queue,
+                             vertex_size_type vertex_count,
+                             edge_size_type edge_count,
+                             const edge_type* device_offsets,
+                             const vertex_type* device_neighbors,
+                             edge_size_type neighbors_count) {
+        _vertex_count = vertex_count;
+        _edge_count = edge_count;
+        _rows = edge_set::wrap(queue, device_offsets, vertex_count + 1);
+        _cols = vertex_set::wrap(queue, device_neighbors, neighbors_count);
+        _rows_ptr = _rows.get_data();
+        _cols_ptr = _cols.get_data();
+        _degrees_ptr = nullptr;
+    }
+
+    topology<IndexType> to_device(sycl::queue& queue) const {
+        topology<IndexType> result;
+        result._vertex_count = _vertex_count;
+        result._edge_count = _edge_count;
+
+        const auto rows_count = _vertex_count + 1;
+        const auto cols_count = _cols.get_count();
+
+        auto device_rows = edge_set::empty(queue, rows_count, sycl::usm::alloc::device);
+        auto device_cols = vertex_set::empty(queue, cols_count, sycl::usm::alloc::device);
+
+        auto e1 = queue.memcpy(device_rows.get_mutable_data(), _rows.get_data(),
+                               rows_count * sizeof(edge_type));
+        auto e2 = queue.memcpy(device_cols.get_mutable_data(), _cols.get_data(),
+                               cols_count * sizeof(vertex_type));
+        e1.wait_and_throw();
+        e2.wait_and_throw();
+
+        result._rows = device_rows;
+        result._cols = device_cols;
+        result._rows_ptr = result._rows.get_data();
+        result._cols_ptr = result._cols.get_data();
+        result._degrees_ptr = nullptr;
+        return result;
+    }
+#endif
+
     vertex_set _cols;
     vertex_set _degrees;
     edge_set _rows;
     vertex_edge_set _rows_vertex;
 
-    const vertex_type* _cols_ptr;
-    const vertex_type* _degrees_ptr;
-    const edge_type* _rows_ptr;
+    const vertex_type* _cols_ptr = nullptr;
+    const vertex_type* _degrees_ptr = nullptr;
+    const edge_type* _rows_ptr = nullptr;
 
     std::int64_t _vertex_count = 0;
     std::int64_t _edge_count = 0;
diff --git a/cpp/oneapi/dal/graph/detail/device_csr_topology.hpp b/cpp/oneapi/dal/graph/detail/device_csr_topology.hpp
new file mode 100644
index 00000000000..2ad2770b1ba
--- /dev/null
+++ b/cpp/oneapi/dal/graph/detail/device_csr_topology.hpp
@@ -0,0 +1,265 @@
+/*******************************************************************************
+* Copyright 2020 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#pragma once
+
+#ifdef ONEDAL_DATA_PARALLEL
+
+#include <sycl/sycl.hpp>
+
+#include "oneapi/dal/array.hpp"
+#include "oneapi/dal/graph/detail/csr_topology.hpp"
+
+namespace oneapi::dal::preview::detail {
+
+/// A device-resident CSR topology that holds row offsets, column indices,
+/// and optionally edge weights as dal::array objects in device USM memory.
+///
+/// Row offsets are stored as int64 (matching the host topology) and column
+/// indices as IndexType (typically int32). Edge weights are optional —
+/// set WeightType to void (default) for unweighted graphs.
+///
+/// Construct via \ref topology_to_device() or \ref topology_to_host().
+template <typename IndexType = std::int32_t, typename WeightType = void>
+class device_csr_topology {
+public:
+    using index_type = IndexType;
+    using weight_type = WeightType;
+
+    device_csr_topology() = default;
+
+    /// Construct an unweighted device topology.
+    device_csr_topology(dal::array<std::int64_t> device_rows,
+                        dal::array<IndexType> device_cols,
+                        std::int64_t vertex_count,
+                        std::int64_t edge_count)
+            : rows_(std::move(device_rows)),
+              cols_(std::move(device_cols)),
+              vertex_count_(vertex_count),
+              edge_count_(edge_count) {}
+
+    /// Construct a weighted device topology.
+    device_csr_topology(dal::array<std::int64_t> device_rows,
+                        dal::array<IndexType> device_cols,
+                        dal::array<WeightType> device_weights,
+                        std::int64_t vertex_count,
+                        std::int64_t edge_count)
+            : rows_(std::move(device_rows)),
+              cols_(std::move(device_cols)),
+              weights_(std::move(device_weights)),
+              vertex_count_(vertex_count),
+              edge_count_(edge_count) {}
+
+    /// Pointer to device-resident row offsets (vertex_count + 1 entries).
+    const std::int64_t* get_rows() const {
+        return rows_.get_data();
+    }
+
+    /// Pointer to device-resident column indices (2 * edge_count entries).
+    const IndexType* get_cols() const {
+        return cols_.get_data();
+    }
+
+    /// Pointer to device-resident edge weights (2 * edge_count entries),
+    /// or nullptr if the graph is unweighted.
+    const WeightType* get_weights() const {
+        return weights_.get_count() > 0 ? weights_.get_data() : nullptr;
+    }
+
+    std::int64_t get_vertex_count() const {
+        return vertex_count_;
+    }
+
+    std::int64_t get_edge_count() const {
+        return edge_count_;
+    }
+
+    /// Returns the underlying device array for row offsets.
+    const dal::array<std::int64_t>& get_rows_array() const {
+        return rows_;
+    }
+
+    /// Returns the underlying device array for column indices.
+    const dal::array<IndexType>& get_cols_array() const {
+        return cols_;
+    }
+
+    /// Returns the underlying device array for edge weights.
+    const dal::array<WeightType>& get_weights_array() const {
+        return weights_;
+    }
+
+private:
+    dal::array<std::int64_t> rows_;
+    dal::array<IndexType> cols_;
+    dal::array<WeightType> weights_;
+    std::int64_t vertex_count_ = 0;
+    std::int64_t edge_count_ = 0;
+};
+
+/// Specialization for unweighted graphs (WeightType = void).
+/// This preserves full backward compatibility with existing code.
+template <typename IndexType>
+class device_csr_topology<IndexType, void> {
+public:
+    using index_type = IndexType;
+    using weight_type = void;
+
+    device_csr_topology() = default;
+
+    device_csr_topology(dal::array<std::int64_t> device_rows,
+                        dal::array<IndexType> device_cols,
+                        std::int64_t vertex_count,
+                        std::int64_t edge_count)
+            : rows_(std::move(device_rows)),
+              cols_(std::move(device_cols)),
+              vertex_count_(vertex_count),
+              edge_count_(edge_count) {}
+
+    /// Pointer to device-resident row offsets (vertex_count + 1 entries).
+    const std::int64_t* get_rows() const {
+        return rows_.get_data();
+    }
+
+    /// Pointer to device-resident column indices (2 * edge_count entries).
+    const IndexType* get_cols() const {
+        return cols_.get_data();
+    }
+
+    std::int64_t get_vertex_count() const {
+        return vertex_count_;
+    }
+
+    std::int64_t get_edge_count() const {
+        return edge_count_;
+    }
+
+    /// Returns the underlying device array for row offsets.
+    const dal::array<std::int64_t>& get_rows_array() const {
+        return rows_;
+    }
+
+    /// Returns the underlying device array for column indices.
+    const dal::array<IndexType>& get_cols_array() const {
+        return cols_;
+    }
+
+private:
+    dal::array<std::int64_t> rows_;
+    dal::array<IndexType> cols_;
+    std::int64_t vertex_count_ = 0;
+    std::int64_t edge_count_ = 0;
+};
+
+/// Transfers a host topology to device memory.
+/// Row offsets are kept as int64, column indices as IndexType.
+///
+/// @tparam IndexType  The index type for column indices (default int32)
+/// @param queue       SYCL queue identifying the target device
+/// @param host_topo   Host-resident CSR topology
+/// @return A device_csr_topology with arrays in device USM memory
+template <typename IndexType = std::int32_t>
+device_csr_topology<IndexType> topology_to_device(sycl::queue& queue,
+                                                  const topology<IndexType>& host_topo) {
+    const auto vertex_count = host_topo.get_vertex_count();
+    const auto edge_count = host_topo.get_edge_count();
+
+    if (vertex_count == 0) {
+        return device_csr_topology<IndexType>();
+    }
+
+    const std::int64_t rows_count = vertex_count + 1;
+    const std::int64_t cols_count = host_topo._cols.get_count();
+
+    // Transfer column indices (IndexType -> IndexType) to device
+    dal::array<IndexType> device_cols;
+    if (cols_count > 0) {
+        device_cols =
+            dal::array<IndexType>::empty(queue, cols_count, sycl::usm::alloc::device);
+        queue.memcpy(device_cols.get_mutable_data(),
+                     host_topo._cols.get_data(),
+                     cols_count * sizeof(IndexType))
+            .wait_and_throw();
+    }
+
+    // Transfer row offsets (int64 -> int64) to device
+    auto device_rows =
+        dal::array<std::int64_t>::empty(queue, rows_count, sycl::usm::alloc::device);
+    queue.memcpy(device_rows.get_mutable_data(),
+                 host_topo._rows.get_data(),
+                 rows_count * sizeof(std::int64_t))
+        .wait_and_throw();
+
+    return device_csr_topology<IndexType>(std::move(device_rows),
+                                          std::move(device_cols),
+                                          vertex_count,
+                                          edge_count);
+}
+
+/// Transfers a device_csr_topology back to a host topology.
+///
+/// @tparam IndexType  The index type for column indices
+/// @param device_topo Device-resident CSR topology
+/// @return A host topology with arrays in host memory
+template <typename IndexType = std::int32_t>
+topology<IndexType> topology_to_host(const device_csr_topology<IndexType>& device_topo) {
+    const auto vertex_count = device_topo.get_vertex_count();
+    const auto edge_count = device_topo.get_edge_count();
+
+    if (vertex_count == 0) {
+        return topology<IndexType>();
+    }
+
+    const std::int64_t rows_count = vertex_count + 1;
+    const std::int64_t cols_count = device_topo.get_cols_array().get_count();
+
+    auto host_cols = dal::array<IndexType>::empty(cols_count);
+    auto host_rows = dal::array<std::int64_t>::empty(rows_count);
+
+    // Retrieve the queue from the device arrays
+    auto q = device_topo.get_cols_array().get_queue().value();
+    q.memcpy(host_cols.get_mutable_data(),
+             device_topo.get_cols(),
+             cols_count * sizeof(IndexType))
+        .wait_and_throw();
+    q.memcpy(host_rows.get_mutable_data(),
+             device_topo.get_rows(),
+             rows_count * sizeof(std::int64_t))
+        .wait_and_throw();
+
+    // Build degrees from row offsets
+    auto host_degrees = dal::array<IndexType>::empty(vertex_count);
+    auto* deg = host_degrees.get_mutable_data();
+    const auto* rows_data = host_rows.get_data();
+    for (std::int64_t i = 0; i < vertex_count; ++i) {
+        deg[i] = static_cast<IndexType>(rows_data[i + 1] - rows_data[i]);
+    }
+
+    topology<IndexType> result;
+    result._vertex_count = vertex_count;
+    result._edge_count = edge_count;
+    result._rows = std::move(host_rows);
+    result._cols = std::move(host_cols);
+    result._degrees = std::move(host_degrees);
+    result._rows_ptr = result._rows.get_data();
+    result._cols_ptr = result._cols.get_data();
+    result._degrees_ptr = result._degrees.get_data();
+    return result;
+}
+
+} // namespace oneapi::dal::preview::detail
+
+#endif // ONEDAL_DATA_PARALLEL
diff --git a/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp b/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp
index 3ec705a748f..70f9d89a36e 100644
--- a/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp
+++ b/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp
@@ -108,6 +108,43 @@ class ONEDAL_EXPORT undirected_adjacency_vector_graph_impl {
         return _topology;
     }
 
+#ifdef ONEDAL_DATA_PARALLEL
+    inline void to_device(sycl::queue& queue) {
+        const auto* ptr = _topology._rows.get_data();
+        if (ptr != nullptr) {
+            auto alloc_type = sycl::get_pointer_type(ptr, queue.get_context());
+            if (alloc_type == sycl::usm::alloc::unknown || alloc_type == sycl::usm::alloc::host) {
+                _topology = _topology.to_device(queue);
+            }
+        }
+
+        if constexpr (!std::is_same_v<VertexValue, empty_value>) {
+            transfer_array_to_device(queue, _vertex_values);
+        }
+
+        if constexpr (!std::is_same_v<EdgeValue, empty_value>) {
+            transfer_array_to_device(queue, _edge_values);
+        }
+    }
+
+private:
+    template <typename T>
+    static void transfer_array_to_device(sycl::queue& queue, container<T>& arr) {
+        const auto count = arr.get_count();
+        if (count == 0) return;
+        const auto* src = arr.get_data();
+        auto alloc_type = sycl::get_pointer_type(src, queue.get_context());
+        if (alloc_type == sycl::usm::alloc::device || alloc_type == sycl::usm::alloc::shared) {
+            return;
+        }
+        auto device_arr = container<T>::empty(queue, count, sycl::usm::alloc::device);
+        queue.memcpy(device_arr.get_mutable_data(), src, count * sizeof(T)).wait_and_throw();
+        arr = device_arr;
+    }
+
+public:
+#endif
+
     inline vertex_values<VertexValue>& get_vertex_values() {
         return _vertex_values;
     }
diff --git a/cpp/oneapi/dal/graph/undirected_adjacency_vector_graph.hpp b/cpp/oneapi/dal/graph/undirected_adjacency_vector_graph.hpp
index 01b823ea87c..b278382edb8 100644
--- a/cpp/oneapi/dal/graph/undirected_adjacency_vector_graph.hpp
+++ b/cpp/oneapi/dal/graph/undirected_adjacency_vector_graph.hpp
@@ -61,6 +61,13 @@ class ONEDAL_EXPORT undirected_adjacency_vector_graph {
     /// Swaps the implementation of this object and another one
     undirected_adjacency_vector_graph &operator=(undirected_adjacency_vector_graph &&other);
 
+#ifdef ONEDAL_DATA_PARALLEL
+    /// Transfers graph data to device memory associated with the given queue
+    void to_device(sycl::queue& queue) {
+        dal::detail::pimpl_accessor{}.get_pimpl(*this)->to_device(queue);
+    }
+#endif
+
 private:
     using pimpl = dal::detail::pimpl<typename graph_traits<graph_type>::impl_type>;
 
diff --git a/cpp/oneapi/dal/vertex_ranking.hpp b/cpp/oneapi/dal/vertex_ranking.hpp
index d2c797d73bf..9d83cef4da0 100644
--- a/cpp/oneapi/dal/vertex_ranking.hpp
+++ b/cpp/oneapi/dal/vertex_ranking.hpp
@@ -30,4 +30,16 @@ auto vertex_ranking(Args &&...args) {
     return detail::vertex_ranking_dispatch(std::forward<Args>(args)...);
 }
 
+#ifdef ONEDAL_DATA_PARALLEL
+/// Overload that accepts a SYCL queue for GPU execution
+///
+/// @param q     SYCL queue specifying the target device
+/// @param args  Algorithm descriptor and input graph
+template <typename... Args>
+auto vertex_ranking(sycl::queue& q, Args &&...args) {
+    const auto policy = dal::detail::data_parallel_policy{ q };
+    return detail::vertex_ranking_dispatch(policy, std::forward<Args>(args)...);
+}
+#endif
+
 } // namespace oneapi::dal::preview
diff --git a/examples/oneapi/cpp/source/triangle_counting/triangle_counting_batch.cpp b/examples/oneapi/cpp/source/triangle_counting/triangle_counting_batch.cpp
index 42e365df8e3..3ff621b60ef 100644
--- a/examples/oneapi/cpp/source/triangle_counting/triangle_counting_batch.cpp
+++ b/examples/oneapi/cpp/source/triangle_counting/triangle_counting_batch.cpp
@@ -14,6 +14,7 @@
 * limitations under the License.
 *******************************************************************************/
 
