Make rejectLowDeposits a single pass instead of O(n^2)

[vrom911]

Resolves #2670
rejectLowDeposits paired each output with its minimum using a nested List.find, which is quadratic in the number of deposit inputs. Both lists come from the same UTxO in the same order, so a single walk does the same work. Also adds a property test over multi-output UTxOs, since the old one only ever checked a single output

---

• CHANGELOG updated or not needed
• Documentation updated or not needed
• Haddocks updated or not needed
• No new TODOs introduced or explained herafter

[github-actions]

Transaction cost differences

No cost or size differences found

[github-actions]

End-to-end benchmark differences

Comparing this PR (new) against master (old). Numbers come from cloud VMs, so changes under 5% are shown as ≈ and are likely run-to-run noise rather than a real regression or improvement. 🟢 = improvement, 🔴 = regression; uncolored rows are neutral measures reported for context.

Sustained load (3 nodes, 3x5000 txs)

Metric	master	PR	Δ
End-to-end TPS (tx/s)	521.80	519.69	≈ -2.11 (-0.4%)
Sustained TPS (tx/s)	985.08	1,063.00	🟢 +77.92 (+7.9%)
Backlog drain time (s)	27.90	28.40	≈ +0.50 (+1.8%)
Snapshots per second (/s)	0.59	0.59	≈ +0.00 (+0.0%)
Avg txs per snapshot	882.40	882.40	≈ +0.00 (+0.0%)
Avg. Confirmation Time (s)	23.202	23.926	≈ +0.724 (+3.1%)
P50 confirmation (s)	24.529	24.890	≈ +0.361 (+1.5%)
P95 confirmation (s)	27.987	28.455	≈ +0.467 (+1.7%)
P99 confirmation (s)	28.071	28.613	≈ +0.541 (+1.9%)
Tx validation time p50 (s)	8.864	9.967	🔴 +1.103 (+12.4%)
Peak node RSS (MB)	436.10	415.30	≈ -20.80 (-4.8%)
Invalid txs	0.00	0.00	≈ +0.00 (n/a%)

Plateau 1000 UTxO (1 node, 4000 txs)

Metric	master	PR	Δ
End-to-end TPS (tx/s)	237.69	222.76	🔴 -14.93 (-6.3%)
Backlog drain time (s)	16.70	17.90	🔴 +1.20 (+7.2%)
Snapshots per second (/s)	0.48	0.39	-0.09 (-18.7%)
Avg txs per snapshot	500.00	571.40	+71.40 (+14.3%)
Avg. Confirmation Time (s)	10.378	11.424	🔴 +1.046 (+10.1%)
P50 confirmation (s)	10.727	11.603	🔴 +0.877 (+8.2%)
P95 confirmation (s)	16.741	17.891	🔴 +1.150 (+6.9%)
P99 confirmation (s)	16.743	17.893	🔴 +1.150 (+6.9%)
Tx validation time p50 (s)	6.341	6.235	≈ -0.107 (-1.7%)
Peak node RSS (MB)	370.10	399.30	+29.20 (+7.9%)
Invalid txs	0.00	0.00	≈ +0.00 (n/a%)

Round-trip latency (3 nodes, closed-loop, 3x250 txs)

Metric	master	PR	Δ
End-to-end TPS (tx/s)	96.98	85.48	🔴 -11.50 (-11.9%)
Sustained TPS (tx/s)	97.47	86.59	🔴 -10.88 (-11.2%)
Backlog drain time (s)	0.00	0.00	≈ +0.00 (n/a%)
Snapshots per second (/s)	65.04	57.67	-7.37 (-11.3%)
Avg txs per snapshot	1.50	1.50	≈ +0.00 (+0.0%)
Avg. Confirmation Time (s)	0.031	0.035	🔴 +0.004 (+13.3%)
P50 confirmation (s)	0.030	0.030	≈ +0.000 (+1.3%)
P95 confirmation (s)	0.040	0.067	🔴 +0.028 (+69.3%)
P99 confirmation (s)	0.045	0.092	🔴 +0.047 (+103.3%)
Tx validation time p50 (s)	0.008	0.008	🟢 -0.000 (-6.1%)
Peak node RSS (MB)	148.10	149.00	≈ +0.90 (+0.6%)
Invalid txs	0.00	0.00	≈ +0.00 (n/a%)

[github-actions]

Transaction costs

Sizes and execution budgets for Hydra protocol transactions. Note that unlisted parameters are currently using arbitrary values and results are not fully deterministic and comparable to previous runs.

