feat: iterative deepening on the bound, dived first by evanlinjin · Pull Request #74 · bitcoindevkit/coin-select

evanlinjin · 2026-08-16T06:39:15Z

Draft, and stacked on #73. Only the last two commits are new — feat: search branch and bound with iterative deepening on the bound and feat: dive before deepening, and keep the incumbent. Everything before them is #73. Read that one first.

Depth-first search (#73) fixed the memory problem — flat 3 MB where the priority queue reached 20 GB — but gave up node ordering. A queue expands the globally most promising open node; a dive expands whatever is under its feet, and then prunes against whatever incumbent that order happened to find.

On pools whose candidates share unconfirmed ancestors, that incumbent is far from the optimum and the dive cannot recover. The sharpest case in the benchmark is 50 candidates:

	nodes	exhausted	fee the child pays
priority queue (pre-#73)	55,737	yes	4,508
depth-first (#73)	40,000,000	no	11,332

That answer is byte-identical at 100 ms, 1 s and 10 s — stuck, not starved.

What this adds

Iterative deepening on the bound. Same depth-first traversal, run in passes under a rising ceiling. Pass k visits the nodes whose bound is at or below the threshold, which is the set a queue expands before it first pops a node of that bound — so the passes reconstruct best-first's expansion order without a frontier.

A pass that ends with the incumbent at or below the threshold proves the incumbent optimal: any better selection would have had every node on its path bounded by its own score, so it could not have been pruned by either the threshold or the incumbent.

The threshold schedule is a speed knob and never a correctness one — raising the threshold past the smallest rejected bound only ever adds nodes to a pass, never skips one.

Then a hybrid, because deepening alone is not anytime. Under a ceiling low enough to be useful, early passes may not reach a complete selection at all, which on a pool too large to exhaust is strictly worse than diving. Alone, deepening is a net +3.95%, costing +70% on a 2000-candidate pool. So: dive first, hand over once the dive has gone as long without an improvement as it took to find the one it holds, and carry the incumbent into the deepening passes.

Results

coinselect-benchmark, wallet track, 42 fixtures, wall-clock budgets with the round cap lifted.

budget	total fee the child pays	improved	regressed	tree exhausted
10 ms	-0.48%	2	0	25 -> 24
100 ms	-3.81%	5	0	28 -> 31 of 42
1000 ms	-3.89%	5	1 (+0.9%)	31 -> 33 of 42

subsidizing_ancestry_50 reaches the optimum — 4,508 — after a 10,001-node dive and 8 passes, in 21 ms. shared_ancestry_200 -41.9%, subsidizing_ancestry_100 -37.2%, nested_ancestry_200 -25.6%. Peak RSS stays at 3.6 MB; #73's memory win is untouched.

It also composes with pool sampling rather than competing with it:

arm	100 ms	1000 ms
depth-first (#73)	—	—
+ pool sampling	-3.73%	-4.66%
+ deepening	-3.81%	-3.76%
+ both	-4.92%	-5.40%

Correctness

The default path is byte-identical to feat!: depth-first branch and bound, and remove the changeless metrics #73 on all 42 fixtures — same selection, same score, same round count, same exhausted flag. The new behaviour is opt-in through bnb_solutions_hybrid.
On the 32 fixtures where both traversals report the tree exhausted, the scores agree 32 of 32.
The harness's brute-force oracle agrees on every fixture small enough to enumerate.
cargo test green on --all-features and --no-default-features.