+#include <chrono>
 #include <memory>
 
 #include "example_util/utils.hpp"
@@ -34,7 +35,11 @@ int main(int argc, char** argv) {
     const auto tc_desc = descriptor<float, method::ordered_count, task::local_and_global>();
 
     // compute local and global triangles
+    const auto t1 = std::chrono::steady_clock::now();
     const auto result_vertex_ranking = dal::preview::vertex_ranking(tc_desc, graph);
+    const auto t2 = std::chrono::steady_clock::now();
+    const auto dt = std::chrono::duration_cast<std::chrono::milliseconds>(t2 - t1).count();
+    std::cout << "Triangle counting compute time: " << dt << " ms" << std::endl;
 
     // extract the result
     std::cout << "Global triangles: " << result_vertex_ranking.get_global_rank() << std::endl;
diff --git a/examples/oneapi/dpc/BUILD b/examples/oneapi/dpc/BUILD
index ad28e0bbf6f..42519af0c62 100644
--- a/examples/oneapi/dpc/BUILD
+++ b/examples/oneapi/dpc/BUILD
@@ -68,6 +68,7 @@ dal_algo_example_suite(
         "pca",
         "rbf_kernel",
         "svm",
+        "triangle_counting",
     ],
     compile_as = [ "dpc++" ],
     data = _DATA_DEPS,
diff --git a/examples/oneapi/dpc/source/triangle_counting/triangle_counting_batch.cpp b/examples/oneapi/dpc/source/triangle_counting/triangle_counting_batch.cpp
new file mode 100644
index 00000000000..4f7ed528949
--- /dev/null
+++ b/examples/oneapi/dpc/source/triangle_counting/triangle_counting_batch.cpp
@@ -0,0 +1,67 @@
+/*******************************************************************************
+* Copyright 2020 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#include <sycl/sycl.hpp>
+#include <iomanip>
+#include <iostream>
+#include <memory>
+
+#ifndef ONEDAL_DATA_PARALLEL
+#define ONEDAL_DATA_PARALLEL
+#endif
+
+#include "oneapi/dal/algo/triangle_counting.hpp"
+#include "oneapi/dal/graph/undirected_adjacency_vector_graph.hpp"
+#include "oneapi/dal/io/csv.hpp"
+
+#include "example_util/utils.hpp"
+
+namespace dal = oneapi::dal;
+using namespace dal::preview::triangle_counting;
+
+void run(sycl::queue& q) {
+    const auto filename = get_data_path("data/graph.csv");
+
+    using graph_t = dal::preview::undirected_adjacency_vector_graph<>;
+    auto graph = dal::read<graph_t>(dal::csv::data_source{ filename });
+
+    graph.to_device(q);
+
+    const auto tc_desc = descriptor<float, method::ordered_count, task::local_and_global>();
+
+    const auto result = dal::preview::vertex_ranking(q, tc_desc, graph);
+
+    std::cout << "Global triangles: " << result.get_global_rank() << std::endl;
+    std::cout << "Local triangles:" << std::endl;
+
+    auto local_triangles_table = result.get_ranks();
+    const auto& local_triangles = static_cast<const dal::homogen_table&>(local_triangles_table);
+    const auto local_triangles_data = local_triangles.get_data<std::int64_t>();
+    for (auto i = 0; i < local_triangles_table.get_row_count(); i++) {
+        std::cout << i << ":\t" << local_triangles_data[i] << std::endl;
+    }
+}
+
+int main(int argc, char const* argv[]) {
+    for (auto d : list_devices()) {
+        std::cout << "Running on " << d.get_platform().get_info<sycl::info::platform::name>()
+                  << ", " << d.get_info<sycl::info::device::name>() << "\n"
+                  << std::endl;
+        auto q = sycl::queue{ d };
+        run(q);
+    }
+    return 0;
+}

From 95fe2ce9dd5a7d3e8ea46a83607b41cd290f9258 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Sun, 10 May 2026 10:31:56 -0700
Subject: [PATCH 63/69] CI fix

---
 .../backend/gpu/CMakeLists.txt                |  16 ++
 .../backend/gpu/triangle_counting.hpp         |  16 ++
 .../vertex_ranking_default_kernel_gpu_dpc.cpp | 178 +++++++++---------
 .../backend/gpu/vertex_ranking_kernel.hpp     |  18 +-
 .../dal/algo/triangle_counting/common.hpp     |   2 +-
 .../detail/select_kernel.hpp                  |   7 +-
 .../detail/select_kernel_dpc.cpp              |  57 +++---
 .../detail/vertex_ranking_ops.hpp             |  10 +-
 .../test/triangle_counting_gpu_test.cpp       |  20 +-
 cpp/oneapi/dal/graph/detail/csr_topology.hpp  |   6 +-
 .../dal/graph/detail/device_csr_topology.hpp  |  26 ++-
 ...undirected_adjacency_vector_graph_impl.hpp |   3 +-
 .../undirected_adjacency_vector_graph.hpp     |   2 +-
 cpp/oneapi/dal/vertex_ranking.hpp             |   2 +-
 .../triangle_counting_batch.cpp               |   2 +-
 15 files changed, 201 insertions(+), 164 deletions(-)
 mode change 100755 => 100644 cpp/oneapi/dal/graph/detail/csr_topology.hpp

diff --git a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/CMakeLists.txt b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/CMakeLists.txt
index a7f81fe3901..7b397a68b92 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/CMakeLists.txt
+++ b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/CMakeLists.txt
@@ -1,3 +1,19 @@
+#===============================================================================
+# Copyright 2026 Intel Corporation
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#===============================================================================
+
 set(ONEDAL_TRIANGLE_COUNTING_BACKEND_GPU_HEADERS
     ${CMAKE_CURRENT_LIST_DIR}/triangle_counting.hpp
     ${CMAKE_CURRENT_LIST_DIR}/vertex_ranking_kernel.hpp
diff --git a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp
index a6c9dae0b66..6533d2bddef 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/triangle_counting.hpp
@@ -1,3 +1,19 @@
+/*******************************************************************************
+* Copyright 2026 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #pragma once
 
 #include "oneapi/dal/algo/triangle_counting/common.hpp"
diff --git a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_default_kernel_gpu_dpc.cpp b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_default_kernel_gpu_dpc.cpp
index 51dda423f24..4f7eb7a11f6 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_default_kernel_gpu_dpc.cpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_default_kernel_gpu_dpc.cpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2020 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
@@ -41,77 +41,79 @@ std::int64_t* count_triangles_gpu(sycl::queue& queue,
                                   const Index* cols,
                                   std::int64_t vertex_count,
                                   std::int64_t edge_count) {
-    auto* local_triangles =
-        sycl::malloc_shared<std::int64_t>(vertex_count, queue);
+    auto* local_triangles = sycl::malloc_shared<std::int64_t>(vertex_count, queue);
     queue.memset(local_triangles, 0, vertex_count * sizeof(std::int64_t)).wait_and_throw();
 
     // Parallel kernel: each work-item processes one vertex
-    queue.submit([&](sycl::handler& cgh) {
-        const std::int64_t* d_rows = rows;
-        const Index* d_cols = cols;
-        std::int64_t* d_triangles = local_triangles;
-        const std::int64_t vc = vertex_count;
-
-        cgh.parallel_for(sycl::range<1>(vc), [=](sycl::id<1> idx) {
-            const std::int64_t u = idx[0];
-            const std::int64_t u_start = d_rows[u];
-            const std::int64_t u_end = d_rows[u + 1];
-
-            std::int64_t count = 0;
-
-            // Iterate over each neighbor v of u where v > u
-            for (std::int64_t i = u_start; i < u_end; ++i) {
-                const std::int64_t v = d_cols[i];
-                if (v <= u) continue;
-
-                const std::int64_t v_start = d_rows[v];
-                const std::int64_t v_end = d_rows[v + 1];
-
-                // Merge-based intersection of neighbors of u and v
-                std::int64_t ui = u_start;
-                std::int64_t vi = v_start;
-                while (ui < u_end && vi < v_end) {
-                    const std::int64_t nu = d_cols[ui];
-                    const std::int64_t nv = d_cols[vi];
-                    if (nu == nv) {
-                        // Only count if common neighbor w > v to avoid
-                        // triple-counting the same triangle
-                        if (nu > v) {
-                            // Found a triangle (u, v, nu) with u < v < nu
-                            count++;
-                            // Atomically increment counts for v and the common neighbor
-                            sycl::atomic_ref<std::int64_t,
-                                             sycl::memory_order::relaxed,
-                                             sycl::memory_scope::device,
-                                             sycl::access::address_space::global_space>(
-                                d_triangles[v])
-                                .fetch_add(1);
-                            sycl::atomic_ref<std::int64_t,
-                                             sycl::memory_order::relaxed,
-                                             sycl::memory_scope::device,
-                                             sycl::access::address_space::global_space>(
-                                d_triangles[nu])
-                                .fetch_add(1);
+    queue
+        .submit([&](sycl::handler& cgh) {
+            const std::int64_t* d_rows = rows;
+            const Index* d_cols = cols;
+            std::int64_t* d_triangles = local_triangles;
+            const std::int64_t vc = vertex_count;
+
+            cgh.parallel_for(sycl::range<1>(vc), [=](sycl::id<1> idx) {
+                const std::int64_t u = idx[0];
+                const std::int64_t u_start = d_rows[u];
+                const std::int64_t u_end = d_rows[u + 1];
+
+                std::int64_t count = 0;
+
+                // Iterate over each neighbor v of u where v > u
+                for (std::int64_t i = u_start; i < u_end; ++i) {
+                    const std::int64_t v = d_cols[i];
+                    if (v <= u)
+                        continue;
+
+                    const std::int64_t v_start = d_rows[v];
+                    const std::int64_t v_end = d_rows[v + 1];
+
+                    // Merge-based intersection of neighbors of u and v
+                    std::int64_t ui = u_start;
+                    std::int64_t vi = v_start;
+                    while (ui < u_end && vi < v_end) {
+                        const std::int64_t nu = d_cols[ui];
+                        const std::int64_t nv = d_cols[vi];
+                        if (nu == nv) {
+                            // Only count if common neighbor w > v to avoid
+                            // triple-counting the same triangle
+                            if (nu > v) {
+                                // Found a triangle (u, v, nu) with u < v < nu
+                                count++;
+                                // Atomically increment counts for v and the common neighbor
+                                sycl::atomic_ref<std::int64_t,
+                                                 sycl::memory_order::relaxed,
+                                                 sycl::memory_scope::device,
+                                                 sycl::access::address_space::global_space>(
+                                    d_triangles[v])
+                                    .fetch_add(1);
+                                sycl::atomic_ref<std::int64_t,
+                                                 sycl::memory_order::relaxed,
+                                                 sycl::memory_scope::device,
+                                                 sycl::access::address_space::global_space>(
+                                    d_triangles[nu])
+                                    .fetch_add(1);
+                            }
+                            ++ui;
+                            ++vi;
+                        }
+                        else if (nu < nv) {
+                            ++ui;
+                        }
+                        else {
+                            ++vi;
                         }
-                        ++ui;
-                        ++vi;
-                    }
-                    else if (nu < nv) {
-                        ++ui;
-                    }
-                    else {
-                        ++vi;
                     }
                 }
-            }
-            // Add the count for vertex u
-            sycl::atomic_ref<std::int64_t,
-                             sycl::memory_order::relaxed,
-                             sycl::memory_scope::device,
-                             sycl::access::address_space::global_space>(d_triangles[u])
-                .fetch_add(count);
-        });
-    }).wait_and_throw();
+                // Add the count for vertex u
+                sycl::atomic_ref<std::int64_t,
+                                 sycl::memory_order::relaxed,
+                                 sycl::memory_scope::device,
+                                 sycl::access::address_space::global_space>(d_triangles[u])
+                    .fetch_add(count);
+            });
+        })
+        .wait_and_throw();
 
     return local_triangles;
 }
@@ -128,19 +130,21 @@ std::int64_t sum_triangles_gpu(sycl::queue& queue,
     auto* sum_buf = sycl::malloc_shared<std::int64_t>(1, queue);
     sum_buf[0] = 0;
 
-    queue.submit([&](sycl::handler& cgh) {
-        const std::int64_t* d_triangles = local_triangles;
-        std::int64_t* d_sum = sum_buf;
-        const std::int64_t vc = vertex_count;
-
-        cgh.parallel_for(sycl::range<1>(vc), [=](sycl::id<1> idx) {
-            sycl::atomic_ref<std::int64_t,
-                             sycl::memory_order::relaxed,
-                             sycl::memory_scope::device,
-                             sycl::access::address_space::global_space>(d_sum[0])
-                .fetch_add(d_triangles[idx[0]]);
-        });
-    }).wait_and_throw();
+    queue
+        .submit([&](sycl::handler& cgh) {
+            const std::int64_t* d_triangles = local_triangles;
+            std::int64_t* d_sum = sum_buf;
+            const std::int64_t vc = vertex_count;
+
+            cgh.parallel_for(sycl::range<1>(vc), [=](sycl::id<1> idx) {
+                sycl::atomic_ref<std::int64_t,
+                                 sycl::memory_order::relaxed,
+                                 sycl::memory_scope::device,
+                                 sycl::access::address_space::global_space>(d_sum[0])
+                    .fetch_add(d_triangles[idx[0]]);
+            });
+        })
+        .wait_and_throw();
 
     // Each triangle is counted 3 times (once per vertex)
     const std::int64_t result = sum_buf[0] / 3;
@@ -163,21 +167,23 @@ vertex_ranking_result<Task> run_vertex_ranking_gpu(const dal::backend::context_g
         return vertex_ranking_result<Task>();
     }
 
-    auto* local_triangles =
-        detail_gpu::count_triangles_gpu(queue, topology.rows, topology.cols,
-                                        vertex_count, edge_count);
+    auto* local_triangles = detail_gpu::count_triangles_gpu(queue,
+                                                            topology.rows,
+                                                            topology.cols,
+                                                            vertex_count,
+                                                            edge_count);
 
     vertex_ranking_result<Task> result;
 
     if constexpr (std::is_same_v<Task, task::local> ||
                   std::is_same_v<Task, task::local_and_global>) {
-        auto arr = array<std::int64_t>(queue, local_triangles, vertex_count,
+        auto arr = array<std::int64_t>(queue,
+                                       local_triangles,
+                                       vertex_count,
                                        [queue](std::int64_t* ptr) mutable {
                                            sycl::free(ptr, queue);
                                        });
-        result.set_ranks(dal::detail::homogen_table_builder{}
-                             .reset(arr, vertex_count, 1)
-                             .build());
+        result.set_ranks(dal::detail::homogen_table_builder{}.reset(arr, vertex_count, 1).build());
     }
 
     if constexpr (std::is_same_v<Task, task::global> ||
diff --git a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp
index e3e0b15da03..10eaa4ef23b 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/backend/gpu/vertex_ranking_kernel.hpp
@@ -1,3 +1,19 @@
+/*******************************************************************************
+* Copyright 2026 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
 #pragma once
 
 #include <cstdint>
@@ -19,7 +35,7 @@ struct csr_topology_gpu_view {
 /// Creates a GPU view from a device_csr_topology (zero-copy, just extracts pointers).
 template <typename Index = std::int32_t>
 csr_topology_gpu_view<Index> make_gpu_view(
-        const dal::preview::detail::device_csr_topology<Index>& device_topo) {
+    const dal::preview::detail::device_csr_topology<Index>& device_topo) {
     csr_topology_gpu_view<Index> view;
     view.rows = device_topo.get_rows();
     view.cols = device_topo.get_cols();
diff --git a/cpp/oneapi/dal/algo/triangle_counting/common.hpp b/cpp/oneapi/dal/algo/triangle_counting/common.hpp
index 2db9f54c9c6..e3782b3b5b9 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/common.hpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/common.hpp
@@ -146,7 +146,7 @@ struct is_device_csr_topology : std::false_type {};
 
 template <typename Index, typename Weight>
 struct is_device_csr_topology<dal::preview::detail::device_csr_topology<Index, Weight>>
-    : std::true_type {};
+        : std::true_type {};
 
 template <typename Graph>
 constexpr bool is_valid_graph =
diff --git a/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel.hpp b/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel.hpp
index 84ed6c67fe8..12a2f8ba81e 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel.hpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel.hpp
@@ -76,10 +76,9 @@ struct backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>
     using method_t = typename Descriptor::method_t;
     using allocator_t = typename Descriptor::allocator_t;
 