Metadata
Generated at	2026-08-10 12:48:23.579607409 UTC
Max. memory units	14000000
Max. CPU units	10000000000
Max. tx size (kB)	16384

Script summary

Name	Hash	Size (Bytes)
νHead	f2dd4ade71e19c2310a86215aa78aea06463aca2d8b818af8dc1b8a4	12805
μHead	4abb8dedbcd6a6f03f4fe227300e2713d73b7680d47baa898b60d27a*	4971
νDeposit	c78e8c9205721eb3ef4410f3db9c6169fa6db497c24641d29c20529c	1615
νCRS	09db7ee6cf7a4b358dd5c8a2f19d2c048336ffc5a01ef35a47ca7072	2736

• The minting policy hash is only usable for comparison. As the script is parameterized, the actual script is unique per head.

Init transaction costs

Parties	Tx size	% max Mem	% max CPU	Min fee ₳
1	5475	9.13	2.99	0.49
2	5571	10.18	3.35	0.50
3	5667	10.32	3.38	0.51
5	5861	11.13	3.63	0.52
10	6342	13.84	4.50	0.57
50	10183	35.07	11.15	0.96
100	14982	61.78	19.49	1.45
114	16324	69.28	21.84	1.59

Cost of Increment Transaction

Parties	Tx size	% max Mem	% max CPU	Min fee ₳
1	2321	20.59	7.33	0.47
2	2452	21.67	8.34	0.49
3	2583	23.20	9.50	0.52
5	2845	24.45	11.22	0.55
10	3501	29.89	16.30	0.66
50	8741	72.01	56.13	1.52
75	12017	97.96	80.90	2.05

Cost of Decrement Transaction

Parties	Tx size	% max Mem	% max CPU	Min fee ₳
1	646	18.46	6.68	0.38
2	773	19.40	7.64	0.40
3	904	20.39	8.62	0.42
5	1167	22.26	10.55	0.46
10	1822	27.03	15.40	0.56
50	7063	67.70	54.78	1.40
75	10338	94.09	79.66	1.94

Close transaction costs

Parties	Tx size	% max Mem	% max CPU	Min fee ₳
1	669	17.78	11.67	0.41
3	931	19.74	13.63	0.45
10	1854	26.50	20.45	0.59
75	10365	93.20	84.76	1.97

Contest transaction costs

Parties	Tx size	% max Mem	% max CPU	Min fee ₳
1	700	21.50	14.91	0.46
2	827	22.64	15.93	0.48
3	963	23.81	16.97	0.51
5	1226	26.07	19.02	0.55
10	1885	31.79	24.16	0.66
50	7118	79.46	65.71	1.58
66	9217	99.56	82.61	1.96

FanOut transaction costs

Involves spending head output and burning head tokens. Uses ada-only UTXO for better comparability.
Rows first grow the UTxO set at a fixed 10 parties, then show the largest set that still fits per number of parties (burning more participation tokens leaves less room for outputs).

Parties	UTxO	UTxO (bytes)	Tx size	% max Mem	% max CPU	Min fee ₳
10	0	0	5644	23.29	42.87	0.90
10	1	57	5678	25.63	45.39	0.93
10	5	285	5814	35.88	55.71	1.10
10	10	569	5983	49.89	68.99	1.31
10	20	1137	6322	82.42	96.97	1.79
1	20	1140	6045	76.20	95.00	1.72
5	20	1140	6170	78.96	95.88	1.75
10	20	1137	6322	82.42	96.97	1.79
20	20	1139	6633	89.74	99.26	1.88
50	15	856	7396	94.70	91.88	1.90

PartialFanOut transaction costs

Largest chunk of ada-only outputs that can be distributed in one partial fanout step, computed dynamically. The last row is the maximum total UTxO count where at least one output can still be distributed.

