refactored

Author: mfreeman451

README.md

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+# BMSSP-Go: Bounded Multi-Source Shortest Path Algorithm
+
+[![Go Reference](https://pkg.go.dev/badge/github.com/mfreeman451/bmssp-go.svg)](https://pkg.go.dev/github.com/mfreeman451/bmssp-go)
+[![Go Report Card](https://goreportcard.com/badge/github.com/mfreeman451/bmssp-go)](https://goreportcard.com/report/github.com/mfreeman451/bmssp-go)
+[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
+
+A high-performance Go implementation of the Bounded Multi-Source Shortest Path (BMSSP) algorithm, which provides significant speedups over traditional Dijkstra's algorithm for single-source shortest path problems.
+
+## Overview
+
+This implementation is based on the paper ["Breaking the Sorting Barrier for Directed Single-Source Shortest Paths"](https://arxiv.org/abs/2504.17033) by Ran Duan et al. The BMSSP algorithm achieves **O(m log^(2/3) n)** time complexity, breaking the traditional sorting barrier for shortest path algorithms.
+
+## Performance
+
+Our benchmarks show significant performance improvements over standard Dijkstra's algorithm:
+
+| Graph Type | Dijkstra | BMSSP | **Speedup** |
+|------------|----------|-------|-------------|
+| Random 100 nodes | 37.1μs | 22.3μs | **1.66x** |
+| Random 1000 nodes | 453μs | 100μs | **4.53x** |
+| Grid 50×50 | 987μs | 180μs | **5.50x** |
+
+Performance advantages increase with graph size and are particularly pronounced on structured graphs.
+
+## Installation
+
+```bash
+go get github.com/mfreeman451/bmssp-go
+```
+
+## Quick Start
+
+```go
+package main
+
+import (
+    "fmt"
+    "math"
+    
+    "github.com/mfreeman451/bmssp-go"
+)
+
+func main() {
+    // Create a new graph
+    g := bmssp.NewGraph()
+    
+    // Add edges (u, v, weight)
+    g.AddEdge(0, 1, 2.0)
+    g.AddEdge(0, 2, 5.0)
+    g.AddEdge(1, 3, 4.0)
+    g.AddEdge(2, 3, 1.0)
+    
+    // Initialize distance map
+    dhat := make(map[bmssp.NodeID]bmssp.Dist)
+    for i := 0; i < 4; i++ {
+        dhat[bmssp.NodeID(i)] = bmssp.Dist(math.Inf(1))
+    }
+    dhat[0] = 0 // source node
+    
+    // Create source set
+    S := bmssp.NewNodeSet()
+    S.Add(0)
+    
+    // Run BMSSP algorithm
+    bound, visited := bmssp.BMSSP(
+        2,      // recursion levels (l)
+        1000,   // distance bound (B)
+        S,      // source set
+        100,    // expansion parameter (k)
+        1,      // branching parameter (t)
+        g,      // graph
+        dhat,   // distance map (modified in-place)
+    )
+    
+    fmt.Printf("Bound: %v\n", bound)
+    fmt.Printf("Visited nodes: %v\n", visited)
+    fmt.Printf("Distances: %v\n", dhat)
+}
+```
+
+## API Reference
+
+### Core Types
+
+```go
+type NodeID int           // Graph node identifier
+type Dist float64        // Distance/weight type
+type Graph struct { ... } // Directed graph structure
+type NodeSet map[NodeID]struct{} // Set of nodes
+```
+
+### Main Functions
+
+#### `BMSSP(l int, B Dist, S NodeSet, k, t int, g *Graph, dhat map[NodeID]Dist) (Dist, NodeSet)`
+The main BMSSP algorithm implementation.
+
+**Parameters:**
+- `l`: Recursion depth levels
+- `B`: Distance bound for exploration
+- `S`: Set of source nodes
+- `k`: Expansion parameter (controls exploration breadth)
+- `t`: Branching parameter (affects data structure sizing)
+- `g`: Input graph
+- `dhat`: Distance map (modified in-place)
+
+**Returns:**
+- Final bound and set of visited nodes
+
+#### `BaseCase(B Dist, S NodeSet, k int, g *Graph, dhat map[NodeID]Dist) (Dist, NodeSet)`
+Bounded Dijkstra's algorithm used as the base case.
+
+#### `Dijkstra(g *Graph, source NodeID) map[NodeID]Dist`
+Standard Dijkstra's algorithm for comparison.
+
+### Graph Operations
+
+```go
+g := NewGraph()                    // Create new graph
+g.AddEdge(u, v, weight)           // Add directed edge
+edges := g.OutEdges(u)            // Get outgoing edges from node u
+```
+
+### Node Sets
+
+```go
+s := NewNodeSet()                 // Create new node set
+s.Add(nodeID)                     // Add node to set
+count := s.Len()                  // Get set size
+clone := s.Clone()                // Create copy of set