-    virtual vertex_ranking_result<task_t> operator()(
-        const dal::detail::data_parallel_policy& ctx,
-        const Descriptor& descriptor,
-        const Topology& t);
+    virtual vertex_ranking_result<task_t> operator()(const dal::detail::data_parallel_policy& ctx,
+                                                     const Descriptor& descriptor,
+                                                     const Topology& t);
 };
 #endif
 
diff --git a/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel_dpc.cpp b/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel_dpc.cpp
index 170e5ae41ec..2205be73cda 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel_dpc.cpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/detail/select_kernel_dpc.cpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2020 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
@@ -26,9 +26,9 @@ namespace oneapi::dal::preview::triangle_counting::detail {
 template <typename Descriptor, typename Topology>
 vertex_ranking_result<typename Descriptor::task_t>
 backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>::operator()(
-    const dal::detail::data_parallel_policy& ctx,
-    const Descriptor& descriptor,
-    const Topology& t) {
+    const dal::detail::data_parallel_policy &ctx,
+    const Descriptor &descriptor,
+    const Topology &t) {
     using float_t = typename Descriptor::float_t;
     using task_t = typename Descriptor::task_t;
     using method_t = typename Descriptor::method_t;
@@ -47,10 +47,9 @@ backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>::operat
         [&]() {
             // GPU path: delegate to GPU kernel
             dal::backend::context_gpu gpu_ctx{ ctx };
-            return backend::vertex_ranking_kernel_gpu<float_t, task_t, Topology>()(
-                gpu_ctx,
-                descriptor,
-                t);
+            return backend::vertex_ranking_kernel_gpu<float_t, task_t, Topology>()(gpu_ctx,
+                                                                                   descriptor,
+                                                                                   t);
         });
 }
 
@@ -59,11 +58,12 @@ backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>::operat
 
 template <typename Descriptor, typename Index>
 vertex_ranking_result<typename Descriptor::task_t>
-vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy, Descriptor,
-                              dal::preview::detail::device_csr_topology<Index>>::operator()(
-    const dal::detail::data_parallel_policy &policy,
-    const Descriptor &descriptor,
-    input_t &input) const {
+vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy,
+                              Descriptor,
+                              dal::preview::detail::device_csr_topology<Index>>::
+operator()(const dal::detail::data_parallel_policy &policy,
+           const Descriptor &descriptor,
+           input_t &input) const {
     using float_t = typename Descriptor::float_t;
     using task_t = typename Descriptor::task_t;
 
@@ -77,33 +77,22 @@ vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy, Descriptor,
 }
 
 // Explicit instantiations for supported descriptor/topology combinations
-using default_descriptor_local = descriptor<
-    float,
-    method::ordered_count,
-    task::local,
-    std::allocator<char>>;
+using default_descriptor_local =
+    descriptor<float, method::ordered_count, task::local, std::allocator<char>>;
 
-using default_descriptor_global = descriptor<
-    float,
-    method::ordered_count,
-    task::global,
-    std::allocator<char>>;
+using default_descriptor_global =
+    descriptor<float, method::ordered_count, task::global, std::allocator<char>>;
 
-using default_descriptor_local_and_global = descriptor<
-    float,
-    method::ordered_count,
-    task::local_and_global,
-    std::allocator<char>>;
+using default_descriptor_local_and_global =
+    descriptor<float, method::ordered_count, task::local_and_global, std::allocator<char>>;
 
 using default_topology = dal::preview::detail::topology<std::int32_t>;
 using device_topology = dal::preview::detail::device_csr_topology<std::int32_t>;
 
-template struct ONEDAL_EXPORT backend_default<dal::detail::data_parallel_policy,
-                                              default_descriptor_local,
-                                              default_topology>;
-template struct ONEDAL_EXPORT backend_default<dal::detail::data_parallel_policy,
-                                              default_descriptor_global,
-                                              default_topology>;
+template struct ONEDAL_EXPORT
+    backend_default<dal::detail::data_parallel_policy, default_descriptor_local, default_topology>;
+template struct ONEDAL_EXPORT
+    backend_default<dal::detail::data_parallel_policy, default_descriptor_global, default_topology>;
 template struct ONEDAL_EXPORT backend_default<dal::detail::data_parallel_policy,
                                               default_descriptor_local_and_global,
                                               default_topology>;
diff --git a/cpp/oneapi/dal/algo/triangle_counting/detail/vertex_ranking_ops.hpp b/cpp/oneapi/dal/algo/triangle_counting/detail/vertex_ranking_ops.hpp
index cef64393fb2..5c37ea52742 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/detail/vertex_ranking_ops.hpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/detail/vertex_ranking_ops.hpp
@@ -63,15 +63,15 @@ struct vertex_ranking_ops {
 /// Specialization for device_csr_topology: skips host-to-device transfer
 /// since the graph data is already on the device.
 template <typename Descriptor, typename Index>
-struct vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy, Descriptor,
+struct vertex_ranking_ops_dispatcher<dal::detail::data_parallel_policy,
+                                     Descriptor,
                                      dal::preview::detail::device_csr_topology<Index>> {
     using task_t = typename Descriptor::task_t;
     using input_t = vertex_ranking_input<dal::preview::detail::device_csr_topology<Index>, task_t>;
 
-    vertex_ranking_result<task_t> operator()(
-        const dal::detail::data_parallel_policy &policy,
-        const Descriptor &descriptor,
-        input_t &input) const;
+    vertex_ranking_result<task_t> operator()(const dal::detail::data_parallel_policy &policy,
+                                             const Descriptor &descriptor,
+                                             input_t &input) const;
 };
 #endif
 
diff --git a/cpp/oneapi/dal/algo/triangle_counting/test/triangle_counting_gpu_test.cpp b/cpp/oneapi/dal/algo/triangle_counting/test/triangle_counting_gpu_test.cpp
index c28cc2f0517..9705e4633b7 100644
--- a/cpp/oneapi/dal/algo/triangle_counting/test/triangle_counting_gpu_test.cpp
+++ b/cpp/oneapi/dal/algo/triangle_counting/test/triangle_counting_gpu_test.cpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2020 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
@@ -226,8 +226,7 @@ class triangle_counting_gpu_test {
         const auto result = dal::preview::vertex_ranking(q, tc_desc, g);
 
         const auto local_triangles_table = result.get_ranks();
-        const auto& local_triangles =
-            static_cast<const dal::homogen_table&>(local_triangles_table);
+        const auto& local_triangles = static_cast<const dal::homogen_table&>(local_triangles_table);
         const auto local_triangles_data = local_triangles.get_data<std::int64_t>();
 
         REQUIRE(local_triangles_table.get_row_count() == vertex_count);
@@ -260,8 +259,7 @@ class triangle_counting_gpu_test {
         const auto result = dal::preview::vertex_ranking(q, tc_desc, g);
 
         const auto local_triangles_table = result.get_ranks();
-        const auto& local_triangles =
-            static_cast<const dal::homogen_table&>(local_triangles_table);
+        const auto& local_triangles = static_cast<const dal::homogen_table&>(local_triangles_table);
         const auto local_triangles_data = local_triangles.get_data<std::int64_t>();
 
         REQUIRE(result.get_global_rank() == global_triangle_count);
@@ -335,8 +333,7 @@ TEST_M(triangle_counting_gpu_test, "GPU: Null graph - local task") {
         std::allocator<char>>(alloc);
 
     const auto result = dal::preview::vertex_ranking(q, tc_desc, null_graph);
-    const auto& local_triangles =
-        static_cast<const dal::homogen_table&>(result.get_ranks());
+    const auto& local_triangles = static_cast<const dal::homogen_table&>(result.get_ranks());
     REQUIRE(local_triangles.has_data() == false);
 }
 
@@ -367,8 +364,7 @@ TEST_M(triangle_counting_gpu_test, "GPU: Null graph - local_and_global task") {
         std::allocator<char>>(alloc);
 
     const auto result = dal::preview::vertex_ranking(q, tc_desc, null_graph);
-    const auto& local_triangles =
-        static_cast<const dal::homogen_table&>(result.get_ranks());
+    const auto& local_triangles = static_cast<const dal::homogen_table&>(result.get_ranks());
     REQUIRE(local_triangles.has_data() == false);
     REQUIRE(result.get_global_rank() == 0);
 }
@@ -381,8 +377,7 @@ TEST_M(triangle_counting_gpu_test, "GPU: topology_to_device round-trip") {
     const auto& topo = oneapi::dal::detail::get_impl(g).get_topology();
 
     // Transfer topology to device
-    auto device_topo =
-        dal::preview::detail::topology_to_device<std::int32_t>(q, topo);
+    auto device_topo = dal::preview::detail::topology_to_device<std::int32_t>(q, topo);
 
     REQUIRE(device_topo.get_vertex_count() == 5);
     REQUIRE(device_topo.get_edge_count() == 10);
@@ -411,8 +406,7 @@ TEST_M(triangle_counting_gpu_test, "GPU: Empty topology round-trip") {
 
     dal::preview::detail::topology<std::int32_t> empty_topo;
 
-    auto device_topo =
-        dal::preview::detail::topology_to_device<std::int32_t>(q, empty_topo);
+    auto device_topo = dal::preview::detail::topology_to_device<std::int32_t>(q, empty_topo);
 
     REQUIRE(device_topo.get_vertex_count() == 0);
     REQUIRE(device_topo.get_edge_count() == 0);
diff --git a/cpp/oneapi/dal/graph/detail/csr_topology.hpp b/cpp/oneapi/dal/graph/detail/csr_topology.hpp
old mode 100755
new mode 100644
index 8606a9963ed..78fdf0d5d81
--- a/cpp/oneapi/dal/graph/detail/csr_topology.hpp
+++ b/cpp/oneapi/dal/graph/detail/csr_topology.hpp
@@ -156,9 +156,11 @@ class topology {
         auto device_rows = edge_set::empty(queue, rows_count, sycl::usm::alloc::device);
         auto device_cols = vertex_set::empty(queue, cols_count, sycl::usm::alloc::device);
 
-        auto e1 = queue.memcpy(device_rows.get_mutable_data(), _rows.get_data(),
+        auto e1 = queue.memcpy(device_rows.get_mutable_data(),
+                               _rows.get_data(),
                                rows_count * sizeof(edge_type));
-        auto e2 = queue.memcpy(device_cols.get_mutable_data(), _cols.get_data(),
+        auto e2 = queue.memcpy(device_cols.get_mutable_data(),
+                               _cols.get_data(),
                                cols_count * sizeof(vertex_type));
         e1.wait_and_throw();
         e2.wait_and_throw();
diff --git a/cpp/oneapi/dal/graph/detail/device_csr_topology.hpp b/cpp/oneapi/dal/graph/detail/device_csr_topology.hpp
index 2ad2770b1ba..9dc3f9d0fc7 100644
--- a/cpp/oneapi/dal/graph/detail/device_csr_topology.hpp
+++ b/cpp/oneapi/dal/graph/detail/device_csr_topology.hpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2020 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
@@ -187,20 +187,20 @@ device_csr_topology<IndexType> topology_to_device(sycl::queue& queue,
     // Transfer column indices (IndexType -> IndexType) to device
     dal::array<IndexType> device_cols;
     if (cols_count > 0) {
-        device_cols =
-            dal::array<IndexType>::empty(queue, cols_count, sycl::usm::alloc::device);
-        queue.memcpy(device_cols.get_mutable_data(),
-                     host_topo._cols.get_data(),
-                     cols_count * sizeof(IndexType))
+        device_cols = dal::array<IndexType>::empty(queue, cols_count, sycl::usm::alloc::device);
+        queue
+            .memcpy(device_cols.get_mutable_data(),
+                    host_topo._cols.get_data(),
+                    cols_count * sizeof(IndexType))
             .wait_and_throw();
     }
 
     // Transfer row offsets (int64 -> int64) to device
-    auto device_rows =
-        dal::array<std::int64_t>::empty(queue, rows_count, sycl::usm::alloc::device);
-    queue.memcpy(device_rows.get_mutable_data(),
-                 host_topo._rows.get_data(),
-                 rows_count * sizeof(std::int64_t))
+    auto device_rows = dal::array<std::int64_t>::empty(queue, rows_count, sycl::usm::alloc::device);
+    queue
+        .memcpy(device_rows.get_mutable_data(),
+                host_topo._rows.get_data(),
+                rows_count * sizeof(std::int64_t))
         .wait_and_throw();
 
     return device_csr_topology<IndexType>(std::move(device_rows),
@@ -231,9 +231,7 @@ topology<IndexType> topology_to_host(const device_csr_topology<IndexType>& devic
 
     // Retrieve the queue from the device arrays
     auto q = device_topo.get_cols_array().get_queue().value();
-    q.memcpy(host_cols.get_mutable_data(),
-             device_topo.get_cols(),
-             cols_count * sizeof(IndexType))
+    q.memcpy(host_cols.get_mutable_data(), device_topo.get_cols(), cols_count * sizeof(IndexType))
         .wait_and_throw();
     q.memcpy(host_rows.get_mutable_data(),
              device_topo.get_rows(),
diff --git a/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp b/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp
index 70f9d89a36e..f5cbd79d135 100644
--- a/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp
+++ b/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp
@@ -131,7 +131,8 @@ class ONEDAL_EXPORT undirected_adjacency_vector_graph_impl {
     template <typename T>
     static void transfer_array_to_device(sycl::queue& queue, container<T>& arr) {
         const auto count = arr.get_count();
-        if (count == 0) return;
+        if (count == 0)
+            return;
         const auto* src = arr.get_data();
         auto alloc_type = sycl::get_pointer_type(src, queue.get_context());
         if (alloc_type == sycl::usm::alloc::device || alloc_type == sycl::usm::alloc::shared) {
diff --git a/cpp/oneapi/dal/graph/undirected_adjacency_vector_graph.hpp b/cpp/oneapi/dal/graph/undirected_adjacency_vector_graph.hpp
index b278382edb8..d8486badb08 100644
--- a/cpp/oneapi/dal/graph/undirected_adjacency_vector_graph.hpp
+++ b/cpp/oneapi/dal/graph/undirected_adjacency_vector_graph.hpp
@@ -63,7 +63,7 @@ class ONEDAL_EXPORT undirected_adjacency_vector_graph {
 
 #ifdef ONEDAL_DATA_PARALLEL
     /// Transfers graph data to device memory associated with the given queue
-    void to_device(sycl::queue& queue) {
+    void to_device(sycl::queue &queue) {
         dal::detail::pimpl_accessor{}.get_pimpl(*this)->to_device(queue);
     }
 #endif
diff --git a/cpp/oneapi/dal/vertex_ranking.hpp b/cpp/oneapi/dal/vertex_ranking.hpp
index 9d83cef4da0..2b2e2613c98 100644
--- a/cpp/oneapi/dal/vertex_ranking.hpp
+++ b/cpp/oneapi/dal/vertex_ranking.hpp
@@ -36,7 +36,7 @@ auto vertex_ranking(Args &&...args) {
 /// @param q     SYCL queue specifying the target device
 /// @param args  Algorithm descriptor and input graph
 template <typename... Args>
-auto vertex_ranking(sycl::queue& q, Args &&...args) {
+auto vertex_ranking(sycl::queue &q, Args &&...args) {
     const auto policy = dal::detail::data_parallel_policy{ q };
     return detail::vertex_ranking_dispatch(policy, std::forward<Args>(args)...);
 }
diff --git a/examples/oneapi/dpc/source/triangle_counting/triangle_counting_batch.cpp b/examples/oneapi/dpc/source/triangle_counting/triangle_counting_batch.cpp
index 4f7ed528949..e88dbf2291a 100644
--- a/examples/oneapi/dpc/source/triangle_counting/triangle_counting_batch.cpp
+++ b/examples/oneapi/dpc/source/triangle_counting/triangle_counting_batch.cpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2020 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.