Total UTxO	Distributed	UTxO (bytes)	Tx size	% max Mem	% max CPU	Min fee ₳
11	10	569	986	34.91	66.33	0.95
25	23	1308	1427	68.24	99.40	1.48
30	23	1309	1428	68.24	99.40	1.48
40	23	1309	1428	68.24	99.40	1.48
50	23	1309	1428	68.24	99.40	1.48
100	23	1310	1429	68.24	99.40	1.48
150	23	1310	1429	68.24	99.40	1.48
200	23	1310	1429	68.24	99.40	1.48
200	23	1309	1428	68.24	99.40	1.48

PartialFanOut transaction costs (with native tokens)

Largest chunk of native-token outputs that can be distributed in one partial fanout step, computed dynamically. The last row is the maximum total UTxO count where at least one output can still be distributed.

Total UTxO	Distributed	UTxO (bytes)	Tx size	% max Mem	% max CPU	Min fee ₳
11	10	940	1411	41.97	68.82	1.05
25	21	2205	2456	76.59	99.17	1.59
30	21	2331	2588	76.56	99.21	1.60
40	21	2058	2302	76.56	99.12	1.58
50	21	2415	2677	76.59	99.22	1.60
100	21	2142	2391	76.59	99.17	1.59
150	21	2331	2589	76.59	99.22	1.60
200	21	2058	2303	76.59	99.12	1.59
200	21	2163	2413	76.56	99.16	1.59

FinalPartialFanOut transaction costs (with native tokens)

Terminal partial fanout step (FanoutProgress → Final) with outputs carrying a native token. Burns all head tokens and proves accumulator exhaustion via BLS proof.

Distributed	UTxO (bytes)	Tx size	% max Mem	% max CPU	Min fee ₳
1	94	5514	21.97	44.27	0.89
5	525	5860	35.70	55.83	1.10
10	1110	6340	53.78	70.61	1.37
10	970	6200	53.90	70.60	1.37

End-to-end benchmark results

This page is intended to collect the latest end-to-end benchmark results produced by Hydra's continuous integration (CI) system from the latest master code.

Please note that these results are approximate as they are currently produced from limited cloud VMs and not controlled hardware. Rather than focusing on the absolute results, the emphasis should be on relative results, such as how the timings for a scenario evolve as the code changes.

Generated at 2026-08-10 12:49:42.424533241 UTC

Baseline Scenario

Number of nodes	1
Number of txs	300
Avg. Confirmation Time (ms)	216.4
P99	220.2ms
P95	220.0ms
P50	216.4ms
Tx validation time p50 (ms)	142.5
End-to-end TPS	1346.41 tx/s
Backlog drain time (s)	0.2
Snapshots observed	3
Snapshots per second	13.46 /s
Avg txs per snapshot	100.0
Peak node RSS (MB)	145.3
Number of Invalid txs	0
Fanout outputs	2

Three local nodes

Number of nodes	3
Number of txs	900
Avg. Confirmation Time (ms)	1009.5
P99	1031.2ms
P95	1030.5ms
P50	1015.9ms
Tx validation time p50 (ms)	503.7
End-to-end TPS	863.02 tx/s
Backlog drain time (s)	1.0
Snapshots observed	3
Snapshots per second	2.88 /s
Avg txs per snapshot	300.0
Peak node RSS (MB)	146.1
Number of Invalid txs	0
Fanout outputs	4

Scenario benchmark results

This page collects results from the scenario matrix: every combination of cluster size, UTxO shape, and incremental-ops mode is exercised by CI from the latest master code and reported below.

Numbers are approximate. They come from cloud VMs rather than controlled hardware, so the useful signal is the relative change between cells and between commits, not the absolute throughput.

Generated at 2026-08-10 13:04:34.161809772 UTC

Summary across cells

TPS columns are rates (transactions per second); Wall clock (s) is the measured elapsed time from the first tx submission to the last confirmation. Times are rounded to one decimal.

