Split MPP by maximizing expected delivered amount

As suggested by @renepickhardt in #2785

Author: thomash-acinq

eclair-core/src/main/resources/reference.conf

@@ -461,6 +461,7 @@ eclair {
         mpp {
           min-amount-satoshis = 15000 // minimum amount sent via partial HTLCs
           max-parts = 5 // maximum number of HTLCs sent per payment: increasing this value will impact performance
+          splitting-strategy = "randomize" // Can be either "full-capacity", "randomize" or "max-expected-amount"
         }
 
         boundaries {

eclair-core/src/main/scala/fr/acinq/eclair/NodeParams.scala

@@ -468,7 +468,12 @@ object NodeParams extends Logging {
         usePastRelaysData = config.getBoolean("use-past-relay-data")),
       mpp = MultiPartParams(
         Satoshi(config.getLong("mpp.min-amount-satoshis")).toMilliSatoshi,
-        config.getInt("mpp.max-parts")),
+        config.getInt("mpp.max-parts"),
+        config.getString("mpp.splitting-strategy") match {
+          case "full-capacity" => MultiPartParams.FullCapacity
+          case "randomize" => MultiPartParams.Randomize
+          case "max-expected-amount" => MultiPartParams.MaxExpectedAmount
+        }),
       experimentName = name,
       experimentPercentage = config.getInt("percentage"))
 

eclair-core/src/main/scala/fr/acinq/eclair/remote/EclairInternalsSerializer.scala

@@ -70,7 +70,17 @@ object EclairInternalsSerializer {
 
   val multiPartParamsCodec: Codec[MultiPartParams] = (
     ("minPartAmount" | millisatoshi) ::
-      ("maxParts" | int32)).as[MultiPartParams]
+      ("maxParts" | int32) ::
+      ("splittingStrategy" | int8.narrow[MultiPartParams.SplittingStrategy]({
+        case 0 => Attempt.successful(MultiPartParams.FullCapacity)
+        case 1 => Attempt.successful(MultiPartParams.Randomize)
+        case 2 => Attempt.successful(MultiPartParams.MaxExpectedAmount)
+        case n => Attempt.failure(Err(s"Invalid value $n"))
+      }, {
+        case MultiPartParams.FullCapacity => 0
+        case MultiPartParams.Randomize => 1
+        case MultiPartParams.MaxExpectedAmount => 2
+      }))).as[MultiPartParams]
 
   val pathFindingConfCodec: Codec[PathFindingConf] = (
     ("randomize" | bool(8)) ::

eclair-core/src/main/scala/fr/acinq/eclair/router/RouteCalculation.scala

@@ -429,7 +429,7 @@ object RouteCalculation {
       // We want to ensure that the set of routes we find have enough capacity to allow sending the total amount,
       // without excluding routes with small capacity when the total amount is small.
       val minPartAmount = routeParams.mpp.minPartAmount.max(amount / numRoutes).min(amount)
-      routeParams.copy(mpp = MultiPartParams(minPartAmount, numRoutes))
+      routeParams.copy(mpp = MultiPartParams(minPartAmount, numRoutes, routeParams.mpp.splittingStrategy))
     }
     findRouteInternal(g, localNodeId, targetNodeId, routeParams1.mpp.minPartAmount, maxFee, routeParams1.mpp.maxParts, extraEdges, ignoredEdges, ignoredVertices, routeParams1, currentBlockHeight) match {
       case Right(routes) =>
@@ -455,16 +455,16 @@ object RouteCalculation {
         // this route doesn't have enough capacity left: we remove it and continue.
         split(amount, paths, usedCapacity, routeParams, selectedRoutes)
       } else {
-        val route = if (routeParams.randomize) {
-          // randomly choose the amount to be between 20% and 100% of the available capacity.
-          val randomizedAmount = candidate.amount * ((20d + Random.nextInt(81)) / 100)
-          if (randomizedAmount < routeParams.mpp.minPartAmount) {
-            candidate.copy(amount = routeParams.mpp.minPartAmount.min(amount))
-          } else {
-            candidate.copy(amount = randomizedAmount.min(amount))
-          }
-        } else {
-          candidate.copy(amount = candidate.amount.min(amount))
+        val route = routeParams.mpp.splittingStrategy match {
+          case MultiPartParams.Randomize =>
+            // randomly choose the amount to be between 20% and 100% of the available capacity.
+            val randomizedAmount = candidate.amount * ((20d + Random.nextInt(81)) / 100)
+            candidate.copy(amount = randomizedAmount.max(routeParams.mpp.minPartAmount).min(amount))
+          case MultiPartParams.MaxExpectedAmount =>
+            val bestAmount = optimizeExpectedValue(current.path, candidate.amount, usedCapacity)
+            candidate.copy(amount = bestAmount.max(routeParams.mpp.minPartAmount).min(amount))
+          case MultiPartParams.FullCapacity =>
+            candidate.copy(amount = candidate.amount.min(amount))
         }
         updateUsedCapacity(route, usedCapacity)
         // NB: we re-enqueue the current path, it may still have capacity for a second HTLC.
@@ -473,6 +473,26 @@ object RouteCalculation {
     }
   }
 