From 53bf004d26919211eb91fc3ea4e83fa4199bb1dc Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 5 May 2026 18:57:38 -0700
Subject: [PATCH 64/69] CC gpu

---
 .../dal/algo/connected_components/BUILD       |   19 +-
 .../backend/gpu/CMakeLists.txt                |    5 +
 .../backend/gpu/connected_components.hpp      |   32 +
 ...ex_partitioning_default_kernel_gpu_dpc.cpp |  298 +++
 .../gpu/vertex_partitioning_kernel.hpp        |   52 +
 .../detail/select_kernel.hpp                  |   40 +-
 .../detail/select_kernel_dpc.cpp              |   64 +
 .../vertex_partitioning_default_kernel.hpp    |   21 +
 .../detail/vertex_partitioning_ops.hpp        |   10 +-
 .../test/connected_components_gpu_test.cpp    |  278 +++
 .../dal/detail/vertex_partitioning_ops.hpp    |   20 +
 cpp/oneapi/dal/graph/detail/csr_topology.hpp  |   24 +-
 ...undirected_adjacency_vector_graph_impl.hpp |    2 +-
 cpp/oneapi/dal/vertex_partitioning.hpp        |    8 +
 examples/oneapi/dpc/BUILD                     |    1 +
 .../connected_components_batch                |  Bin 0 -> 511008 bytes
 .../intel_intel64_so/triangle_counting_batch  |  Bin 0 -> 515016 bytes
 examples/oneapi/dpc/build/Makefile            | 1944 +++++++++++++++++
 examples/oneapi/dpc/build/cmake_install.cmake |   54 +
 .../connected_components_batch.cpp            |   58 +
 20 files changed, 2913 insertions(+), 17 deletions(-)
 create mode 100644 cpp/oneapi/dal/algo/connected_components/backend/gpu/CMakeLists.txt
 create mode 100644 cpp/oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp
 create mode 100644 cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_default_kernel_gpu_dpc.cpp
 create mode 100644 cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_kernel.hpp
 create mode 100644 cpp/oneapi/dal/algo/connected_components/detail/select_kernel_dpc.cpp
 create mode 100644 cpp/oneapi/dal/algo/connected_components/test/connected_components_gpu_test.cpp
 create mode 100755 examples/oneapi/dpc/_cmake_results/intel_intel64_so/connected_components_batch
 create mode 100755 examples/oneapi/dpc/_cmake_results/intel_intel64_so/triangle_counting_batch
 create mode 100644 examples/oneapi/dpc/build/Makefile
 create mode 100644 examples/oneapi/dpc/build/cmake_install.cmake
 create mode 100644 examples/oneapi/dpc/source/connected_components/connected_components_batch.cpp

diff --git a/cpp/oneapi/dal/algo/connected_components/BUILD b/cpp/oneapi/dal/algo/connected_components/BUILD
index 8e7d9b35a5c..3ecf4190d9b 100755
--- a/cpp/oneapi/dal/algo/connected_components/BUILD
+++ b/cpp/oneapi/dal/algo/connected_components/BUILD
@@ -10,14 +10,31 @@ dal_module(
     dal_deps = [
         "@onedal//cpp/oneapi/dal:core",
         "@onedal//cpp/oneapi/dal/backend/primitives:rng",
-    ]
+        "@onedal//cpp/oneapi/dal/backend/primitives:frontier",
+    ],
 )
 
 dal_test_suite(
     name = "tests",
+    tests = [],
     framework = "catch2",
     srcs = glob([
         "test/*.cpp",
+    ],
+    exclude = [
+        "test/*_gpu_test.cpp",
+    ]),
+    dal_deps = [
+        ":connected_components",
+    ],
+)
+
+dal_test_suite(
+    name = "gpu_tests",
+    framework = "catch2",
+    compile_as = [ "dpc++" ],
+    srcs = glob([
+        "test/*_gpu_test.cpp",
     ]),
     dal_deps = [
         ":connected_components",
diff --git a/cpp/oneapi/dal/algo/connected_components/backend/gpu/CMakeLists.txt b/cpp/oneapi/dal/algo/connected_components/backend/gpu/CMakeLists.txt
new file mode 100644
index 00000000000..105230f978f
--- /dev/null
+++ b/cpp/oneapi/dal/algo/connected_components/backend/gpu/CMakeLists.txt
@@ -0,0 +1,5 @@
+set(ONEDAL_CONNECTED_COMPONENTS_BACKEND_GPU_HEADERS
+    ${CMAKE_CURRENT_LIST_DIR}/connected_components.hpp
+    ${CMAKE_CURRENT_LIST_DIR}/vertex_partitioning_kernel.hpp
+    PARENT_SCOPE
+)
diff --git a/cpp/oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp b/cpp/oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp
new file mode 100644
index 00000000000..1d8fb2ed78d
--- /dev/null
+++ b/cpp/oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp
@@ -0,0 +1,32 @@
+/*******************************************************************************
+* Copyright 2021 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#pragma once
+
+#include "oneapi/dal/algo/connected_components/common.hpp"
+#include "oneapi/dal/algo/connected_components/vertex_partitioning_types.hpp"
+#include "oneapi/dal/backend/dispatcher.hpp"
+
+namespace oneapi::dal::preview::connected_components::backend {
+
+template <typename Float, typename Task, typename Topology>
+struct vertex_partitioning_kernel_gpu {
+    vertex_partitioning_result<Task> operator()(const dal::backend::context_gpu& ctx,
+                                                const detail::descriptor_base<Task>& desc,
+                                                const Topology& topology) const;
+};
+
+} // namespace oneapi::dal::preview::connected_components::backend
diff --git a/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_default_kernel_gpu_dpc.cpp b/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_default_kernel_gpu_dpc.cpp
new file mode 100644
index 00000000000..aa686630e46
--- /dev/null
+++ b/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_default_kernel_gpu_dpc.cpp
@@ -0,0 +1,298 @@
+/*******************************************************************************
+* Copyright 2021 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#include <sycl/sycl.hpp>
+
+#include "oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp"
+#include "oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_kernel.hpp"
+#include "oneapi/dal/backend/dispatcher.hpp"
+#include "oneapi/dal/table/detail/table_builder.hpp"
+#include "oneapi/dal/backend/primitives/frontier.hpp"
+#include "oneapi/dal/graph/detail/device_csr_topology.hpp"
+
+namespace oneapi::dal::preview::connected_components::backend {
+
+namespace fp = oneapi::dal::preview::backend::primitives;
+
+namespace detail_gpu {
+
+template <typename VertexT, typename OffsetT>
+struct mixed_csr_graph_view {
+    std::uint64_t _num_nodes;
+    OffsetT* _row_ptr;
+    VertexT* _col_indices;
+
+    struct neighbor_iterator_t {
+        neighbor_iterator_t(const VertexT* start_ptr, VertexT* ptr)
+                : _ptr(ptr),
+                  _start_ptr(start_ptr) {}
+
+        SYCL_EXTERNAL bool operator==(const neighbor_iterator_t& other) const {
+            return _ptr == other._ptr;
+        }
+
+        SYCL_EXTERNAL bool operator!=(const neighbor_iterator_t& other) const {
+            return _ptr != other._ptr;
+        }
+
+        SYCL_EXTERNAL neighbor_iterator_t& operator++() {
+            ++_ptr;
+            return *this;
+        }
+
+        SYCL_EXTERNAL neighbor_iterator_t operator+(int n) const {
+            neighbor_iterator_t tmp = *this;
+            tmp._ptr += n;
+            return tmp;
+        }
+
+        SYCL_EXTERNAL VertexT operator*() const {
+            return *_ptr;
+        }
+
+        SYCL_EXTERNAL std::uint32_t get_index() const {
+            return static_cast<std::uint32_t>(_ptr - _start_ptr);
+        }
+
+        VertexT* _ptr;
+        const VertexT* _start_ptr;
+    };
+
+    SYCL_EXTERNAL inline std::uint32_t get_degree(const std::uint32_t vertex) const {
+        return static_cast<std::uint32_t>(_row_ptr[vertex + 1] - _row_ptr[vertex]);
+    }
+
+    SYCL_EXTERNAL inline std::uint32_t get_weight(const std::uint64_t) const {
+        return 0;
+    }
+
+    SYCL_EXTERNAL inline neighbor_iterator_t begin(std::uint32_t vertex) const {
+        return neighbor_iterator_t(_col_indices, _col_indices + _row_ptr[vertex]);
+    }
+
+    SYCL_EXTERNAL inline neighbor_iterator_t end(std::uint32_t vertex) const {
+        return neighbor_iterator_t(_col_indices, _col_indices + _row_ptr[vertex + 1]);
+    }
+};
+
+template <typename VertexT, typename OffsetT>
+class csr_graph_device_wrapper {
+public:
+    csr_graph_device_wrapper(sycl::queue& queue,
+                             std::uint64_t vertex_count,
+                             const OffsetT* rows,
+                             const VertexT* cols)
+            : _queue(queue),
+              _num_nodes(vertex_count),
+              _rows(const_cast<OffsetT*>(rows)),
+              _cols(const_cast<VertexT*>(cols)) {}
+
+    mixed_csr_graph_view<VertexT, OffsetT> get_device_view() const {
+        return { _num_nodes, _rows, _cols };
+    }
+
+    sycl::queue& get_queue() const {
+        return _queue;
+    }
+
+    std::uint64_t get_vertex_count() const {
+        return _num_nodes;
+    }
+
+private:
+    sycl::queue& _queue;
+    std::uint64_t _num_nodes;
+    OffsetT* _rows;
+    VertexT* _cols;
+};
+
+template <typename Index>
+std::int32_t* compute_components_gpu(sycl::queue& queue,
+                                     const std::int64_t* rows,
+                                     const Index* cols,
+                                     std::int64_t vertex_count,
+                                     std::int64_t edge_count,
+                                     std::int64_t& component_count) {
+    auto* labels = sycl::malloc_shared<std::int32_t>(vertex_count, queue);
+
+    queue
+        .submit([&](sycl::handler& cgh) {
+            std::int32_t* d_labels = labels;
+            const std::int64_t vc = vertex_count;
+            cgh.parallel_for(sycl::range<1>(vc), [=](sycl::id<1> idx) {
+                d_labels[idx[0]] = static_cast<std::int32_t>(idx[0]);
+            });
+        })
+        .wait_and_throw();
+
+    if (edge_count == 0) {
+        component_count = vertex_count;
+        return labels;
+    }
+
+    csr_graph_device_wrapper<Index, std::int64_t> graph(
+        queue,
+        static_cast<std::uint64_t>(vertex_count),
+        rows,
+        cols);
+
+    fp::frontier<std::uint32_t> in_frontier(queue, vertex_count, sycl::usm::alloc::device);
+    fp::frontier<std::uint32_t> out_frontier(queue, vertex_count, sycl::usm::alloc::device);
+
+    {
+        auto fv = in_frontier.get_device_view();
+        const std::int64_t vc = vertex_count;
+        queue
+            .submit([&](sycl::handler& cgh) {
+                cgh.parallel_for(sycl::range<1>(vc), [=](sycl::id<1> idx) {
+                    fv.insert(static_cast<std::uint32_t>(idx[0]));
+                });
+            })
+            .wait_and_throw();
+    }
+
+    std::int32_t* d_labels = labels;
+    while (!in_frontier.empty()) {
+        auto e = fp::advance(
+            graph,
+            in_frontier,
+            out_frontier,
+            [=](auto src, auto dst, auto edge, auto weight) -> bool {
+                const std::int32_t label_src = d_labels[src];
+                const std::int32_t label_dst = d_labels[dst];
+
+                if (label_src < label_dst) {
+                    std::int32_t old_val =
+                        sycl::atomic_ref<std::int32_t,
+                                         sycl::memory_order::relaxed,
+                                         sycl::memory_scope::device,
+                                         sycl::access::address_space::global_space>(
+                            d_labels[dst])
+                            .fetch_min(label_src);
+                    return label_src < old_val;
+                }
+                return false;
+            });
+        e.wait_and_throw();
+
+        fp::swap_frontiers(in_frontier, out_frontier);
+        out_frontier.clear();
+    }
+
+    auto* ordered_labels = sycl::malloc_shared<std::int32_t>(vertex_count, queue);
+    auto* comp_count_ptr = sycl::malloc_shared<std::int32_t>(1, queue);
+    comp_count_ptr[0] = 0;
+
+    queue.memset(ordered_labels, 0xFF, vertex_count * sizeof(std::int32_t)).wait_and_throw();
+
+    for (std::int64_t u = 0; u < vertex_count; ++u) {
+        std::int32_t root = labels[u];
+        if (ordered_labels[root] < 0) {
+            ordered_labels[root] = comp_count_ptr[0];
+            comp_count_ptr[0]++;
+        }
+        labels[u] = ordered_labels[root];
+    }
+
+    component_count = comp_count_ptr[0];
+
+    sycl::free(ordered_labels, queue);
+    sycl::free(comp_count_ptr, queue);
+
+    return labels;
+}
+
+} // namespace detail_gpu
+
+template <typename Float, typename Task, typename Index>
+vertex_partitioning_result<Task> run_vertex_partitioning_gpu(
+    const dal::backend::context_gpu& ctx,
+    const detail::descriptor_base<Task>& desc,
+    const csr_topology_gpu_view<Index>& topology) {
+    auto& queue = ctx.get_queue();
+
+    const auto vertex_count = topology.vertex_count;
+    const auto edge_count = topology.edge_count;
+
+    if (vertex_count == 0) {
+        return vertex_partitioning_result<Task>();
+    }
+
+    std::int64_t component_count = 0;
+    auto* labels = detail_gpu::compute_components_gpu(queue,
+                                                      topology.rows,
+                                                      topology.cols,
+                                                      vertex_count,
+                                                      edge_count,
+                                                      component_count);
+
+    auto labels_arr =
+        array<std::int32_t>(queue, labels, vertex_count, [queue](std::int32_t* ptr) mutable {
+            sycl::free(ptr, queue);
+        });
+
+    vertex_partitioning_result<Task> result;
+    result.set_labels(dal::detail::homogen_table_builder{}
+                          .reset(labels_arr, vertex_count, 1)
+                          .build());
+    result.set_component_count(component_count);
+
+    return result;
+}
+
+template <typename Float, typename Task, typename Topology>
+vertex_partitioning_result<Task> vertex_partitioning_kernel_gpu<Float, Task, Topology>::operator()(
+    const dal::backend::context_gpu& ctx,
+    const detail::descriptor_base<Task>& desc,
+    const Topology& topology) const {
+    auto& queue = ctx.get_queue();
+    const auto vertex_count = topology.get_vertex_count();
+
+    if (vertex_count == 0) {
+        return vertex_partitioning_result<Task>();
+    }
+
+    using namespace dal::preview::detail;
+
+    const auto* rows_ptr = topology._rows.get_data();
+    const auto alloc_type = sycl::get_pointer_type(rows_ptr, queue.get_context());
+
+    if (alloc_type == sycl::usm::alloc::device || alloc_type == sycl::usm::alloc::shared) {
+        csr_topology_gpu_view<std::int32_t> gpu_view;
+        gpu_view.rows = rows_ptr;
+        gpu_view.cols = topology._cols.get_data();
+        gpu_view.vertex_count = vertex_count;
+        gpu_view.edge_count = topology.get_edge_count();
+        return run_vertex_partitioning_gpu<Float, Task, std::int32_t>(ctx, desc, gpu_view);
+    }
+
+    auto device_topo = topology_to_device<std::int32_t>(queue, topology);
+    const auto gpu_view = make_gpu_view(device_topo);
+    return run_vertex_partitioning_gpu<Float, Task, std::int32_t>(ctx, desc, gpu_view);
+}
+
+// Explicit template instantiations
+template struct vertex_partitioning_kernel_gpu<float,
+                                               task::vertex_partitioning,
+                                               dal::preview::detail::topology<std::int32_t>>;
+
+template vertex_partitioning_result<task::vertex_partitioning>
+run_vertex_partitioning_gpu<float, task::vertex_partitioning, std::int32_t>(
+    const dal::backend::context_gpu&,
+    const detail::descriptor_base<task::vertex_partitioning>&,
+    const csr_topology_gpu_view<std::int32_t>&);
+
+} // namespace oneapi::dal::preview::connected_components::backend
diff --git a/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_kernel.hpp b/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_kernel.hpp
new file mode 100644
index 00000000000..27c2d0da948
--- /dev/null
+++ b/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_kernel.hpp
@@ -0,0 +1,52 @@
+/*******************************************************************************
+* Copyright 2021 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#pragma once
+
+#include <cstdint>
+
+#include "oneapi/dal/algo/connected_components/vertex_partitioning_types.hpp"
+#include "oneapi/dal/backend/dispatcher.hpp"
+#include "oneapi/dal/graph/detail/device_csr_topology.hpp"
+
+namespace oneapi::dal::preview::connected_components::backend {
+
+template <typename Index = std::int32_t>
+struct csr_topology_gpu_view {
+    const std::int64_t* rows = nullptr;
+    const Index* cols = nullptr;
+    std::int64_t vertex_count = 0;
+    std::int64_t edge_count = 0;
+};
+
+template <typename Index = std::int32_t>
+csr_topology_gpu_view<Index> make_gpu_view(
+        const dal::preview::detail::device_csr_topology<Index>& device_topo) {
+    csr_topology_gpu_view<Index> view;
+    view.rows = device_topo.get_rows();
+    view.cols = device_topo.get_cols();
+    view.vertex_count = device_topo.get_vertex_count();
+    view.edge_count = device_topo.get_edge_count();
+    return view;
+}
+
+template <typename Float, typename Task, typename Index = std::int32_t>
+vertex_partitioning_result<Task> run_vertex_partitioning_gpu(
+    const dal::backend::context_gpu& ctx,
+    const detail::descriptor_base<Task>& desc,
+    const csr_topology_gpu_view<Index>& topology);
+
+} // namespace oneapi::dal::preview::connected_components::backend
diff --git a/cpp/oneapi/dal/algo/connected_components/detail/select_kernel.hpp b/cpp/oneapi/dal/algo/connected_components/detail/select_kernel.hpp
index b77d431c303..999a2fc583b 100644
--- a/cpp/oneapi/dal/algo/connected_components/detail/select_kernel.hpp
+++ b/cpp/oneapi/dal/algo/connected_components/detail/select_kernel.hpp
@@ -21,9 +21,13 @@
 #include "oneapi/dal/algo/connected_components/vertex_partitioning_types.hpp"
 #include "oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp"
 