What a reviewer should push back on

Two constants. The threshold step (eps = 0.1) and the dive floor (200 x candidates). Both were swept over 42 fixtures at three budgets, neither is sharply peaked, but neither is derived from anything.
The dive floor exists because of a subtlety: the greedy incumbent is set before the first node, so "time since the last improvement" has nothing to measure against and the handover fires immediately without it. It scales on candidate count because the budget is not visible inside the iterator — which means it goes inert on very large pools, where 200 x candidates exceeds the nodes a short budget can afford.
The +0.9% regression is opportunity cost, not a lost incumbent. Handing over ends the dive, so against a dive that keeps the whole budget the hybrid can come out behind. It cannot come out behind the dive it actually ran.
Pool sampling alone is still stronger on total fee at a round budget (-10.28%). What this adds over it is that it proves optimality rather than only finding it, needs no randomness or seeds, and lifts the exhausted count — and the two stack.

Plan, measurements and the things that did not work — including an ancestry-aware branching order that costs +0.81% — are in ITERATIVE-DEEPENING-PLAN.md and FINDINGS.md finding 3 of the benchmark repo.

🤖 Generated with Claude Code

https://claude.ai/code/session_01HLiTkESMktypGJhFag2ZBM

…y_count Fixes CoinSelector::input_weight undercounting candidates that group multiple legacy inputs in a segwit transaction (where each legacy input serializes a 1 WU empty witness). Tracking segwit and legacy input counts separately also allows a single Candidate to mix legacy and segwit inputs.

…legacy Replaces the boolean is_segwit parameter in Candidate::new with explicit new_segwit and new_legacy constructors. Clarifies in doc comments that satisfaction_weight is the additional weight required beyond TXIN_BASE_WEIGHT (which already accounts for a 1-byte scriptSigLen).

…call A selector was built for one target and evaluated against it throughout, but every method took the target as a parameter, so nothing stopped `cs.excess(target_a, drain)` being followed by `cs.is_funded(target_b)`. The correctness arguments in the metrics are all stated at a fixed target -- `LowestFee::bound`'s proof that a changeless superset always costs more, `Changeless::change_unavoidable`'s assumption that the drain decision is monotone in the excess -- and were held together by convention rather than by types. `CoinSelector::new` now takes the target and owns it. Twenty signatures *lose* a parameter rather than gaining one: fifteen public methods (`excess`, `implied_fee`, `is_funded`, `drain`, `select_until_target_met`, the four `*_excess`, ...), plus `bnb_solutions` and `run_bnb`, plus all three `BnbMetric` methods. The crate had already reached this conclusion one layer down: `BnbIter` stored the target as a field, took it once in `BnbIter::new`, and then re-passed it into `metric.score` and `metric.bound` at every node. That field and the re-threading are both gone. This is a breaking change, and it reaches `BnbMetric`, so metrics implemented outside this crate need their signatures updated: fn score(&mut self, cs: &CoinSelector<'_>) -> Option<Ordf32>; fn bound(&mut self, cs: &CoinSelector<'_>) -> Option<Ordf32>; fn drain(&mut self, cs: &CoinSelector<'_>) -> Drain; `CoinSelector::target()` exposes the target for metrics that need to read it. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

Move the fixed target, candidates, and optional ancestor graph into one immutable problem object. CoinSelector now borrows that object, keeping all calculations tied to the same inputs and allowing ancestry metadata to remain separate from Candidate. Provide new_no_ancestors for prebuilt candidates and new for constructing candidates from input groups and their unconfirmed transaction graph.

Selecting an unconfirmed coin means paying to bump its ancestors. The feerate obligation includes the shortfall of the union of ancestors the selected candidates drag in (each charged once; weight and fee netted; saturates at 0). Score is still the child fee — the bump is already inside it. With ancestors, LowestFee falls back to a loose but admissible fee floor; tightening is a follow-up. BnB only batch-bans look-alikes with the same drags_in; Changeless disables its prune when ancestors are present.

Precompute ancestors reachable through exactly one candidate as summed private packages. Keep bitset de-duplication only for ancestors shared by multiple candidates, preserving exact union accounting while reducing the common-path work in every fee calculation. Add Criterion coverage for private and shared ancestry at 20, 50, and 100 candidates, plus exhaustive regressions for the optimized representation.