+  private def optimizeExpectedValue(route: Seq[GraphEdge], capacity: MilliSatoshi, usedCapacity: mutable.Map[ShortChannelId, MilliSatoshi]): MilliSatoshi = {
+    // We search the maximum value of a polynomial between its two smallest roots (0 and the minimum channel capacity on the path).
+    // We use binary search to find where the derivative changes sign.
+    var low = 1L
+    var high = capacity.toLong
+    while (high - low > 1L) {
+      val mid = (high + low) / 2
+      val d = route.drop(1).foldLeft(1.0 / mid) { case (x, edge) =>
+        val availableCapacity = edge.capacity - usedCapacity.getOrElse(edge.desc.shortChannelId, 0 msat)
+        x - 1.0 / (availableCapacity.toLong - mid)
+      }
+      if (d > 0.0) {
+        low = mid
+      } else {
+        high = mid
+      }
+    }
+    MilliSatoshi(high)
+  }
+
   /** Compute the maximum amount that we can send through the given route. */
   private def computeRouteMaxAmount(route: Seq[GraphEdge], usedCapacity: mutable.Map[ShortChannelId, MilliSatoshi]): Route = {
     val firstHopMaxAmount = route.head.maxHtlcAmount(usedCapacity.getOrElse(route.head.desc.shortChannelId, 0 msat))

eclair-core/src/main/scala/fr/acinq/eclair/router/Router.scala

@@ -577,7 +577,20 @@ object Router {
     override def fee(amount: MilliSatoshi): MilliSatoshi = fee
   }
 
-  case class MultiPartParams(minPartAmount: MilliSatoshi, maxParts: Int)
+  object MultiPartParams {
+    sealed trait SplittingStrategy
+
+    /** Send the full capacity of the route */
+    object FullCapacity extends SplittingStrategy
+
+    /** Send between 20% and 100% of the capacity of the route */
+    object Randomize extends SplittingStrategy
+
+    /** Maximize the expected delivered amount */
+    object MaxExpectedAmount extends SplittingStrategy
+  }
+
+  case class MultiPartParams(minPartAmount: MilliSatoshi, maxParts: Int, splittingStrategy: MultiPartParams.SplittingStrategy)
 
   case class RouteParams(randomize: Boolean,
                          boundaries: SearchBoundaries,

eclair-core/src/test/scala/fr/acinq/eclair/TestConstants.scala

@@ -231,6 +231,7 @@ object TestConstants {
           mpp = MultiPartParams(
             minPartAmount = 15000000 msat,
             maxParts = 10,
+            splittingStrategy = MultiPartParams.FullCapacity
           ),
           experimentName = "alice-test-experiment",
           experimentPercentage = 100))),
@@ -422,6 +423,7 @@ object TestConstants {
           mpp = MultiPartParams(
             minPartAmount = 15000000 msat,
             maxParts = 10,
+            splittingStrategy = MultiPartParams.FullCapacity
           ),
           experimentName = "bob-test-experiment",
           experimentPercentage = 100))),

eclair-core/src/test/scala/fr/acinq/eclair/integration/IntegrationSpec.scala

@@ -64,7 +64,7 @@ abstract class IntegrationSpec extends TestKitBaseClass with BitcoindService wit
       useLogProbability = false,
       usePastRelaysData = false
     ),
-    mpp = MultiPartParams(15000000 msat, 6),
+    mpp = MultiPartParams(15000000 msat, 6, MultiPartParams.FullCapacity),
     experimentName = "my-test-experiment",
     experimentPercentage = 100
   ).getDefaultRouteParams

eclair-core/src/test/scala/fr/acinq/eclair/payment/MultiPartPaymentLifecycleSpec.scala