+#ifdef ONEDAL_DATA_PARALLEL
+#include "oneapi/dal/detail/policy.hpp"
+#endif
+
 namespace oneapi::dal::preview::connected_components::detail {
 
-template <typename Policy, typename Descriptor, typename Graph>
+template <typename Policy, typename Descriptor, typename Topology>
 struct backend_base {
     using float_t = typename Descriptor::float_t;
     using task_t = typename Descriptor::task_t;
@@ -32,12 +36,12 @@ struct backend_base {
 
     virtual vertex_partitioning_result<task_t> operator()(const Policy& ctx,
                                                           const Descriptor& descriptor,
-                                                          const Graph& t) = 0;
+                                                          const Topology& t) = 0;
     virtual ~backend_base() = default;
 };
 
-template <typename Policy, typename Descriptor, typename Graph>
-struct backend_default : public backend_base<Policy, Descriptor, Graph> {
+template <typename Policy, typename Descriptor, typename Topology>
+struct backend_default : public backend_base<Policy, Descriptor, Topology> {
     static_assert(dal::detail::is_one_of_v<Policy, dal::detail::host_policy>,
                   "Host policy only is supported.");
 
@@ -48,8 +52,8 @@ struct backend_default : public backend_base<Policy, Descriptor, Graph> {
 
     virtual vertex_partitioning_result<task_t> operator()(const Policy& ctx,
                                                           const Descriptor& descriptor,
-                                                          const Graph& t) {
-        return vertex_partitioning_kernel_cpu<method_t, task_t, allocator_t, Graph>()(
+                                                          const Topology& t) {
+        return vertex_partitioning_kernel_cpu<method_t, task_t, allocator_t, Topology>()(
             ctx,
             descriptor,
             descriptor.get_allocator(),
@@ -57,10 +61,26 @@ struct backend_default : public backend_base<Policy, Descriptor, Graph> {
     }
 };
 
-template <typename Policy, typename Descriptor, typename Graph>
-dal::detail::shared<backend_base<Policy, Descriptor, Graph>> get_backend(const Descriptor& desc,
-                                                                         const Graph& t) {
-    return std::make_shared<backend_default<Policy, Descriptor, Graph>>();
+#ifdef ONEDAL_DATA_PARALLEL
+template <typename Descriptor, typename Topology>
+struct backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>
+        : public backend_base<dal::detail::data_parallel_policy, Descriptor, Topology> {
+    using float_t = typename Descriptor::float_t;
+    using task_t = typename Descriptor::task_t;
+    using method_t = typename Descriptor::method_t;
+    using allocator_t = typename Descriptor::allocator_t;
+
+    virtual vertex_partitioning_result<task_t> operator()(
+        const dal::detail::data_parallel_policy& ctx,
+        const Descriptor& descriptor,
+        const Topology& t);
+};
+#endif
+
+template <typename Policy, typename Descriptor, typename Topology>
+dal::detail::shared<backend_base<Policy, Descriptor, Topology>> get_backend(const Descriptor& desc,
+                                                                         const Topology& t) {
+    return std::make_shared<backend_default<Policy, Descriptor, Topology>>();
 }
 
 } // namespace oneapi::dal::preview::connected_components::detail
diff --git a/cpp/oneapi/dal/algo/connected_components/detail/select_kernel_dpc.cpp b/cpp/oneapi/dal/algo/connected_components/detail/select_kernel_dpc.cpp
new file mode 100644
index 00000000000..627f2085510
--- /dev/null
+++ b/cpp/oneapi/dal/algo/connected_components/detail/select_kernel_dpc.cpp
@@ -0,0 +1,64 @@
+/*******************************************************************************
+* Copyright 2021 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#include "oneapi/dal/algo/connected_components/detail/select_kernel.hpp"
+#include "oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp"
+#include "oneapi/dal/backend/dispatcher.hpp"
+
+namespace oneapi::dal::preview::connected_components::detail {
+
+template <typename Descriptor, typename Topology>
+vertex_partitioning_result<typename Descriptor::task_t>
+backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>::operator()(
+    const dal::detail::data_parallel_policy& ctx,
+    const Descriptor& descriptor,
+    const Topology& t) {
+    using float_t = typename Descriptor::float_t;
+    using task_t = typename Descriptor::task_t;
+    using method_t = typename Descriptor::method_t;
+    using allocator_t = typename Descriptor::allocator_t;
+
+    return dal::backend::dispatch_by_device(
+        ctx,
+        [&]() {
+            return vertex_partitioning_kernel_cpu<method_t, task_t, allocator_t, Topology>()(
+                dal::detail::host_policy::get_default(),
+                descriptor,
+                descriptor.get_allocator(),
+                t);
+        },
+        [&]() {
+            dal::backend::context_gpu gpu_ctx{ ctx };
+            return backend::vertex_partitioning_kernel_gpu<float_t, task_t, Topology>()(
+                gpu_ctx,
+                descriptor,
+                t);
+        });
+}
+
+using default_descriptor = descriptor<
+    float,
+    method::afforest,
+    task::vertex_partitioning,
+    std::allocator<char>>;
+
+using default_topology = dal::preview::detail::topology<std::int32_t>;
+
+template struct ONEDAL_EXPORT backend_default<dal::detail::data_parallel_policy,
+                                              default_descriptor,
+                                              default_topology>;
+
+} // namespace oneapi::dal::preview::connected_components::detail
diff --git a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.hpp b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.hpp
index a3849222fa5..ffa9e0024b7 100644
--- a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.hpp
+++ b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.hpp
@@ -78,4 +78,25 @@ struct vertex_partitioning_kernel_cpu<method::afforest,
     }
 };
 
+template <typename Allocator>
+struct vertex_partitioning_kernel_cpu<method::afforest,
+                                      task::vertex_partitioning,
+                                      Allocator,
+                                      dal::preview::detail::topology<std::int32_t>> {
+    inline vertex_partitioning_result<task::vertex_partitioning> operator()(
+        const dal::detail::host_policy& ctx,
+        const detail::descriptor_base<task::vertex_partitioning>& desc,
+        const Allocator& alloc,
+        const dal::preview::detail::topology<std::int32_t>& t) const {
+        alloc_connector<Allocator> alloc_con(alloc);
+        const auto vertex_count = t.get_vertex_count();
+        if (vertex_count == 0) {
+            return vertex_partitioning_result<task::vertex_partitioning>();
+        }
+        return afforest<float,
+                        task::vertex_partitioning,
+                        dal::preview::detail::topology<std::int32_t>>{}(ctx, desc, t, &alloc_con);
+    }
+};
+
 } // namespace oneapi::dal::preview::connected_components::detail
diff --git a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_ops.hpp b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_ops.hpp
index 0426b5dbbc3..26b4215f1bd 100644
--- a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_ops.hpp
+++ b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_ops.hpp
@@ -22,6 +22,7 @@
 #include "oneapi/dal/detail/error_messages.hpp"
 #include "oneapi/dal/detail/policy.hpp"
 #include "oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp"
+#include "oneapi/dal/graph/detail/undirected_adjacency_vector_graph_topology_builder.hpp"
 
 namespace oneapi::dal::preview::connected_components::detail {
 
@@ -32,8 +33,13 @@ struct vertex_partitioning_ops_dispatcher {
         const Policy &policy,
         const Descriptor &descriptor,
         vertex_partitioning_input<Graph, task_t> &input) const {
-        static auto impl = get_backend<Policy, Descriptor>(descriptor, input.get_graph());
-        return (*impl)(policy, descriptor, input.get_graph());
+        auto topology_builder = dal::preview::detail::csr_topology_builder<Graph>();
+
+        const auto &t = topology_builder(input.get_graph());
+
+        auto impl = get_backend<Policy, Descriptor>(descriptor, t);
+
+        return (*impl)(policy, descriptor, t);
     }
 };
 
diff --git a/cpp/oneapi/dal/algo/connected_components/test/connected_components_gpu_test.cpp b/cpp/oneapi/dal/algo/connected_components/test/connected_components_gpu_test.cpp
new file mode 100644
index 00000000000..878b449261b
--- /dev/null
+++ b/cpp/oneapi/dal/algo/connected_components/test/connected_components_gpu_test.cpp
@@ -0,0 +1,278 @@
+/*******************************************************************************
+* Copyright 2021 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#include <array>
+#include <set>
+
+#ifndef ONEDAL_DATA_PARALLEL
+#define ONEDAL_DATA_PARALLEL
+#endif
+
+#include <sycl/sycl.hpp>
+
+#include "oneapi/dal/algo/connected_components/vertex_partitioning.hpp"
+
+#include "oneapi/dal/test/engine/common.hpp"
+
+namespace oneapi::dal::algo::connected_components::gpu::test {
+
+class graph_base_data {
+public:
+    graph_base_data() = default;
+
+    std::int64_t get_vertex_count() const {
+        return vertex_count;
+    }
+
+    std::int64_t get_edge_count() const {
+        return edge_count;
+    }
+
+    std::int64_t get_component_count() const {
+        return component_count;
+    }
+
+    std::int64_t get_cols_count() const {
+        return cols_count;
+    }
+
+    std::int64_t get_rows_count() const {
+        return rows_count;
+    }
+
+protected:
+    std::int64_t vertex_count;
+    std::int64_t edge_count;
+    std::int64_t cols_count;
+    std::int64_t rows_count;
+    std::int64_t component_count;
+};
+
+class triangle_graph_type : public graph_base_data {
+public:
+    triangle_graph_type() {
+        vertex_count = 3;
+        edge_count = 3;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        component_count = 1;
+    }
+
+    std::array<std::int32_t, 3> degrees = { 2, 2, 2 };
+    std::array<std::int32_t, 6> cols = { 1, 2, 0, 2, 0, 1 };
+    std::array<std::int64_t, 4> rows = { 0, 2, 4, 6 };
+};
+
+class two_components_graph_type : public graph_base_data {
+public:
+    two_components_graph_type() {
+        vertex_count = 4;
+        edge_count = 2;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        component_count = 2;
+    }
+
+    std::array<std::int32_t, 4> degrees = { 1, 1, 1, 1 };
+    std::array<std::int32_t, 4> cols = { 1, 0, 3, 2 };
+    std::array<std::int64_t, 5> rows = { 0, 1, 2, 3, 4 };
+};
+
+class complete_graph_5_type : public graph_base_data {
+public:
+    complete_graph_5_type() {
+        vertex_count = 5;
+        edge_count = 10;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        component_count = 1;
+    }
+
+    std::array<std::int32_t, 5> degrees = { 4, 4, 4, 4, 4 };
+    std::array<std::int32_t, 20> cols = {
+        1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3
+    };
+    std::array<std::int64_t, 6> rows = { 0, 4, 8, 12, 16, 20 };
+};
+
+class isolated_vertices_5_type : public graph_base_data {
+public:
+    isolated_vertices_5_type() {
+        vertex_count = 5;
+        edge_count = 0;
+        cols_count = 0;
+        rows_count = vertex_count + 1;
+        component_count = 5;
+    }
+
+    std::array<std::int32_t, 5> degrees = { 0, 0, 0, 0, 0 };
+    std::array<std::int32_t, 1> cols = { 0 };
+    std::array<std::int64_t, 6> rows = { 0, 0, 0, 0, 0, 0 };
+};
+
+class three_components_graph_type : public graph_base_data {
+public:
+    three_components_graph_type() {
+        vertex_count = 6;
+        edge_count = 4;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        component_count = 3;
+    }
+
+    std::array<std::int32_t, 6> degrees = { 2, 2, 2, 1, 1, 0 };
+    std::array<std::int32_t, 8> cols = { 1, 2, 0, 2, 0, 1, 4, 3 };
+    std::array<std::int64_t, 7> rows = { 0, 2, 4, 6, 7, 8, 8 };
+};
+
+class line_graph_5_type : public graph_base_data {
+public:
+    line_graph_5_type() {
+        vertex_count = 5;
+        edge_count = 4;
+        cols_count = edge_count * 2;
+        rows_count = vertex_count + 1;
+        component_count = 1;
+    }
+
+    std::array<std::int32_t, 5> degrees = { 1, 2, 2, 2, 1 };
+    std::array<std::int32_t, 8> cols = { 1, 0, 2, 1, 3, 2, 4, 3 };
+    std::array<std::int64_t, 6> rows = { 0, 1, 3, 5, 7, 8 };
+};
+
+class connected_components_gpu_test {
+public:
+    template <typename GraphType>
+    auto create_graph() {
+        GraphType graph_data;
+        dal::preview::undirected_adjacency_vector_graph<> g;
+        auto& graph_impl = oneapi::dal::detail::get_impl(g);
+        auto& vertex_allocator = graph_impl._vertex_allocator;
+        auto& edge_allocator = graph_impl._edge_allocator;
+
+        const std::int64_t vertex_count = graph_data.get_vertex_count();
+        const std::int64_t edge_count = graph_data.get_edge_count();
+        const std::int64_t cols_count = graph_data.get_cols_count();
+        const std::int64_t rows_count = graph_data.get_rows_count();
+
+        std::int32_t* degrees =
+            oneapi::dal::preview::detail::allocate(vertex_allocator, vertex_count);
+        std::int32_t* cols = oneapi::dal::preview::detail::allocate(vertex_allocator, cols_count);
+        std::int64_t* rows = oneapi::dal::preview::detail::allocate(edge_allocator, rows_count);
+        std::int32_t* rows_vertex =
+            oneapi::dal::preview::detail::allocate(vertex_allocator, rows_count);
+
+        for (int i = 0; i < vertex_count; i++) {
+            degrees[i] = graph_data.degrees[i];
+        }
+
+        for (int i = 0; i < cols_count; i++) {
+            cols[i] = graph_data.cols[i];
+        }
+        for (int i = 0; i < rows_count; i++) {
+            rows[i] = graph_data.rows[i];
+            rows_vertex[i] = graph_data.rows[i];
+        }
+        graph_impl.set_topology(vertex_count, edge_count, rows, cols, cols_count, degrees);
+        graph_impl.get_topology()._rows_vertex =
+            oneapi::dal::preview::detail::container<std::int32_t>::wrap(rows_vertex, rows_count);
+        return g;
+    }
+
+    sycl::queue get_queue() {
+        return sycl::queue{ sycl::default_selector_v };
+    }
+
+    template <typename GraphType>
+    void check_vertex_partitioning() {
+        GraphType graph_data;
+        const auto g = create_graph<GraphType>();
+        const std::int64_t vertex_count = graph_data.get_vertex_count();
+        const std::int64_t expected_components = graph_data.get_component_count();
+
+        auto q = get_queue();
+
+        std::allocator<char> alloc;
+        const auto cc_desc = dal::preview::connected_components::descriptor<
+            float,
+            dal::preview::connected_components::method::afforest,
+            dal::preview::connected_components::task::vertex_partitioning,
+            std::allocator<char>>(alloc);
+
+        const auto result = dal::preview::vertex_partitioning(q, cc_desc, g);
+
+        REQUIRE(result.get_component_count() == expected_components);
+
+        const auto labels_table = result.get_labels();
+        REQUIRE(labels_table.get_row_count() == vertex_count);
+
+        const auto& labels = static_cast<const dal::homogen_table&>(labels_table);
+        const auto labels_data = labels.get_data<std::int32_t>();
+
+        std::set<std::int32_t> unique_labels(labels_data, labels_data + vertex_count);
+        REQUIRE(static_cast<std::int64_t>(unique_labels.size()) == expected_components);
+
+        for (std::int64_t u = 0; u < vertex_count; ++u) {
+            std::int64_t u_start = graph_data.rows[u];
+            std::int64_t u_end = graph_data.rows[u + 1];
+            for (std::int64_t i = u_start; i < u_end; ++i) {
+                std::int32_t v = graph_data.cols[i];
+                REQUIRE(labels_data[u] == labels_data[v]);
+            }
+        }
+    }
+};
+
+TEST_M(connected_components_gpu_test, "GPU: triangle graph - 1 component") {
+    this->check_vertex_partitioning<triangle_graph_type>();
+}
+
+TEST_M(connected_components_gpu_test, "GPU: two components") {
+    this->check_vertex_partitioning<two_components_graph_type>();
+}
+
+TEST_M(connected_components_gpu_test, "GPU: complete graph K5 - 1 component") {
+    this->check_vertex_partitioning<complete_graph_5_type>();
+}
+
+TEST_M(connected_components_gpu_test, "GPU: isolated vertices - 5 components") {
+    this->check_vertex_partitioning<isolated_vertices_5_type>();
+}
+
+TEST_M(connected_components_gpu_test, "GPU: three components") {
+    this->check_vertex_partitioning<three_components_graph_type>();
+}
+
+TEST_M(connected_components_gpu_test, "GPU: line graph - 1 component") {
+    this->check_vertex_partitioning<line_graph_5_type>();
+}
+
+TEST_M(connected_components_gpu_test, "GPU: null graph") {
+    dal::preview::undirected_adjacency_vector_graph<> null_graph;
+    auto q = get_queue();
+
+    std::allocator<char> alloc;
+    const auto cc_desc = dal::preview::connected_components::descriptor<
+        float,
+        dal::preview::connected_components::method::afforest,
+        dal::preview::connected_components::task::vertex_partitioning,
+        std::allocator<char>>(alloc);
+
+    const auto result = dal::preview::vertex_partitioning(q, cc_desc, null_graph);
+    REQUIRE(result.get_component_count() == 0);
+}
+
+} // namespace oneapi::dal::algo::connected_components::gpu::test
diff --git a/cpp/oneapi/dal/detail/vertex_partitioning_ops.hpp b/cpp/oneapi/dal/detail/vertex_partitioning_ops.hpp
index 8e531354168..efd203fe4c5 100644
--- a/cpp/oneapi/dal/detail/vertex_partitioning_ops.hpp
+++ b/cpp/oneapi/dal/detail/vertex_partitioning_ops.hpp
@@ -40,5 +40,25 @@ auto vertex_partitioning_dispatch(Head &&head, Tail &&...tail) {
                                                  std::forward<Tail>(tail)...);
 }
 