For funded nodes, subtract the ancestor surplus still reachable by a descendant. For unfunded nodes, derive a minimum added child weight from independent fractional relaxations of the target-rate, absolute-fee, and RBF constraints, then evaluate the fee floor at that weight. Candidate ancestry is deliberately represented only by the global bump lower bound: package surplus can absorb a later private deficit, so a per-candidate ancestor cost is not admissible. Keep infeasibility prunes off because ancestor funding is non-monotone. Add regressions for package subsidy, absolute/RBF double counting, and large-float cancellation, plus the existing exhaustive proptests.

Maintain aggregate selection state per branch and expose it through SelectionView so metric evaluation avoids repeatedly walking selected candidates. Track each branch's candidate cursor to skip repeated scans, and extend benchmarks across wallet- and exchange-scale pools.

Keep SelectionView's hypothetical updates set-like and synchronize ancestor reachability when branches exclude candidates. Remove unsound funding and changeless assumptions exposed by non-monotone ancestor debt, and preserve conservative fee rounding in the bound. Add regressions for public view updates, exclusion transitions, weight caps, mixed serialization overhead, and floating-point edge cases.

Separate deterministic solution-finding cases from larger pools expected to exhaust the fixed round cap. Assert each fixture's expected search outcome before measuring it so benchmark comparisons cannot silently time different paths.

Store private ancestor totals directly and allocate shared reference tracking only when the problem actually has shared ancestry. Preserve an explicit precision allowance for large floating-point ancestor fees so the smaller cache does not tighten the admissible bound.

Replace generic metric composition with a changeless metric that reuses LowestFee's funding, weight-cap, dust, and change decisions. Add a monotone selected-value bound for pools up to 24 candidates while retaining LowestFee's ordering for larger pools to avoid finite-round starvation. Cover the constrained objective with exhaustive and serialization-edge regressions, and document the migration from Changeless and tuple metrics.

Replace the best-first BinaryHeap frontier with depth-first search that visits the better-bound child first and backtracks in place. This drops per-branch selector/cache clones and, under a round cap, finds complete solutions on large pools where the old frontier often exhausted the budget without a selection.

`LowestFeeChangeless` only applied its selected-value bound to pools of at most 24 candidates. The cap existed because best-first search treats a bound as a priority: a bound that grows with the selection pushed funded branches to the back of the heap, so on a big pool the frontier starved before it reached one. Depth-first search reads a bound as a cut instead of a ranking — it finishes a branch's descendants before its siblings — so the bound can be applied at every pool size, where it prunes inclusion branches that have already overshot the incumbent.

Yield the greedy selection before expanding the first node, and adopt its score as the incumbent. The search is otherwise not anytime: a caller whose round budget runs out before the first complete selection gets `NoBnbSolution::RoundLimit` and falls through to whatever fallback it has, which on a large pool is far worse than the selection a single greedy pass would have handed it for free. Only the incumbent changes, not the bound, so the optimum stays reachable and the improving-solutions contract is unaffected. Metrics that reject the greedy prefix outright — `LowestFeeChangeless`, which will not score a selection that overshoots — are unchanged, and `RoundLimit` still means what it did for them. The two round-count assertions in `tests/bnb.rs` each move by one: the seed is a round.

Bitcoin Core's `SelectCoinsBnB` computes `is_feerate_high` once and lets it decide whether a prune that is only sometimes valid may fire; it does not drop the prune because the general case is unsound. `bound_with_ancestors` took the other route — "never returns `None`" — on the grounds that a fat private deficit can un-fund a prefix a subset would have funded, so infeasibility is not something it may claim. That argument covers "select everything and it is still unfunded". It does not cover the case this relaxation can prove outright: a fee constraint whose deficit the best input still available cannot close at *any* weight. Descendants only add, the deficit is already computed against the branch-wide `ancestor_bump_lower_bound`, and the gain already ignores whatever ancestors those inputs would drag in — so the estimate is optimistic on every axis, and a deficit it still cannot close belongs to an empty subtree. The scan that finds the best value-per-weight candidate already runs, so the test is free. It also prunes the unfunded leaves that had nothing left to add, which the old path could only rank.