@@ -697,7 +697,7 @@ object MultiPartPaymentLifecycleSpec {
       6,
       CltvExpiryDelta(1008)),
     HeuristicsConstants(0, RelayFees(0 msat, 0), RelayFees(0 msat, 0), useLogProbability = false, usePastRelaysData = false),
-    MultiPartParams(1000 msat, 5),
+    MultiPartParams(1000 msat, 5, MultiPartParams.FullCapacity),
     experimentName = "my-test-experiment",
     experimentPercentage = 100
   ).getDefaultRouteParams

eclair-core/src/test/scala/fr/acinq/eclair/payment/PaymentLifecycleSpec.scala

@@ -302,7 +302,7 @@ class PaymentLifecycleSpec extends BaseRouterSpec {
       randomize = false,
       boundaries = SearchBoundaries(100 msat, 0.0, 20, CltvExpiryDelta(2016)),
       HeuristicsConstants(0, RelayFees(0 msat, 0), RelayFees(0 msat, 0), useLogProbability = false, usePastRelaysData = false),
-      MultiPartParams(10_000 msat, 5),
+      MultiPartParams(10_000 msat, 5, MultiPartParams.FullCapacity),
       "my-test-experiment",
       experimentPercentage = 100
     ).getDefaultRouteParams

eclair-core/src/test/scala/fr/acinq/eclair/router/RouteCalculationSpec.scala

@@ -905,7 +905,7 @@ class RouteCalculationSpec extends AnyFunSuite with ParallelTestExecution {
       makeEdge(4L, a, b, 100 msat, 20, minHtlc = 1 msat, balance_opt = Some(16000 msat)),
     )), 1 day)
     // We set max-parts to 3, but it should be ignored when sending to a direct neighbor.
-    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = MultiPartParams(2500 msat, 3))
+    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = MultiPartParams(2500 msat, 3, DEFAULT_ROUTE_PARAMS.mpp.splittingStrategy))
 
     {
       val Success(routes) = findMultiPartRoute(g, a, b, amount, 1 msat, routeParams = routeParams, currentBlockHeight = BlockHeight(400000))
@@ -921,7 +921,7 @@ class RouteCalculationSpec extends AnyFunSuite with ParallelTestExecution {
     }
     {
       // We set min-part-amount to a value that excludes channels 1 and 4.
-      val failure = findMultiPartRoute(g, a, b, amount, 1 msat, routeParams = routeParams.copy(mpp = MultiPartParams(16500 msat, 3)), currentBlockHeight = BlockHeight(400000))
+      val failure = findMultiPartRoute(g, a, b, amount, 1 msat, routeParams = routeParams.copy(mpp = MultiPartParams(16500 msat, 3, routeParams.mpp.splittingStrategy)), currentBlockHeight = BlockHeight(400000))
       assert(failure == Failure(RouteNotFound))
     }
   }
@@ -1048,7 +1048,7 @@ class RouteCalculationSpec extends AnyFunSuite with ParallelTestExecution {
     )), 1 day)
 