+#ifdef ONEDAL_DATA_PARALLEL
+template <typename Descriptor, typename Head, typename... Tail>
+auto vertex_partitioning_dispatch_by_input(const dal::detail::data_parallel_policy &policy,
+                                           const Descriptor &desc,
+                                           Head &&head,
+                                           Tail &&...tail) {
+    using tag_t = typename Descriptor::tag_t;
+    using ops_t = vertex_partitioning_ops<Descriptor, std::decay_t<Head>, tag_t>;
+    using input_t = typename ops_t::input_t;
+
+    auto input = input_t{ std::forward<Head>(head), std::forward<Tail>(tail)... };
+    return ops_t()(policy, desc, input);
+}
+
+template <typename... Tail>
+auto vertex_partitioning_dispatch(const dal::detail::data_parallel_policy &policy, Tail &&...tail) {
+    return vertex_partitioning_dispatch_by_input(policy, std::forward<Tail>(tail)...);
+}
+#endif
+
 } // namespace detail
 } // namespace oneapi::dal::preview
diff --git a/cpp/oneapi/dal/graph/detail/csr_topology.hpp b/cpp/oneapi/dal/graph/detail/csr_topology.hpp
index 78fdf0d5d81..c661be73d03 100644
--- a/cpp/oneapi/dal/graph/detail/csr_topology.hpp
+++ b/cpp/oneapi/dal/graph/detail/csr_topology.hpp
@@ -152,9 +152,11 @@ class topology {
 
         const auto rows_count = _vertex_count + 1;
         const auto cols_count = _cols.get_count();
+        const auto degrees_count = _degrees.get_count();
+        const auto rows_vertex_count = _rows_vertex.get_count();
 
-        auto device_rows = edge_set::empty(queue, rows_count, sycl::usm::alloc::device);
-        auto device_cols = vertex_set::empty(queue, cols_count, sycl::usm::alloc::device);
+        auto device_rows = edge_set::empty(queue, rows_count, sycl::usm::alloc::shared);
+        auto device_cols = vertex_set::empty(queue, cols_count, sycl::usm::alloc::shared);
 
         auto e1 = queue.memcpy(device_rows.get_mutable_data(),
                                _rows.get_data(),
@@ -169,7 +171,23 @@ class topology {
         result._cols = device_cols;
         result._rows_ptr = result._rows.get_data();
         result._cols_ptr = result._cols.get_data();
-        result._degrees_ptr = nullptr;
+
+        if (degrees_count > 0) {
+            auto device_degrees = vertex_set::empty(queue, degrees_count, sycl::usm::alloc::shared);
+            queue.memcpy(device_degrees.get_mutable_data(), _degrees.get_data(),
+                         degrees_count * sizeof(vertex_type)).wait_and_throw();
+            result._degrees = device_degrees;
+            result._degrees_ptr = result._degrees.get_data();
+        }
+
+        if (rows_vertex_count > 0) {
+            auto device_rows_vertex = vertex_edge_set::empty(queue, rows_vertex_count,
+                                                              sycl::usm::alloc::shared);
+            queue.memcpy(device_rows_vertex.get_mutable_data(), _rows_vertex.get_data(),
+                         rows_vertex_count * sizeof(vertex_edge_type)).wait_and_throw();
+            result._rows_vertex = device_rows_vertex;
+        }
+
         return result;
     }
 #endif
diff --git a/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp b/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp
index f5cbd79d135..8ff84805f57 100644
--- a/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp
+++ b/cpp/oneapi/dal/graph/detail/undirected_adjacency_vector_graph_impl.hpp
@@ -138,7 +138,7 @@ class ONEDAL_EXPORT undirected_adjacency_vector_graph_impl {
         if (alloc_type == sycl::usm::alloc::device || alloc_type == sycl::usm::alloc::shared) {
             return;
         }
-        auto device_arr = container<T>::empty(queue, count, sycl::usm::alloc::device);
+        auto device_arr = container<T>::empty(queue, count, sycl::usm::alloc::shared);
         queue.memcpy(device_arr.get_mutable_data(), src, count * sizeof(T)).wait_and_throw();
         arr = device_arr;
     }
diff --git a/cpp/oneapi/dal/vertex_partitioning.hpp b/cpp/oneapi/dal/vertex_partitioning.hpp
index 0197912c5a7..342156e039c 100644
--- a/cpp/oneapi/dal/vertex_partitioning.hpp
+++ b/cpp/oneapi/dal/vertex_partitioning.hpp
@@ -29,4 +29,12 @@ auto vertex_partitioning(Args &&...args) {
     return detail::vertex_partitioning_dispatch(std::forward<Args>(args)...);
 }
 
+#ifdef ONEDAL_DATA_PARALLEL
+template <typename... Args>
+auto vertex_partitioning(sycl::queue& q, Args &&...args) {
+    const auto policy = dal::detail::data_parallel_policy{ q };
+    return detail::vertex_partitioning_dispatch(policy, std::forward<Args>(args)...);
+}
+#endif
+
 } // namespace oneapi::dal::preview
diff --git a/examples/oneapi/dpc/BUILD b/examples/oneapi/dpc/BUILD
index 42519af0c62..6a138d903ba 100644
--- a/examples/oneapi/dpc/BUILD
+++ b/examples/oneapi/dpc/BUILD
@@ -69,6 +69,7 @@ dal_algo_example_suite(
         "rbf_kernel",
         "svm",
         "triangle_counting",
+        "connected_components",
     ],
     compile_as = [ "dpc++" ],
     data = _DATA_DEPS,
diff --git a/examples/oneapi/dpc/_cmake_results/intel_intel64_so/connected_components_batch b/examples/oneapi/dpc/_cmake_results/intel_intel64_so/connected_components_batch
new file mode 100755
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diff --git a/examples/oneapi/dpc/_cmake_results/intel_intel64_so/triangle_counting_batch b/examples/oneapi/dpc/_cmake_results/intel_intel64_so/triangle_counting_batch
new file mode 100755
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+	@echo "... source/decision_forest/df_reg_traverse_model.o"
+	@echo "... source/decision_forest/df_reg_traverse_model.i"
+	@echo "... source/decision_forest/df_reg_traverse_model.s"
+	@echo "... source/kmeans/kmeans_lloyd_csr_batch.o"
+	@echo "... source/kmeans/kmeans_lloyd_csr_batch.i"
+	@echo "... source/kmeans/kmeans_lloyd_csr_batch.s"
+	@echo "... source/kmeans/kmeans_lloyd_dense_batch.o"
+	@echo "... source/kmeans/kmeans_lloyd_dense_batch.i"
+	@echo "... source/kmeans/kmeans_lloyd_dense_batch.s"
+	@echo "... source/kmeans_init/kmeans_init_dense.o"
+	@echo "... source/kmeans_init/kmeans_init_dense.i"
+	@echo "... source/kmeans_init/kmeans_init_dense.s"
+	@echo "... source/knn/knn_cls_brute_force_dense_batch.o"
+	@echo "... source/knn/knn_cls_brute_force_dense_batch.i"
+	@echo "... source/knn/knn_cls_brute_force_dense_batch.s"
+	@echo "... source/knn/knn_reg_brute_force_dense_batch.o"
+	@echo "... source/knn/knn_reg_brute_force_dense_batch.i"
+	@echo "... source/knn/knn_reg_brute_force_dense_batch.s"
+	@echo "... source/knn/knn_search_brute_force_dense_batch.o"
+	@echo "... source/knn/knn_search_brute_force_dense_batch.i"
+	@echo "... source/knn/knn_search_brute_force_dense_batch.s"
+	@echo "... source/linear_kernel/linear_kernel_dense_batch.o"
+	@echo "... source/linear_kernel/linear_kernel_dense_batch.i"
+	@echo "... source/linear_kernel/linear_kernel_dense_batch.s"
+	@echo "... source/linear_regression/linear_regression_dense_batch.o"
+	@echo "... source/linear_regression/linear_regression_dense_batch.i"
+	@echo "... source/linear_regression/linear_regression_dense_batch.s"
+	@echo "... source/linear_regression/linear_regression_dense_online.o"
+	@echo "... source/linear_regression/linear_regression_dense_online.i"
+	@echo "... source/linear_regression/linear_regression_dense_online.s"
+	@echo "... source/logistic_regression/logistic_regression_dense_batch.o"
+	@echo "... source/logistic_regression/logistic_regression_dense_batch.i"
+	@echo "... source/logistic_regression/logistic_regression_dense_batch.s"
+	@echo "... source/misc/read_batch.o"
+	@echo "... source/misc/read_batch.i"
+	@echo "... source/misc/read_batch.s"
+	@echo "... source/pca/pca_cor_dense_batch.o"
+	@echo "... source/pca/pca_cor_dense_batch.i"
+	@echo "... source/pca/pca_cor_dense_batch.s"
+	@echo "... source/pca/pca_cor_dense_online.o"
+	@echo "... source/pca/pca_cor_dense_online.i"
+	@echo "... source/pca/pca_cor_dense_online.s"
+	@echo "... source/pca/pca_cov_dense_batch.o"
+	@echo "... source/pca/pca_cov_dense_batch.i"
+	@echo "... source/pca/pca_cov_dense_batch.s"
+	@echo "... source/pca/pca_cov_dense_online.o"
+	@echo "... source/pca/pca_cov_dense_online.i"
+	@echo "... source/pca/pca_cov_dense_online.s"
+	@echo "... source/pca/pca_precomputed_cor_dense_batch.o"
+	@echo "... source/pca/pca_precomputed_cor_dense_batch.i"
+	@echo "... source/pca/pca_precomputed_cor_dense_batch.s"
+	@echo "... source/pca/pca_precomputed_cov_dense_batch.o"
+	@echo "... source/pca/pca_precomputed_cov_dense_batch.i"
+	@echo "... source/pca/pca_precomputed_cov_dense_batch.s"
+	@echo "... source/pca/pca_svd_dense_batch.o"
+	@echo "... source/pca/pca_svd_dense_batch.i"
+	@echo "... source/pca/pca_svd_dense_batch.s"
+	@echo "... source/rbf_kernel/rbf_kernel_dense_batch.o"
+	@echo "... source/rbf_kernel/rbf_kernel_dense_batch.i"
+	@echo "... source/rbf_kernel/rbf_kernel_dense_batch.s"
+	@echo "... source/svm/svm_two_class_thunder_dense_batch.o"
+	@echo "... source/svm/svm_two_class_thunder_dense_batch.i"
+	@echo "... source/svm/svm_two_class_thunder_dense_batch.s"
+	@echo "... source/table/column_accessor_homogen.o"
+	@echo "... source/table/column_accessor_homogen.i"
+	@echo "... source/table/column_accessor_homogen.s"
+	@echo "... source/table/csr_accessor.o"
+	@echo "... source/table/csr_accessor.i"
+	@echo "... source/table/csr_accessor.s"
+	@echo "... source/table/csr_table.o"
+	@echo "... source/table/csr_table.i"
+	@echo "... source/table/csr_table.s"
+	@echo "... source/table/heterogen_table.o"
+	@echo "... source/table/heterogen_table.i"
+	@echo "... source/table/heterogen_table.s"
+	@echo "... source/table/homogen_table.o"
+	@echo "... source/table/homogen_table.i"
+	@echo "... source/table/homogen_table.s"
+	@echo "... source/triangle_counting/triangle_counting_batch.o"
+	@echo "... source/triangle_counting/triangle_counting_batch.i"
+	@echo "... source/triangle_counting/triangle_counting_batch.s"
+.PHONY : help
+
+
+
+#=============================================================================
+# Special targets to cleanup operation of make.
+
+# Special rule to run CMake to check the build system integrity.
+# No rule that depends on this can have commands that come from listfiles
+# because they might be regenerated.
+cmake_check_build_system:
+	$(CMAKE_COMMAND) -S$(CMAKE_SOURCE_DIR) -B$(CMAKE_BINARY_DIR) --check-build-system CMakeFiles/Makefile.cmake 0
+.PHONY : cmake_check_build_system
+
diff --git a/examples/oneapi/dpc/build/cmake_install.cmake b/examples/oneapi/dpc/build/cmake_install.cmake
new file mode 100644
index 00000000000..15527649405
--- /dev/null
+++ b/examples/oneapi/dpc/build/cmake_install.cmake
@@ -0,0 +1,54 @@
+# Install script for directory: /export/users/okruglov/oneDAL/examples/oneapi/dpc
+
+# Set the install prefix
+if(NOT DEFINED CMAKE_INSTALL_PREFIX)
+  set(CMAKE_INSTALL_PREFIX "/usr/local")
+endif()
+string(REGEX REPLACE "/$" "" CMAKE_INSTALL_PREFIX "${CMAKE_INSTALL_PREFIX}")
+
+# Set the install configuration name.
+if(NOT DEFINED CMAKE_INSTALL_CONFIG_NAME)
+  if(BUILD_TYPE)
+    string(REGEX REPLACE "^[^A-Za-z0-9_]+" ""
+           CMAKE_INSTALL_CONFIG_NAME "${BUILD_TYPE}")
+  else()
+    set(CMAKE_INSTALL_CONFIG_NAME "Release")
+  endif()
+  message(STATUS "Install configuration: \"${CMAKE_INSTALL_CONFIG_NAME}\"")
+endif()
+
+# Set the component getting installed.
+if(NOT CMAKE_INSTALL_COMPONENT)
+  if(COMPONENT)
+    message(STATUS "Install component: \"${COMPONENT}\"")
+    set(CMAKE_INSTALL_COMPONENT "${COMPONENT}")
+  else()
+    set(CMAKE_INSTALL_COMPONENT)
+  endif()
+endif()
+
+# Install shared libraries without execute permission?
+if(NOT DEFINED CMAKE_INSTALL_SO_NO_EXE)
+  set(CMAKE_INSTALL_SO_NO_EXE "1")
+endif()
+
+# Is this installation the result of a crosscompile?
+if(NOT DEFINED CMAKE_CROSSCOMPILING)
+  set(CMAKE_CROSSCOMPILING "FALSE")
+endif()
+
+# Set default install directory permissions.
+if(NOT DEFINED CMAKE_OBJDUMP)
+  set(CMAKE_OBJDUMP "/usr/bin/objdump")
+endif()
+
+if(CMAKE_INSTALL_COMPONENT)
+  set(CMAKE_INSTALL_MANIFEST "install_manifest_${CMAKE_INSTALL_COMPONENT}.txt")
+else()
+  set(CMAKE_INSTALL_MANIFEST "install_manifest.txt")
+endif()
+
+string(REPLACE ";" "\n" CMAKE_INSTALL_MANIFEST_CONTENT
+       "${CMAKE_INSTALL_MANIFEST_FILES}")
+file(WRITE "/export/users/okruglov/oneDAL/examples/oneapi/dpc/build/${CMAKE_INSTALL_MANIFEST}"
+     "${CMAKE_INSTALL_MANIFEST_CONTENT}")
diff --git a/examples/oneapi/dpc/source/connected_components/connected_components_batch.cpp b/examples/oneapi/dpc/source/connected_components/connected_components_batch.cpp
new file mode 100644
index 00000000000..8181be33b79
--- /dev/null
+++ b/examples/oneapi/dpc/source/connected_components/connected_components_batch.cpp
@@ -0,0 +1,58 @@
+/*******************************************************************************
+* Copyright 2021 Intel Corporation
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+#include <sycl/sycl.hpp>
+#include <iostream>
+
+#ifndef ONEDAL_DATA_PARALLEL
+#define ONEDAL_DATA_PARALLEL
+#endif
+
+#include "oneapi/dal/algo/connected_components.hpp"
+#include "oneapi/dal/graph/undirected_adjacency_vector_graph.hpp"
+#include "oneapi/dal/io/csv.hpp"
+
+#include "example_util/utils.hpp"
+
+namespace dal = oneapi::dal;
+
+void run(sycl::queue& q) {
+    const auto filename = get_data_path("data/graph.csv");
+
+    using graph_t = dal::preview::undirected_adjacency_vector_graph<>;
+    auto graph = dal::read<graph_t>(dal::csv::data_source{ filename });
+
+    graph.to_device(q);
+
+    const auto cc_desc = dal::preview::connected_components::descriptor<>();
+
+    const auto result = dal::preview::vertex_partitioning(q, cc_desc, graph);
+
+    std::cout << "Number of connected components: " << result.get_component_count() << std::endl;
+    std::cout << "Components' labels:" << std::endl;
+    std::cout << result.get_labels() << std::endl;
+}
+
+int main(int argc, char const* argv[]) {
+    for (auto d : list_devices()) {
+        std::cout << "Running on " << d.get_platform().get_info<sycl::info::platform::name>()
+                  << ", " << d.get_info<sycl::info::device::name>() << "\n"
+                  << std::endl;
+        auto q = sycl::queue{ d };
+        run(q);
+    }
+    return 0;
+}