Scenario	Txs	Wall clock (s)	End-to-end TPS (tx/s)	Sustained TPS (tx/s)	Avg conf (ms)	P95 conf (ms)
Nodes=1, Constant, fire and forget	30	0.3	92.16	n/a	315.0	325.2
Nodes=1, Constant, wait for tx valid	30	0.7	40.72	55.29	24.5	142.3
Nodes=1, Growing, fire and forget	30	0.2	180.05	n/a	166.0	166.3
Nodes=1, Growing, wait for tx valid	30	1.2	24.45	22.95	40.8	185.5
Nodes=1, Mixed, fire and forget	30	0.1	302.09	n/a	98.6	99.1
Nodes=1, Mixed, wait for tx valid	30	3.1	9.66	7.88	103.4	429.4
Nodes=2, Constant, fire and forget	60	0.2	331.15	n/a	179.0	180.9
Nodes=2, Constant, wait for tx valid	60	1.1	55.64	48.26	35.8	190.0
Nodes=2, Growing, fire and forget	60	0.3	194.21	n/a	302.1	307.9
Nodes=2, Growing, wait for tx valid	60	0.6	103.97	110.16	19.1	30.6
Nodes=2, Mixed, fire and forget	60	0.1	1022.24	n/a	57.9	58.2
Nodes=2, Mixed, wait for tx valid	60	0.7	82.47	75.14	23.9	56.3
Nodes=3, Constant, fire and forget	90	0.1	700.59	n/a	125.8	127.2
Nodes=3, Constant, wait for tx valid	90	0.8	113.01	115.10	26.2	55.9
Nodes=3, Growing, fire and forget	90	0.2	362.91	n/a	244.5	247.7
Nodes=3, Growing, wait for tx valid	90	1.9	46.49	43.02	64.3	219.7
Nodes=3, Mixed, fire and forget	90	0.3	258.17	n/a	344.3	348.3
Nodes=3, Mixed, wait for tx valid	90	1.4	64.19	73.61	46.1	106.4

Nodes=1, Constant, fire and forget

Number of nodes	1
Number of txs	30
Avg. Confirmation Time (ms)	315.0
P99	325.3ms
P95	325.2ms
P50	325.1ms
Tx validation time p50 (ms)	15.8
End-to-end TPS	92.16 tx/s
Backlog drain time (s)	0.3
Snapshots observed	2
Snapshots per second	6.14 /s
Avg txs per snapshot	15.0
Peak node RSS (MB)	143.5
Number of Invalid txs	0
Fanout outputs	2

Nodes=1, Constant, wait for tx valid

Number of nodes	1
Number of txs	30
Avg. Confirmation Time (ms)	24.5
P99	220.0ms
P95	142.3ms
P50	5.4ms
Tx validation time p50 (ms)	1.7
End-to-end TPS	40.72 tx/s
Sustained TPS	55.29 tx/s
Backlog drain time (s)	0.0
Snapshots observed	30
Snapshots per second	40.72 /s
Avg txs per snapshot	1.0
Peak node RSS (MB)	143.6
Number of Invalid txs	0
Fanout outputs	2

Nodes=1, Growing, fire and forget

Number of nodes	1
Number of txs	30
Avg. Confirmation Time (ms)	166.0
P99	166.3ms
P95	166.3ms
P50	166.2ms
Tx validation time p50 (ms)	152.1
End-to-end TPS	180.05 tx/s
Backlog drain time (s)	0.2
Snapshots observed	2
Snapshots per second	12.00 /s
Avg txs per snapshot	15.0
Peak node RSS (MB)	144.0
Number of Invalid txs	0
Fanout outputs	31

Nodes=1, Growing, wait for tx valid

Number of nodes	1
Number of txs	30
Avg. Confirmation Time (ms)	40.8
P99	325.7ms
P95	185.5ms
P50	6.5ms
Tx validation time p50 (ms)	1.9
End-to-end TPS	24.45 tx/s
Sustained TPS	22.95 tx/s
Backlog drain time (s)	0.0
Snapshots observed	30
Snapshots per second	24.45 /s
Avg txs per snapshot	1.0
Peak node RSS (MB)	144.4
Number of Invalid txs	0
Fanout outputs	31

Nodes=1, Mixed, fire and forget

Each client first grows its UTxO set (1-in to 2-out) for half of its tx budget, then contracts it back (2-in to 1-out) for the remainder.