     val amount = 30000 msat
-    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = MultiPartParams(2500 msat, 5))
+    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = MultiPartParams(2500 msat, 5, DEFAULT_ROUTE_PARAMS.mpp.splittingStrategy))
     val Success(routes) = findMultiPartRoute(g, a, b, amount, 1 msat, routeParams = routeParams, currentBlockHeight = BlockHeight(400000))
     assert(routes.forall(_.hops.length == 1), routes)
     assert(routes.length == 3, routes)
@@ -1180,7 +1180,7 @@ class RouteCalculationSpec extends AnyFunSuite with ParallelTestExecution {
     // |               |
     // +--- B --- D ---+
     // Our balance and the amount we want to send are below the minimum part amount.
-    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = MultiPartParams(5000 msat, 5))
+    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = MultiPartParams(5000 msat, 5, DEFAULT_ROUTE_PARAMS.mpp.splittingStrategy))
     val g = GraphWithBalanceEstimates(DirectedGraph(List(
       makeEdge(1L, a, b, 50 msat, 100, minHtlc = 1 msat, balance_opt = Some(1500 msat)),
       makeEdge(2L, b, d, 15 msat, 0, minHtlc = 1 msat, capacity = 25 sat),
@@ -1300,22 +1300,22 @@ class RouteCalculationSpec extends AnyFunSuite with ParallelTestExecution {
     {
       val amount = 15_000_000 msat
       val maxFee = 50_000 msat // this fee is enough to go through the preferred route
-      val routeParams = DEFAULT_ROUTE_PARAMS.copy(randomize = false, mpp = MultiPartParams(50_000 msat, 5))
+      val routeParams = DEFAULT_ROUTE_PARAMS.copy(randomize = false, mpp = MultiPartParams(50_000 msat, 5, DEFAULT_ROUTE_PARAMS.mpp.splittingStrategy))
       val Success(routes) = findMultiPartRoute(g, a, d, amount, maxFee, routeParams = routeParams, currentBlockHeight = BlockHeight(400000))
       checkRouteAmounts(routes, amount, maxFee)
       assert(routes2Ids(routes) == Set(Seq(100L, 101L)))
     }
     {
       val amount = 15_000_000 msat
       val maxFee = 10_000 msat // this fee is too low to go through the preferred route
-      val routeParams = DEFAULT_ROUTE_PARAMS.copy(randomize = false, mpp = MultiPartParams(50_000 msat, 5))
+      val routeParams = DEFAULT_ROUTE_PARAMS.copy(randomize = false, mpp = MultiPartParams(50_000 msat, 5, DEFAULT_ROUTE_PARAMS.mpp.splittingStrategy))
       val failure = findMultiPartRoute(g, a, d, amount, maxFee, routeParams = routeParams, currentBlockHeight = BlockHeight(400000))
       assert(failure == Failure(RouteNotFound))
     }
     {
       val amount = 5_000_000 msat
       val maxFee = 10_000 msat // this fee is enough to go through the preferred route, but the cheaper ones can handle it
-      val routeParams = DEFAULT_ROUTE_PARAMS.copy(randomize = false, mpp = MultiPartParams(50_000 msat, 5))
+      val routeParams = DEFAULT_ROUTE_PARAMS.copy(randomize = false, mpp = MultiPartParams(50_000 msat, 5, DEFAULT_ROUTE_PARAMS.mpp.splittingStrategy))
       val Success(routes) = findMultiPartRoute(g, a, d, amount, maxFee, routeParams = routeParams, currentBlockHeight = BlockHeight(400000))
       assert(routes.length == 5)
       routes.foreach(route => {
@@ -1405,7 +1405,7 @@ class RouteCalculationSpec extends AnyFunSuite with ParallelTestExecution {
       makeEdge(6L, b, c, 5 msat, 50, minHtlc = 1000 msat, capacity = 20 sat),
       makeEdge(7L, c, f, 5 msat, 10, minHtlc = 1500 msat, capacity = 50 sat)
     )), 1 day)
-    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = MultiPartParams(1500 msat, 10))
+    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = MultiPartParams(1500 msat, 10, DEFAULT_ROUTE_PARAMS.mpp.splittingStrategy))
 
     {
       val (amount, maxFee) = (15000 msat, 50 msat)
@@ -1535,6 +1535,56 @@ class RouteCalculationSpec extends AnyFunSuite with ParallelTestExecution {
     }
   }
 