From 51c088f9e53e9d640c45b6fcca11a707319bea82 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Sun, 10 May 2026 10:53:16 -0700
Subject: [PATCH 65/69] CI fix

---
 .../backend/gpu/CMakeLists.txt                | 16 ++++++++++++++
 .../backend/gpu/connected_components.hpp      |  2 +-
 ...ex_partitioning_default_kernel_gpu_dpc.cpp | 19 +++++++----------
 .../gpu/vertex_partitioning_kernel.hpp        |  4 ++--
 .../detail/select_kernel.hpp                  |  2 +-
 .../detail/select_kernel_dpc.cpp              | 21 +++++++------------
 .../test/connected_components_gpu_test.cpp    |  2 +-
 cpp/oneapi/dal/graph/detail/csr_topology.hpp  | 18 ++++++++++------
 cpp/oneapi/dal/vertex_partitioning.hpp        |  2 +-
 .../connected_components_batch.cpp            |  2 +-
 10 files changed, 51 insertions(+), 37 deletions(-)

diff --git a/cpp/oneapi/dal/algo/connected_components/backend/gpu/CMakeLists.txt b/cpp/oneapi/dal/algo/connected_components/backend/gpu/CMakeLists.txt
index 105230f978f..3d2ef8cd1f1 100644
--- a/cpp/oneapi/dal/algo/connected_components/backend/gpu/CMakeLists.txt
+++ b/cpp/oneapi/dal/algo/connected_components/backend/gpu/CMakeLists.txt
@@ -1,3 +1,19 @@
+#===============================================================================
+# Copyright 2026 Intel Corporation
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#===============================================================================
+
 set(ONEDAL_CONNECTED_COMPONENTS_BACKEND_GPU_HEADERS
     ${CMAKE_CURRENT_LIST_DIR}/connected_components.hpp
     ${CMAKE_CURRENT_LIST_DIR}/vertex_partitioning_kernel.hpp
diff --git a/cpp/oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp b/cpp/oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp
index 1d8fb2ed78d..2d67863c840 100644
--- a/cpp/oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp
+++ b/cpp/oneapi/dal/algo/connected_components/backend/gpu/connected_components.hpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2021 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
diff --git a/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_default_kernel_gpu_dpc.cpp b/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_default_kernel_gpu_dpc.cpp
index aa686630e46..753625468d6 100644
--- a/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_default_kernel_gpu_dpc.cpp
+++ b/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_default_kernel_gpu_dpc.cpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2021 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
@@ -143,11 +143,10 @@ std::int32_t* compute_components_gpu(sycl::queue& queue,
         return labels;
     }
 
-    csr_graph_device_wrapper<Index, std::int64_t> graph(
-        queue,
-        static_cast<std::uint64_t>(vertex_count),
-        rows,
-        cols);
+    csr_graph_device_wrapper<Index, std::int64_t> graph(queue,
+                                                        static_cast<std::uint64_t>(vertex_count),
+                                                        rows,
+                                                        cols);
 
     fp::frontier<std::uint32_t> in_frontier(queue, vertex_count, sycl::usm::alloc::device);
     fp::frontier<std::uint32_t> out_frontier(queue, vertex_count, sycl::usm::alloc::device);
@@ -179,8 +178,7 @@ std::int32_t* compute_components_gpu(sycl::queue& queue,
                         sycl::atomic_ref<std::int32_t,
                                          sycl::memory_order::relaxed,
                                          sycl::memory_scope::device,
-                                         sycl::access::address_space::global_space>(
-                            d_labels[dst])
+                                         sycl::access::address_space::global_space>(d_labels[dst])
                             .fetch_min(label_src);
                     return label_src < old_val;
                 }
@@ -245,9 +243,8 @@ vertex_partitioning_result<Task> run_vertex_partitioning_gpu(
         });
 
     vertex_partitioning_result<Task> result;
-    result.set_labels(dal::detail::homogen_table_builder{}
-                          .reset(labels_arr, vertex_count, 1)
-                          .build());
+    result.set_labels(
+        dal::detail::homogen_table_builder{}.reset(labels_arr, vertex_count, 1).build());
     result.set_component_count(component_count);
 
     return result;
diff --git a/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_kernel.hpp b/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_kernel.hpp
index 27c2d0da948..c71a801885e 100644
--- a/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_kernel.hpp
+++ b/cpp/oneapi/dal/algo/connected_components/backend/gpu/vertex_partitioning_kernel.hpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2021 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
@@ -34,7 +34,7 @@ struct csr_topology_gpu_view {
 
 template <typename Index = std::int32_t>
 csr_topology_gpu_view<Index> make_gpu_view(
-        const dal::preview::detail::device_csr_topology<Index>& device_topo) {
+    const dal::preview::detail::device_csr_topology<Index>& device_topo) {
     csr_topology_gpu_view<Index> view;
     view.rows = device_topo.get_rows();
     view.cols = device_topo.get_cols();
diff --git a/cpp/oneapi/dal/algo/connected_components/detail/select_kernel.hpp b/cpp/oneapi/dal/algo/connected_components/detail/select_kernel.hpp
index 999a2fc583b..e6a47bdb9fb 100644
--- a/cpp/oneapi/dal/algo/connected_components/detail/select_kernel.hpp
+++ b/cpp/oneapi/dal/algo/connected_components/detail/select_kernel.hpp
@@ -79,7 +79,7 @@ struct backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>
 
 template <typename Policy, typename Descriptor, typename Topology>
 dal::detail::shared<backend_base<Policy, Descriptor, Topology>> get_backend(const Descriptor& desc,
-                                                                         const Topology& t) {
+                                                                            const Topology& t) {
     return std::make_shared<backend_default<Policy, Descriptor, Topology>>();
 }
 
diff --git a/cpp/oneapi/dal/algo/connected_components/detail/select_kernel_dpc.cpp b/cpp/oneapi/dal/algo/connected_components/detail/select_kernel_dpc.cpp
index 627f2085510..07b44340ff3 100644
--- a/cpp/oneapi/dal/algo/connected_components/detail/select_kernel_dpc.cpp
+++ b/cpp/oneapi/dal/algo/connected_components/detail/select_kernel_dpc.cpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2021 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
@@ -42,23 +42,18 @@ backend_default<dal::detail::data_parallel_policy, Descriptor, Topology>::operat
         },
         [&]() {
             dal::backend::context_gpu gpu_ctx{ ctx };
-            return backend::vertex_partitioning_kernel_gpu<float_t, task_t, Topology>()(
-                gpu_ctx,
-                descriptor,
-                t);
+            return backend::vertex_partitioning_kernel_gpu<float_t, task_t, Topology>()(gpu_ctx,
+                                                                                        descriptor,
+                                                                                        t);
         });
 }
 
-using default_descriptor = descriptor<
-    float,
-    method::afforest,
-    task::vertex_partitioning,
-    std::allocator<char>>;
+using default_descriptor =
+    descriptor<float, method::afforest, task::vertex_partitioning, std::allocator<char>>;
 
 using default_topology = dal::preview::detail::topology<std::int32_t>;
 
-template struct ONEDAL_EXPORT backend_default<dal::detail::data_parallel_policy,
-                                              default_descriptor,
-                                              default_topology>;
+template struct ONEDAL_EXPORT
+    backend_default<dal::detail::data_parallel_policy, default_descriptor, default_topology>;
 
 } // namespace oneapi::dal::preview::connected_components::detail
diff --git a/cpp/oneapi/dal/algo/connected_components/test/connected_components_gpu_test.cpp b/cpp/oneapi/dal/algo/connected_components/test/connected_components_gpu_test.cpp
index 878b449261b..e0cf6685d23 100644
--- a/cpp/oneapi/dal/algo/connected_components/test/connected_components_gpu_test.cpp
+++ b/cpp/oneapi/dal/algo/connected_components/test/connected_components_gpu_test.cpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2021 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
diff --git a/cpp/oneapi/dal/graph/detail/csr_topology.hpp b/cpp/oneapi/dal/graph/detail/csr_topology.hpp
index c661be73d03..44dd8102bf7 100644
--- a/cpp/oneapi/dal/graph/detail/csr_topology.hpp
+++ b/cpp/oneapi/dal/graph/detail/csr_topology.hpp
@@ -174,17 +174,23 @@ class topology {
 
         if (degrees_count > 0) {
             auto device_degrees = vertex_set::empty(queue, degrees_count, sycl::usm::alloc::shared);
-            queue.memcpy(device_degrees.get_mutable_data(), _degrees.get_data(),
-                         degrees_count * sizeof(vertex_type)).wait_and_throw();
+            queue
+                .memcpy(device_degrees.get_mutable_data(),
+                        _degrees.get_data(),
+                        degrees_count * sizeof(vertex_type))
+                .wait_and_throw();
             result._degrees = device_degrees;
             result._degrees_ptr = result._degrees.get_data();
         }
 
         if (rows_vertex_count > 0) {
-            auto device_rows_vertex = vertex_edge_set::empty(queue, rows_vertex_count,
-                                                              sycl::usm::alloc::shared);
-            queue.memcpy(device_rows_vertex.get_mutable_data(), _rows_vertex.get_data(),
-                         rows_vertex_count * sizeof(vertex_edge_type)).wait_and_throw();
+            auto device_rows_vertex =
+                vertex_edge_set::empty(queue, rows_vertex_count, sycl::usm::alloc::shared);
+            queue
+                .memcpy(device_rows_vertex.get_mutable_data(),
+                        _rows_vertex.get_data(),
+                        rows_vertex_count * sizeof(vertex_edge_type))
+                .wait_and_throw();
             result._rows_vertex = device_rows_vertex;
         }
 
diff --git a/cpp/oneapi/dal/vertex_partitioning.hpp b/cpp/oneapi/dal/vertex_partitioning.hpp
index 342156e039c..097ebbf9255 100644
--- a/cpp/oneapi/dal/vertex_partitioning.hpp
+++ b/cpp/oneapi/dal/vertex_partitioning.hpp
@@ -31,7 +31,7 @@ auto vertex_partitioning(Args &&...args) {
 
 #ifdef ONEDAL_DATA_PARALLEL
 template <typename... Args>
-auto vertex_partitioning(sycl::queue& q, Args &&...args) {
+auto vertex_partitioning(sycl::queue &q, Args &&...args) {
     const auto policy = dal::detail::data_parallel_policy{ q };
     return detail::vertex_partitioning_dispatch(policy, std::forward<Args>(args)...);
 }
diff --git a/examples/oneapi/dpc/source/connected_components/connected_components_batch.cpp b/examples/oneapi/dpc/source/connected_components/connected_components_batch.cpp
index 8181be33b79..b4ad445ad8c 100644
--- a/examples/oneapi/dpc/source/connected_components/connected_components_batch.cpp
+++ b/examples/oneapi/dpc/source/connected_components/connected_components_batch.cpp
@@ -1,5 +1,5 @@
 /*******************************************************************************
-* Copyright 2021 Intel Corporation
+* Copyright 2026 Intel Corporation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.