Number of nodes	1
Number of txs	30
Avg. Confirmation Time (ms)	98.6
P99	99.1ms
P95	99.1ms
P50	98.9ms
Tx validation time p50 (ms)	29.0
End-to-end TPS	302.09 tx/s
Backlog drain time (s)	0.1
Snapshots observed	2
Snapshots per second	20.14 /s
Avg txs per snapshot	15.0
Peak node RSS (MB)	143.7
Number of Invalid txs	0
Fanout outputs	2

Nodes=1, Mixed, wait for tx valid

Each client first grows its UTxO set (1-in to 2-out) for half of its tx budget, then contracts it back (2-in to 1-out) for the remainder.

Number of nodes	1
Number of txs	30
Avg. Confirmation Time (ms)	103.4
P99	701.2ms
P95	429.4ms
P50	19.5ms
Tx validation time p50 (ms)	2.1
End-to-end TPS	9.66 tx/s
Sustained TPS	7.88 tx/s
Backlog drain time (s)	0.0
Snapshots observed	30
Snapshots per second	9.66 /s
Avg txs per snapshot	1.0
Peak node RSS (MB)	144.0
Number of Invalid txs	0
Fanout outputs	2

Nodes=2, Constant, fire and forget

Number of nodes	2
Number of txs	60
Avg. Confirmation Time (ms)	179.0
P99	181.0ms
P95	180.9ms
P50	180.4ms
Tx validation time p50 (ms)	82.7
End-to-end TPS	331.15 tx/s
Backlog drain time (s)	0.2
Snapshots observed	2
Snapshots per second	11.04 /s
Avg txs per snapshot	30.0
Peak node RSS (MB)	143.6
Number of Invalid txs	0
Fanout outputs	3

Nodes=2, Constant, wait for tx valid

Number of nodes	2
Number of txs	60
Avg. Confirmation Time (ms)	35.8
P99	201.3ms
P95	190.0ms
P50	13.4ms
Tx validation time p50 (ms)	3.4
End-to-end TPS	55.64 tx/s
Sustained TPS	48.26 tx/s
Backlog drain time (s)	0.0
Snapshots observed	60
Snapshots per second	55.64 /s
Avg txs per snapshot	1.0
Peak node RSS (MB)	144.7
Number of Invalid txs	0
Fanout outputs	3

Nodes=2, Growing, fire and forget

Number of nodes	2
Number of txs	60
Avg. Confirmation Time (ms)	302.1
P99	308.3ms
P95	307.9ms
P50	305.4ms
Tx validation time p50 (ms)	85.4
End-to-end TPS	194.21 tx/s
Backlog drain time (s)	0.3
Snapshots observed	2
Snapshots per second	6.47 /s
Avg txs per snapshot	30.0
Peak node RSS (MB)	145.9
Number of Invalid txs	0
Fanout outputs	62

Nodes=2, Growing, wait for tx valid

Number of nodes	2
Number of txs	60
Avg. Confirmation Time (ms)	19.1
P99	46.8ms
P95	30.6ms
P50	16.9ms
Tx validation time p50 (ms)	5.0
End-to-end TPS	103.97 tx/s
Sustained TPS	110.16 tx/s
Backlog drain time (s)	0.0
Snapshots observed	60
Snapshots per second	103.97 /s
Avg txs per snapshot	1.0
Peak node RSS (MB)	146.2
Number of Invalid txs	0
Fanout outputs	62

Nodes=2, Mixed, fire and forget

Each client first grows its UTxO set (1-in to 2-out) for half of its tx budget, then contracts it back (2-in to 1-out) for the remainder.

Number of nodes	2
Number of txs	60
Avg. Confirmation Time (ms)	57.9
P99	58.2ms
P95	58.2ms
P50	58.1ms
Tx validation time p50 (ms)	14.1
End-to-end TPS	1022.24 tx/s
Backlog drain time (s)	0.1
Snapshots observed	2
Snapshots per second	34.07 /s
Avg txs per snapshot	30.0
Peak node RSS (MB)	144.4
Number of Invalid txs	0
Fanout outputs	3

Nodes=2, Mixed, wait for tx valid

Each client first grows its UTxO set (1-in to 2-out) for half of its tx budget, then contracts it back (2-in to 1-out) for the remainder.