Port Bitcoin Core's `SelectCoinsBnB` lookahead. Core keeps a running `curr_available_value` over the coins it has not decided on yet and backtracks as soon as that total cannot close the gap to the target; the cut needs no incumbent, so it fires from the very first descent. We had the same idea only in `LowestFee::bound`'s no-ancestor path, as an O(n) rescan that ran after the relaxation had already been set up, and not at all when the problem has ancestors. `SelectionCache` now carries the value and weight of the undecided candidates worth selecting, maintained by the same add/sub/ban/unban hooks that already track reachable ancestor surplus, so the test is O(1). Two one-sided relaxations keep it from pruning a branch that holds a solution: only candidates with positive standalone effective value count toward the total, and the current ancestor bump is swapped for `ancestor_bump_lower_bound`, which holds for the whole subtree. That second one is what lets the prune run with ancestors present, where funding is not monotone and "select everything and it is still unfunded" would have been an unsound claim.

LowestFee already decides for itself whether a selection should carry a change output, adding one only when it lowers the long-term fee, clears the dust threshold and fits max_weight. A separate changeless objective duplicates that decision and constrains it, and nothing in the crate needs the constraint. Removes LowestFeeChangeless along with the Changeless wrapper the unreleased changelog already retired, plus their tests and proptest regressions. BREAKING CHANGE: LowestFeeChangeless and Changeless are gone. Callers that required a changeless transaction should use LowestFee and inspect the Drain it returns.

`bound_with_ancestors` scanned every undecided candidate at each unfunded node to find the greatest value-per-weight and to notice weightless value. Branch and bound asks for that bound at every unfunded node, so an O(n) scan there made per-node cost grow with the pool: measured on shared_ancestry_*, 2389 ns/round at n=500 rising to 9384 at n=2000, against 385-2056 for the no-ancestry fixtures. The metric already requires candidates in descending value-per-weight order, and that order is keyed on f32. The exact f64 maximum can therefore only lie inside the run sharing the first undecided candidate's f32 key, which is why the old code scanned in f64 rather than taking the first: two exact ratios can tie in f32 and be ordered either way. Scanning just that run keeps the exact answer without touching the tail. Weightless value becomes a counter kept where the undecided aggregates already are. 5.9x to 8.8x faster per round at n=500 to 2000, and byte-identical results: across all 42 benchmark fixtures the score, selection, round count and exhausted flag are unchanged. A debug assertion checks the tie-run result against a full scan, so the ordering assumption is verified on every node the test suite searches.

`SelectionView` overrides these with cache-backed versions, so every call site in the crate and its tests already resolved to the view; the `CoinSelector` copies recomputed the same answers by iterating and had no callers left. Removes `effective_value`, `implied_feerate`, `rate_excess_wu`, `replacement_excess_wu` and `waste`, plus the two private helpers they were the last users of. `missing` and `drain` are deliberately kept even though the view also has them: the crate's own front-page example calls them on a bare `CoinSelector`, which is the case they exist for. The same argument keeps the rest of the overlap -- `weight`, `excess`, `is_funded` and friends all have live callers holding a selector rather than a view, and routing those through `compute_view` would cost an O(n) cache build to replace an O(n) method. BREAKING CHANGE: obtain a `SelectionView` with `CoinSelector::compute_view` and call the removed methods there.