+  test("calculate multipart route to remote node using max expected amount splitting strategy") {
+    // A-------------E
+    // |             |
+    // +----- B -----+
+    // |             |
+    // +----- C ---- +
+    // |             |
+    // +----- D -----+
+    val (amount, maxFee) = (60000 msat, 1000 msat)
+    val g = GraphWithBalanceEstimates(DirectedGraph(List(
+      // The A -> B -> E route is the most economic one, but we already have a pending HTLC in it.
+      makeEdge(0L, a, e, 50 msat, 0, minHtlc = 100 msat, balance_opt = Some(10000 msat)),
+      makeEdge(1L, a, b, 50 msat, 0, minHtlc = 100 msat, balance_opt = Some(100000 msat)),
+      makeEdge(2L, b, e, 50 msat, 0, minHtlc = 100 msat, capacity = 50 sat),
+      makeEdge(3L, a, c, 50 msat, 0, minHtlc = 100 msat, balance_opt = Some(100000 msat)),
+      makeEdge(4L, c, e, 50 msat, 0, minHtlc = 100 msat, capacity = 25 sat),
+      makeEdge(5L, a, d, 50 msat, 0, minHtlc = 100 msat, balance_opt = Some(100000 msat)),
+      makeEdge(6L, d, e, 50 msat, 0, minHtlc = 100 msat, capacity = 25 sat),
+    )), 1 day)
+
+    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = DEFAULT_ROUTE_PARAMS.mpp.copy(splittingStrategy = MultiPartParams.MaxExpectedAmount))
+    val Success(routes) = findMultiPartRoute(g, a, e, amount, maxFee, routeParams = routeParams, currentBlockHeight = BlockHeight(400000))
+    checkRouteAmounts(routes, amount, maxFee)
+    assert(routes.map(route => (route.amount, route.hops.head.shortChannelId.toLong)).toSet == Set((10000 msat, 0L), (25000 msat, 1L), (12500 msat, 3L), (12500 msat, 5L)))
+  }
+
+  test("calculate multipart route to remote node using max expected amount splitting strategy, respect minPartAmount") {
+    // +----- B -----+
+    // |             |
+    // A----- C ---- E
+    // |             |
+    // +----- D -----+
+    val (amount, maxFee) = (55000 msat, 1000 msat)
+    val g = GraphWithBalanceEstimates(DirectedGraph(List(
+      // The A -> B -> E route is the most economic one, but we already have a pending HTLC in it.
+      makeEdge(1L, a, b, 50 msat, 0, minHtlc = 100 msat, balance_opt = Some(100000 msat)),
+      makeEdge(2L, b, e, 50 msat, 0, minHtlc = 100 msat, capacity = 50 sat),
+      makeEdge(3L, a, c, 50 msat, 0, minHtlc = 100 msat, balance_opt = Some(100000 msat)),
+      makeEdge(4L, c, e, 50 msat, 0, minHtlc = 100 msat, capacity = 25 sat),
+      makeEdge(5L, a, d, 50 msat, 0, minHtlc = 100 msat, balance_opt = Some(100000 msat)),
+      makeEdge(6L, d, e, 50 msat, 0, minHtlc = 100 msat, capacity = 25 sat),
+    )), 1 day)
+
+    val routeParams = DEFAULT_ROUTE_PARAMS.copy(mpp = DEFAULT_ROUTE_PARAMS.mpp.copy(minPartAmount = 15000 msat, splittingStrategy = MultiPartParams.MaxExpectedAmount))
+    val Success(routes) = findMultiPartRoute(g, a, e, amount, maxFee, routeParams = routeParams, currentBlockHeight = BlockHeight(400000))
+    assert(routes.forall(_.hops.length == 2), routes)
+    checkRouteAmounts(routes, amount, maxFee)
+    assert(routes.map(route => (route.amount, route.hops.head.shortChannelId.toLong)).toSet == Set((25000 msat, 1L), (15000 msat, 3L), (15000 msat, 5L)))
+  }
+
   test("loop trap") {
     //       +-----------------+
     //       |                 |
@@ -1899,7 +1949,7 @@ object RouteCalculationSpec {
     randomize = false,
     boundaries = SearchBoundaries(21000 msat, 0.03, 6, CltvExpiryDelta(2016)),
     NO_WEIGHT_RATIOS,
-    MultiPartParams(1000 msat, 10),
+    MultiPartParams(1000 msat, 10, MultiPartParams.FullCapacity),
     experimentName = "my-test-experiment",
     experimentPercentage = 100).getDefaultRouteParams