Number of nodes	2
Number of txs	60
Avg. Confirmation Time (ms)	23.9
P99	158.0ms
P95	56.3ms
P50	16.5ms
Tx validation time p50 (ms)	4.2
End-to-end TPS	82.47 tx/s
Sustained TPS	75.14 tx/s
Backlog drain time (s)	0.0
Snapshots observed	60
Snapshots per second	82.47 /s
Avg txs per snapshot	1.0
Peak node RSS (MB)	145.4
Number of Invalid txs	0
Fanout outputs	3

Nodes=3, Constant, fire and forget

Number of nodes	3
Number of txs	90
Avg. Confirmation Time (ms)	125.8
P99	127.3ms
P95	127.2ms
P50	127.0ms
Tx validation time p50 (ms)	78.7
End-to-end TPS	700.59 tx/s
Backlog drain time (s)	0.1
Snapshots observed	2
Snapshots per second	15.57 /s
Avg txs per snapshot	45.0
Peak node RSS (MB)	144.8
Number of Invalid txs	0
Fanout outputs	4

Nodes=3, Constant, wait for tx valid

Number of nodes	3
Number of txs	90
Avg. Confirmation Time (ms)	26.2
P99	95.8ms
P95	55.9ms
P50	21.7ms
Tx validation time p50 (ms)	5.9
End-to-end TPS	113.01 tx/s
Sustained TPS	115.10 tx/s
Backlog drain time (s)	0.0
Snapshots observed	61
Snapshots per second	76.59 /s
Avg txs per snapshot	1.5
Peak node RSS (MB)	145.9
Number of Invalid txs	0
Fanout outputs	4

Nodes=3, Growing, fire and forget

Number of nodes	3
Number of txs	90
Avg. Confirmation Time (ms)	244.5
P99	247.8ms
P95	247.7ms
P50	245.8ms
Tx validation time p50 (ms)	38.7
End-to-end TPS	362.91 tx/s
Backlog drain time (s)	0.2
Snapshots observed	2
Snapshots per second	8.06 /s
Avg txs per snapshot	45.0
Peak node RSS (MB)	145.4
Number of Invalid txs	0
Fanout outputs	0

Nodes=3, Growing, wait for tx valid

Number of nodes	3
Number of txs	90
Avg. Confirmation Time (ms)	64.3
P99	292.1ms
P95	219.7ms
P50	44.9ms
Tx validation time p50 (ms)	9.0
End-to-end TPS	46.49 tx/s
Sustained TPS	43.02 tx/s
Backlog drain time (s)	0.1
Snapshots observed	61
Snapshots per second	31.51 /s
Avg txs per snapshot	1.5
Peak node RSS (MB)	146.8
Number of Invalid txs	0
Fanout outputs	0

Nodes=3, Mixed, fire and forget

Each client first grows its UTxO set (1-in to 2-out) for half of its tx budget, then contracts it back (2-in to 1-out) for the remainder.

Number of nodes	3
Number of txs	90
Avg. Confirmation Time (ms)	344.3
P99	348.3ms
P95	348.3ms
P50	345.7ms
Tx validation time p50 (ms)	197.8
End-to-end TPS	258.17 tx/s
Backlog drain time (s)	0.3
Snapshots observed	2
Snapshots per second	5.74 /s
Avg txs per snapshot	45.0
Peak node RSS (MB)	145.1
Number of Invalid txs	0
Fanout outputs	4

Nodes=3, Mixed, wait for tx valid

Each client first grows its UTxO set (1-in to 2-out) for half of its tx budget, then contracts it back (2-in to 1-out) for the remainder.

Number of nodes	3
Number of txs	90
Avg. Confirmation Time (ms)	46.1
P99	137.7ms
P95	106.4ms
P50	36.9ms
Tx validation time p50 (ms)	7.3
End-to-end TPS	64.19 tx/s
Sustained TPS	73.61 tx/s
Backlog drain time (s)	0.0
Snapshots observed	62
Snapshots per second	44.22 /s
Avg txs per snapshot	1.5
Peak node RSS (MB)	146.1
Number of Invalid txs	0
Fanout outputs	4