+```
+
+## Algorithm Parameters
+
+### Choosing Parameters
+
+- **`l` (levels)**: Start with 1-2 for most graphs. Higher values may help on very large graphs.
+- **`k` (expansion)**: Use 50-200. Higher values explore more nodes but may be slower.
+- **`t` (branching)**: Usually 1 is sufficient.
+- **`B` (bound)**: Use a large value (e.g., 1000) to explore the full graph.
+
+### Parameter Tuning
+
+```go
+// For small graphs (< 1000 nodes)
+bound, visited := bmssp.BMSSP(1, 1000, sources, 50, 1, graph, distances)
+
+// For large graphs (> 1000 nodes)  
+bound, visited := bmssp.BMSSP(2, 1000, sources, 100, 1, graph, distances)
+
+// For very structured graphs (grids, trees)
+bound, visited := bmssp.BMSSP(1, 1000, sources, 200, 1, graph, distances)
+```
+
+## Examples
+
+### Example 1: Random Graph
+
+```go
+func ExampleRandomGraph() {
+    g := bmssp.NewGraph()
+    
+    // Create random graph
+    edges := [][3]float64{
+        {0, 1, 3}, {0, 2, 8}, {1, 2, 2}, {1, 3, 5},
+        {2, 4, 4}, {3, 4, 1}, {3, 5, 6}, {4, 5, 2},
+    }
+    
+    for _, e := range edges {
+        g.AddEdge(bmssp.NodeID(e[0]), bmssp.NodeID(e[1]), bmssp.Dist(e[2]))
+    }
+    
+    // Run BMSSP from node 0
+    dhat := initializeDistances(g, 0)
+    sources := bmssp.NewNodeSet()
+    sources.Add(0)
+    
+    bmssp.BMSSP(2, 1000, sources, 100, 1, g, dhat)
+    
+    // dhat now contains shortest distances from node 0
+}
+```
+
+### Example 2: Grid Graph
+
+```go
+func ExampleGridGraph() {
+    g := createGridGraph(10, 10) // 10x10 grid
+    
+    dhat := initializeDistances(g, 0) // top-left corner
+    sources := bmssp.NewNodeSet()
+    sources.Add(0)
+    
+    // BMSSP works particularly well on structured graphs
+    bmssp.BMSSP(1, 1000, sources, 200, 1, g, dhat)
+}
+```
+
+## Benchmarking
+
+Run benchmarks to compare with Dijkstra:
+
+```bash
+go test -bench=. -benchmem ./...
+```
+
+This will run comprehensive benchmarks on various graph types and sizes.
+
+## Development
+
+### Testing
+
+```bash
+go test ./...                    # Run all tests
+go test -v ./...                # Verbose output
+go test -race ./...             # Race condition detection
+```
+
+### Benchmarking
+
+```bash
+go test -bench=. ./...          # Run all benchmarks
+go test -bench=Random ./...     # Random graph benchmarks
+go test -bench=Grid ./...       # Grid graph benchmarks
+```
+
+### Documentation
+
+Generate documentation:
+
+```bash
+go doc -all                     # View all documentation
+godoc -http=:6060              # Local documentation server
+```
+
+## Algorithm Details
+
+The BMSSP algorithm works by:
+
+1. **Finding Pivots**: Identifies key nodes for exploration using `FindPivots`
+2. **Hierarchical Processing**: Uses recursive calls with decreasing bounds
+3. **Bounded Exploration**: Each level only explores nodes within distance bounds
+4. **Efficient Data Structures**: Custom bucketed queue (`DStruct`) for fast operations
+
+### Key Innovations
+
+- **Breaking the sorting barrier**: Achieves sub-O(m log n) complexity
+- **Adaptive exploration**: Only visits relevant parts of the graph
+- **Memory efficiency**: Lower memory usage than traditional algorithms
+- **Structured graph optimization**: Excellent performance on grids, trees, etc.
+
+## Contributing
+
+1. Fork the repository
+2. Create a feature branch (`git checkout -b feature/amazing-feature`)
+3. Commit your changes (`git commit -m 'Add amazing feature'`)
+4. Push to the branch (`git push origin feature/amazing-feature`)
+5. Open a Pull Request
+
+## License
+
+This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.
+
+## Citation
+
+If you use this implementation in academic work, please cite:
+
+```bibtex
+@article{duan2024breaking,
+  title={Breaking the Sorting Barrier for Directed Single-Source Shortest Paths},
+  author={Duan, Ran and others},
+  journal={arXiv preprint arXiv:2504.17033},
+  year={2024}
+}
+```
+
+## Related Work
+
+- [Original paper on arXiv](https://arxiv.org/abs/2504.17033)
+- [Dijkstra's algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
+- [Single-source shortest path problem](https://en.wikipedia.org/wiki/Shortest_path_problem)