askrene: prune un-used arcs

From the multiple arcs that derive from the same channel we consider
only those with the smallest cost such that the payment amount and HTLC
max can fit in their combined capacity, ie. we prune high cost arcs that
surely will never be used by the optimal solution.

This reduces the number of arcs in the graph approximately from 8 arcs
per channel to approximately 2 arcs per channel.

No pruning.
amount:		100 	1000 	10000 	100000 	1000000
channels:	104741	106163	106607	106654	106666
arcs:		837928	849304	852856	853232	853328

Prune, limit the channel capacity by its HTLC max
amount:		100 	1000 	10000 	100000 	1000000
channels:	104741	106163	106607	106654	106666
arcs:		255502	259314	260538	260676	260704

Prune, limit the channel capacity to the payment amount
amount:		100 	1000 	10000 	100000 	1000000
channels:	104741	106163	106607	106654	106666
arcs:		209482	216270	228618	295450	432468

Prune, limit the channel capacity to the payment amount and its HTLC max
amount:		100 	1000 	10000 	100000 	1000000
channels:	104741	106163	106607	106654	106666
arcs:		209480	212324	213242	215726	228018

This produces a slight speedup for MCF computations:

Amount (sats) | speedup
-----------------------
          100 | 1.89
         1000 | 1.77
        10000 | 1.25
       100000 | 1.25
      1000000 | 1.18

Changelog-None

Signed-off-by: Lagrang3 <lagrang3@protonmail.com>

Author: Lagrang3

plugins/askrene/mcf.c

@@ -360,9 +360,18 @@ static void linearize_channel(const struct pay_parameters *params,
 	    b = 1 + amount_msat_ratio_floor(maxcap, params->accuracy);
 
 	/* An extra bound on capacity, here we use it to reduce the flow such
-	 * that it does not exceed htlcmax. */
+	 * that it does not exceed htlcmax.
+	 * The cap con capacity is not greater than the amount of payment units
+	 * (msat/accuracy). The way a channel is decomposed into linear cost
+	 * arcs (code below) in ascending cost order ensures that the only the
+	 * necessary capacity to forward the payment is allocated in the lower
+	 * cost arcs. This may lead to some arcs in the decomposition (at the
+	 * high cost end) to have a capacity of 0, and we can prune them while
+	 * keeping the solution optimal. */
 	u64 cap_on_capacity =
-	    amount_msat_ratio_floor(gossmap_chan_htlc_max(c, dir), params->accuracy);
+	    MIN(amount_msat_ratio_floor(gossmap_chan_htlc_max(c, dir),
+					params->accuracy),
+		amount_msat_ratio_ceil(params->amount, params->accuracy));
 
 	set_capacity(&capacity[0], a, &cap_on_capacity);
 	cost[0]=0;
@@ -598,8 +607,9 @@ static void init_linear_network(const tal_t *ctx,
 			// when the `i` hits the `next` node.
 			for(size_t k=0;k<CHANNEL_PARTS;++k)
 			{
-				/* FIXME: Can we prune arcs with 0 capacity?
-				 * if(capacity[k]==0)continue; */
+				/* prune arcs with 0 capacity */
+				if (capacity[k] == 0)
+					continue;
 
 				struct arc arc = arc_from_parts(chan_id, half, k, false);
 

tests/test_askrene.py

@@ -1204,10 +1204,10 @@ def test_real_data(node_factory, bitcoind):
     # CI, it's slow.
     if SLOW_MACHINE:
         limit = 25
-        expected = (6, 25, 1544756, 142986, 91)
+        expected = (5, 25, 1567535, 142772, 91)
     else:
         limit = 100
-        expected = (9, 95, 6347877, 566288, 92)
+        expected = (9, 96, 6563767, 629671, 91)
 
     fees = {}
     for n in range(0, limit):
@@ -1321,10 +1321,10 @@ def test_real_biases(node_factory, bitcoind):
     # CI, it's slow.
     if SLOW_MACHINE:
         limit = 25
-        expected = ({1: 5, 2: 7, 4: 7, 8: 11, 16: 14, 32: 19, 64: 25, 100: 25}, 0)
+        expected = ({1: 6, 2: 6, 4: 7, 8: 12, 16: 14, 32: 19, 64: 25, 100: 25}, 0)
     else:
         limit = 100
-        expected = ({1: 23, 2: 31, 4: 40, 8: 53, 16: 70, 32: 82, 64: 96, 100: 96}, 0)
+        expected = ({1: 22, 2: 25, 4: 36, 8: 52, 16: 69, 32: 80, 64: 96, 100: 96}, 0)
 
     l1.rpc.askrene_create_layer('biases')
     num_changed = {}