mpp_split: add penalty for exhaustion of channels

A penalty is added for split configurations which saturate a channel.
Saturation of channels is discouraged as we don't know the fees
beforehand. The penalty is accomplished via an exponential function that
kicks in when the subamount reaches about the total funds available
(this amount is controlled by the parameter EXHAUST_DECAY_FRACTION).

electrum/mpp_split.py

@@ -1,20 +1,26 @@
 import random
+import math
 from typing import List, Tuple, Optional, Sequence, Dict
 from collections import defaultdict
+
 from .util import profiler
 from .lnutil import NoPathFound
 
 PART_PENALTY = 1.0  # 1.0 results in avoiding splits
 MIN_PART_MSAT = 10_000_000  # we don't want to split indefinitely
+EXHAUST_DECAY_FRACTION = 10  # fraction of the local balance that should be reserved if possible
 
 # these parameters determine the granularity of the newly suggested configurations
-REDISTRIBUTION_FRACTION = 10
-SPLIT_FRACTION = 10
+REDISTRIBUTION_FRACTION = 50
+SPLIT_FRACTION = 50
 
 # these parameters affect the computational work in the probabilistic algorithm
 STARTING_CONFIGS = 50
 CANDIDATES_PER_LEVEL = 10
-REDISTRIBUTE = 10
+REDISTRIBUTE = 20
+
+# maximum number of parts for splitting
+MAX_PARTS = 5
 
 
 def unique_hierarchy(hierarchy: Dict[int, List[Dict[bytes, int]]]) -> Dict[int, List[Dict[bytes, int]]]:
@@ -167,12 +173,16 @@ def suggest_splits(amount_msat: int, channels_with_funds, exclude_single_parts=T
         amounts that are equally distributed and have less parts are rated
         lowest."""
         F = 0
-        amount = sum([v for v in config.values()])
+        total_amount = sum([v for v in config.values()])
+
+        for channel, amount in config.items():
+            funds = channels_with_funds[channel]
+            if amount:
+                F += amount * amount / (total_amount * total_amount)  # a penalty to favor distribution of amounts
+                F += PART_PENALTY * PART_PENALTY  # a penalty for each part
+                decay = funds / EXHAUST_DECAY_FRACTION
+                F += math.exp((amount - funds) / decay)  # a penalty for channel saturation
 
-        for channel, value in config.items():
-            if value:
-                value /= amount  # normalize
-                F += value * value + PART_PENALTY * PART_PENALTY
         return F
 
     def rated_sorted_configurations(hierarchy: dict) -> Sequence[Tuple[Dict[bytes, int], float]]:
@@ -189,9 +199,8 @@ def suggest_splits(amount_msat: int, channels_with_funds, exclude_single_parts=T
     # create initial guesses
     split_hierarchy = create_starting_split_hierarchy(amount_msat, channels_with_funds)
 
-    # randomize initial guesses
-    MAX_PARTS = 5
-    # generate splittings of different split levels up to number of channels
+    # randomize initial guesses and generate splittings of different split
+    # levels up to number of channels
     for level in range(2, min(MAX_PARTS, len(channels_with_funds) + 1)):
         # generate a set of random configurations for each level
         for _ in range(CANDIDATES_PER_LEVEL):

electrum/tests/test_mpp_split.py

@@ -28,7 +28,7 @@ class TestMppSplit(ElectrumTestCase):
     def test_suggest_splits(self):
         with self.subTest(msg="do a payment with the maximal amount spendable over a single channel"):
             splits = mpp_split.suggest_splits(1_000_000_000, self.channels_with_funds, exclude_single_parts=True)
-            self.assertEqual({0: 500_000_000, 1: 500_000_000, 2: 0, 3: 0}, splits[0][0])
+            self.assertEqual({0: 660_000_000, 1: 340_000_000, 2: 0, 3: 0}, splits[0][0])
 
         with self.subTest(msg="do a payment with a larger amount than what is supported by a single channel"):
             splits = mpp_split.suggest_splits(1_100_000_000, self.channels_with_funds, exclude_single_parts=True)
@@ -43,6 +43,18 @@ class TestMppSplit(ElectrumTestCase):
             for s in splits[:4]:
                 self.assertEqual(1, mpp_split.number_nonzero_parts(s[0]))
 
+    def test_saturation(self):
+        """Split configurations which spend the full amount in a channel should be avoided."""
+        channels_with_funds = {0: 159_799_733_076, 1: 499_986_152_000}
+        splits = mpp_split.suggest_splits(600_000_000_000, channels_with_funds, exclude_single_parts=True)
+
+        uses_full_amount = False
+        for c, a in splits[0][0].items():
+            if a == channels_with_funds[c]:
+                uses_full_amount |= True
+
+        self.assertFalse(uses_full_amount)
+
     def test_payment_below_min_part_size(self):
         amount = mpp_split.MIN_PART_MSAT // 2
         splits = mpp_split.suggest_splits(amount, self.channels_with_funds, exclude_single_parts=False)