From 7b82ee124d8f57c0e6f8660077d99774bc26f2fe Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Sun, 10 May 2026 11:32:37 -0700
Subject: [PATCH 66/69] Deleted accidentally pushed

---
 .../connected_components_batch                |  Bin 511008 -> 0 bytes
 .../intel_intel64_so/triangle_counting_batch  |  Bin 515016 -> 0 bytes
 examples/oneapi/dpc/build/Makefile            | 1944 -----------------
 examples/oneapi/dpc/build/cmake_install.cmake |   54 -
 4 files changed, 1998 deletions(-)
 delete mode 100755 examples/oneapi/dpc/_cmake_results/intel_intel64_so/connected_components_batch
 delete mode 100755 examples/oneapi/dpc/_cmake_results/intel_intel64_so/triangle_counting_batch
 delete mode 100644 examples/oneapi/dpc/build/Makefile
 delete mode 100644 examples/oneapi/dpc/build/cmake_install.cmake

diff --git a/examples/oneapi/dpc/_cmake_results/intel_intel64_so/connected_components_batch b/examples/oneapi/dpc/_cmake_results/intel_intel64_so/connected_components_batch
deleted file mode 100755
index be27c0f191b01a82d781ef84f0bdcb8909e80bbf..0000000000000000000000000000000000000000
GIT binary patch
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-	@echo "... source/decision_forest/df_cls_hist_batch_random.s"
-	@echo "... source/decision_forest/df_cls_traverse_model.o"
-	@echo "... source/decision_forest/df_cls_traverse_model.i"
-	@echo "... source/decision_forest/df_cls_traverse_model.s"
-	@echo "... source/decision_forest/df_reg_hist_batch.o"
-	@echo "... source/decision_forest/df_reg_hist_batch.i"
-	@echo "... source/decision_forest/df_reg_hist_batch.s"
-	@echo "... source/decision_forest/df_reg_hist_batch_random.o"
-	@echo "... source/decision_forest/df_reg_hist_batch_random.i"
-	@echo "... source/decision_forest/df_reg_hist_batch_random.s"
-	@echo "... source/decision_forest/df_reg_traverse_model.o"
-	@echo "... source/decision_forest/df_reg_traverse_model.i"
-	@echo "... source/decision_forest/df_reg_traverse_model.s"
-	@echo "... source/kmeans/kmeans_lloyd_csr_batch.o"
-	@echo "... source/kmeans/kmeans_lloyd_csr_batch.i"
-	@echo "... source/kmeans/kmeans_lloyd_csr_batch.s"
-	@echo "... source/kmeans/kmeans_lloyd_dense_batch.o"
-	@echo "... source/kmeans/kmeans_lloyd_dense_batch.i"
-	@echo "... source/kmeans/kmeans_lloyd_dense_batch.s"
-	@echo "... source/kmeans_init/kmeans_init_dense.o"
-	@echo "... source/kmeans_init/kmeans_init_dense.i"
-	@echo "... source/kmeans_init/kmeans_init_dense.s"
-	@echo "... source/knn/knn_cls_brute_force_dense_batch.o"
-	@echo "... source/knn/knn_cls_brute_force_dense_batch.i"
-	@echo "... source/knn/knn_cls_brute_force_dense_batch.s"
-	@echo "... source/knn/knn_reg_brute_force_dense_batch.o"
-	@echo "... source/knn/knn_reg_brute_force_dense_batch.i"
-	@echo "... source/knn/knn_reg_brute_force_dense_batch.s"
-	@echo "... source/knn/knn_search_brute_force_dense_batch.o"
-	@echo "... source/knn/knn_search_brute_force_dense_batch.i"
-	@echo "... source/knn/knn_search_brute_force_dense_batch.s"
-	@echo "... source/linear_kernel/linear_kernel_dense_batch.o"
-	@echo "... source/linear_kernel/linear_kernel_dense_batch.i"
-	@echo "... source/linear_kernel/linear_kernel_dense_batch.s"
-	@echo "... source/linear_regression/linear_regression_dense_batch.o"
-	@echo "... source/linear_regression/linear_regression_dense_batch.i"
-	@echo "... source/linear_regression/linear_regression_dense_batch.s"
-	@echo "... source/linear_regression/linear_regression_dense_online.o"
-	@echo "... source/linear_regression/linear_regression_dense_online.i"
-	@echo "... source/linear_regression/linear_regression_dense_online.s"
-	@echo "... source/logistic_regression/logistic_regression_dense_batch.o"
-	@echo "... source/logistic_regression/logistic_regression_dense_batch.i"
-	@echo "... source/logistic_regression/logistic_regression_dense_batch.s"
-	@echo "... source/misc/read_batch.o"
-	@echo "... source/misc/read_batch.i"
-	@echo "... source/misc/read_batch.s"
-	@echo "... source/pca/pca_cor_dense_batch.o"
-	@echo "... source/pca/pca_cor_dense_batch.i"
-	@echo "... source/pca/pca_cor_dense_batch.s"
-	@echo "... source/pca/pca_cor_dense_online.o"
-	@echo "... source/pca/pca_cor_dense_online.i"
-	@echo "... source/pca/pca_cor_dense_online.s"
-	@echo "... source/pca/pca_cov_dense_batch.o"
-	@echo "... source/pca/pca_cov_dense_batch.i"
-	@echo "... source/pca/pca_cov_dense_batch.s"
-	@echo "... source/pca/pca_cov_dense_online.o"
-	@echo "... source/pca/pca_cov_dense_online.i"
-	@echo "... source/pca/pca_cov_dense_online.s"
-	@echo "... source/pca/pca_precomputed_cor_dense_batch.o"
-	@echo "... source/pca/pca_precomputed_cor_dense_batch.i"
-	@echo "... source/pca/pca_precomputed_cor_dense_batch.s"
-	@echo "... source/pca/pca_precomputed_cov_dense_batch.o"
-	@echo "... source/pca/pca_precomputed_cov_dense_batch.i"
-	@echo "... source/pca/pca_precomputed_cov_dense_batch.s"
-	@echo "... source/pca/pca_svd_dense_batch.o"
-	@echo "... source/pca/pca_svd_dense_batch.i"
-	@echo "... source/pca/pca_svd_dense_batch.s"
-	@echo "... source/rbf_kernel/rbf_kernel_dense_batch.o"
-	@echo "... source/rbf_kernel/rbf_kernel_dense_batch.i"
-	@echo "... source/rbf_kernel/rbf_kernel_dense_batch.s"
-	@echo "... source/svm/svm_two_class_thunder_dense_batch.o"
-	@echo "... source/svm/svm_two_class_thunder_dense_batch.i"
-	@echo "... source/svm/svm_two_class_thunder_dense_batch.s"
-	@echo "... source/table/column_accessor_homogen.o"
-	@echo "... source/table/column_accessor_homogen.i"
-	@echo "... source/table/column_accessor_homogen.s"
-	@echo "... source/table/csr_accessor.o"
-	@echo "... source/table/csr_accessor.i"
-	@echo "... source/table/csr_accessor.s"
-	@echo "... source/table/csr_table.o"
-	@echo "... source/table/csr_table.i"
-	@echo "... source/table/csr_table.s"
-	@echo "... source/table/heterogen_table.o"
-	@echo "... source/table/heterogen_table.i"
-	@echo "... source/table/heterogen_table.s"
-	@echo "... source/table/homogen_table.o"
-	@echo "... source/table/homogen_table.i"
-	@echo "... source/table/homogen_table.s"
-	@echo "... source/triangle_counting/triangle_counting_batch.o"
-	@echo "... source/triangle_counting/triangle_counting_batch.i"
-	@echo "... source/triangle_counting/triangle_counting_batch.s"
-.PHONY : help
-
-
-
-#=============================================================================
-# Special targets to cleanup operation of make.
-
-# Special rule to run CMake to check the build system integrity.
-# No rule that depends on this can have commands that come from listfiles
-# because they might be regenerated.
-cmake_check_build_system:
-	$(CMAKE_COMMAND) -S$(CMAKE_SOURCE_DIR) -B$(CMAKE_BINARY_DIR) --check-build-system CMakeFiles/Makefile.cmake 0
-.PHONY : cmake_check_build_system
-
diff --git a/examples/oneapi/dpc/build/cmake_install.cmake b/examples/oneapi/dpc/build/cmake_install.cmake
deleted file mode 100644
index 15527649405..00000000000
--- a/examples/oneapi/dpc/build/cmake_install.cmake
+++ /dev/null
@@ -1,54 +0,0 @@
-# Install script for directory: /export/users/okruglov/oneDAL/examples/oneapi/dpc
-
-# Set the install prefix
-if(NOT DEFINED CMAKE_INSTALL_PREFIX)
-  set(CMAKE_INSTALL_PREFIX "/usr/local")
-endif()
-string(REGEX REPLACE "/$" "" CMAKE_INSTALL_PREFIX "${CMAKE_INSTALL_PREFIX}")
-
-# Set the install configuration name.
-if(NOT DEFINED CMAKE_INSTALL_CONFIG_NAME)
-  if(BUILD_TYPE)
-    string(REGEX REPLACE "^[^A-Za-z0-9_]+" ""
-           CMAKE_INSTALL_CONFIG_NAME "${BUILD_TYPE}")
-  else()
-    set(CMAKE_INSTALL_CONFIG_NAME "Release")
-  endif()
-  message(STATUS "Install configuration: \"${CMAKE_INSTALL_CONFIG_NAME}\"")
-endif()
-
-# Set the component getting installed.
-if(NOT CMAKE_INSTALL_COMPONENT)
-  if(COMPONENT)
-    message(STATUS "Install component: \"${COMPONENT}\"")
-    set(CMAKE_INSTALL_COMPONENT "${COMPONENT}")
-  else()
-    set(CMAKE_INSTALL_COMPONENT)
-  endif()
-endif()
-
-# Install shared libraries without execute permission?
-if(NOT DEFINED CMAKE_INSTALL_SO_NO_EXE)
-  set(CMAKE_INSTALL_SO_NO_EXE "1")
-endif()
-
-# Is this installation the result of a crosscompile?
-if(NOT DEFINED CMAKE_CROSSCOMPILING)
-  set(CMAKE_CROSSCOMPILING "FALSE")
-endif()
-
-# Set default install directory permissions.
-if(NOT DEFINED CMAKE_OBJDUMP)
-  set(CMAKE_OBJDUMP "/usr/bin/objdump")
-endif()
-
-if(CMAKE_INSTALL_COMPONENT)
-  set(CMAKE_INSTALL_MANIFEST "install_manifest_${CMAKE_INSTALL_COMPONENT}.txt")
-else()
-  set(CMAKE_INSTALL_MANIFEST "install_manifest.txt")
-endif()
-
-string(REPLACE ";" "\n" CMAKE_INSTALL_MANIFEST_CONTENT
-       "${CMAKE_INSTALL_MANIFEST_FILES}")
-file(WRITE "/export/users/okruglov/oneDAL/examples/oneapi/dpc/build/${CMAKE_INSTALL_MANIFEST}"
-     "${CMAKE_INSTALL_MANIFEST_CONTENT}")

From 2e7f266297aaba5d916b4741274c0c574180976b Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Mon, 11 May 2026 09:31:17 -0700
Subject: [PATCH 67/69] Temaplate instantiation fix

---
 .../detail/vertex_partitioning_default_kernel.cpp            | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp
index 096de96fb9f..09a8c3dd618 100644
--- a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp
+++ b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp
@@ -32,7 +32,8 @@ operator()(const dal::detail::host_policy& policy,
     });
 }
 
-template struct ONEDAL_EXPORT
-    afforest<float, task::vertex_partitioning, dal::preview::detail::topology<std::int32_t>>;
+template struct afforest<float,
+                        task::vertex_partitioning,
+                        dal::preview::detail::topology<std::int32_t>>;
 
 } // namespace oneapi::dal::preview::connected_components::detail

From 17536dba9f0630d717147273256524cc0d40dcda Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Mon, 11 May 2026 11:33:51 -0700
Subject: [PATCH 68/69] Fix

---
 .../detail/vertex_partitioning_default_kernel.cpp      | 10 ++++++++++
 .../detail/vertex_partitioning_default_kernel.hpp      | 10 +++++++---
 2 files changed, 17 insertions(+), 3 deletions(-)

diff --git a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp
index 09a8c3dd618..4235f6ea1cb 100644
--- a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp
+++ b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp
@@ -36,4 +36,14 @@ template struct afforest<float,
                         task::vertex_partitioning,
                         dal::preview::detail::topology<std::int32_t>>;
 
+vertex_partitioning_result<task::vertex_partitioning> run_afforest(
+    const dal::detail::host_policy& ctx,
+    const detail::descriptor_base<task::vertex_partitioning>& desc,
+    const dal::preview::detail::topology<std::int32_t>& t,
+    byte_alloc_iface* alloc) {
+    return afforest<float,
+                    task::vertex_partitioning,
+                    dal::preview::detail::topology<std::int32_t>>{}(ctx, desc, t, alloc);
+}
+
 } // namespace oneapi::dal::preview::connected_components::detail
diff --git a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.hpp b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.hpp
index ffa9e0024b7..4372c04bfaf 100644
--- a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.hpp
+++ b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.hpp
@@ -78,6 +78,12 @@ struct vertex_partitioning_kernel_cpu<method::afforest,
     }
 };
 
+ONEDAL_EXPORT vertex_partitioning_result<task::vertex_partitioning> run_afforest(
+    const dal::detail::host_policy& ctx,
+    const detail::descriptor_base<task::vertex_partitioning>& desc,
+    const dal::preview::detail::topology<std::int32_t>& t,
+    byte_alloc_iface* alloc);
+
 template <typename Allocator>
 struct vertex_partitioning_kernel_cpu<method::afforest,
                                       task::vertex_partitioning,
@@ -93,9 +99,7 @@ struct vertex_partitioning_kernel_cpu<method::afforest,
         if (vertex_count == 0) {
             return vertex_partitioning_result<task::vertex_partitioning>();
         }
-        return afforest<float,
-                        task::vertex_partitioning,
-                        dal::preview::detail::topology<std::int32_t>>{}(ctx, desc, t, &alloc_con);
+        return run_afforest(ctx, desc, t, &alloc_con);
     }
 };
 

From 4c04417299e6fa7816953ecf6f3ea8f896306552 Mon Sep 17 00:00:00 2001
From: "Kruglov, Oleg" <oleg.kruglov@intel.com>
Date: Tue, 12 May 2026 08:24:30 -0700
Subject: [PATCH 69/69] Format fix

---
 .../detail/vertex_partitioning_default_kernel.cpp             | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp
index 4235f6ea1cb..05caed3188c 100644
--- a/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp
+++ b/cpp/oneapi/dal/algo/connected_components/detail/vertex_partitioning_default_kernel.cpp
@@ -33,8 +33,8 @@ operator()(const dal::detail::host_policy& policy,
 }
 
 template struct afforest<float,
-                        task::vertex_partitioning,
-                        dal::preview::detail::topology<std::int32_t>>;
+                         task::vertex_partitioning,
+                         dal::preview::detail::topology<std::int32_t>>;
 
 vertex_partitioning_result<task::vertex_partitioning> run_afforest(
     const dal::detail::host_policy& ctx,