`SelectionView` answered every one of these from its cache while the `CoinSelector` copy recomputed the same figure by iterating the selection. Keeping both meant two implementations of the weight model, the excess model and the ancestor bump, and the slower one was the default a caller reached for. Removes `absolute_excess`, `ancestor_bump`, `ancestor_bump_lower_bound`, `drain`, `drain_value`, `excess`, `fee`, `implied_fee`, `input_weight`, `is_funded`, `is_funded_with_drain`, `is_within_max_weight`, `missing`, `rate_excess`, `replacement_excess`, `selected_value` and `weight` from `CoinSelector`, along with the two private helpers they were the last users of. `select_until` now hands its predicate a `&SelectionView` and maintains that view's cache incrementally, so the greedy pass behind `select_until_target_met` -- which seeds every branch-and-bound search -- costs one cache build plus O(1) per step instead of rescanning the selection on every iteration. The crate's own front-page example now goes through `compute_view` too, which is what the removed methods were kept for. BREAKING CHANGE: obtain a `SelectionView` with `CoinSelector::compute_view` and call the removed methods there. `CoinSelector::select_until` takes a predicate over `&SelectionView` rather than `&CoinSelector`. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01HLiTkESMktypGJhFag2ZBM

`seed` carried `(CoinSelector, Ordf32)` while `best` separately held the same score. They are set together in `seed_greedy_incumbent` and nothing runs between construction and the first `next()`, so the score in the tuple was always exactly `best`. Store the selection alone and read the score from `best` when yielding. No behaviour change: identical score, selection, round count and exhausted flag on all 42 benchmark fixtures.

Depth-first traversal is linear in memory but expands whatever is under its feet, so it prunes against whatever incumbent its dive order happened to find. On problems whose candidates share unconfirmed ancestors that is far from the optimum, and the search cannot recover: `subsidizing_ancestry_50` burns forty million nodes without improving on an incumbent 2.5x worse than the answer a priority queue proves in 55,737. This runs the same depth-first traversal in passes under a rising ceiling on the bound. Pass k visits the nodes whose bound is at or below the threshold, which is the set a priority queue expands before it first pops a node of that bound, so the passes reconstruct best-first's expansion order without a frontier. The incumbent carries across passes, and a pass ending with the incumbent at or below the threshold proves it optimal: any better selection would have had every node on its path bounded by its own score, so it could not have been pruned by either rule. The threshold schedule is a speed knob and never a correctness one — raising the threshold past the smallest rejected bound only ever adds nodes to a pass, never skips one — so `eps` is free to trade re-expansion against how closely the queue's order is followed. `bnb_solutions` is unchanged and takes the plain dive; the new behaviour is opt-in through `bnb_solutions_with_deepening`. Measured on coinselect-benchmark's 42 fixtures at a wall-clock budget, eps=0.1: subsidizing_ancestry_50 40,000,000 nodes, not exhausted, child fee 11,332 -> 64,544 nodes, exhausted, child fee 4,508 shared_ancestry_200 36,242 -> 21,069 nested_ancestry_200 30,203 -> 22,477 subsidizing_ancestry_100 30,140 -> 18,925 subsidizing_ancestry_200 27,281 -> 22,999 Exhausted rises from 31 to 34 of 42 and peak RSS stays flat at 3.5 MB. Where both traversals exhaust they agree on all 32 fixtures, and the brute-force oracle confirms the optimum on all 9 fixtures small enough to enumerate. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01HLiTkESMktypGJhFag2ZBM

Iterative deepening reconstructs a priority queue's node ordering, but it is not anytime: under a ceiling low enough to be useful the early passes may not reach a complete selection at all. On a pool too large to exhaust that is strictly worse than diving, which reaches leaves immediately — measured at +70% on `wallet_mixed_2000`, and no threshold step fixes both ends, because a step large enough to protect it is large enough to lose `subsidizing_ancestry_50` outright. So dive first and deepen after, carrying the incumbent across. The dive hands over once it has gone as long without an improvement as it took to find the one it holds, which keeps its budget on a pool that is still creeping downward and gives up quickly on one that is stuck — the failure this exists to fix. That rule needs a floor, because the greedy incumbent is set before the first node and so leaves it nothing to measure against. The floor scales on candidate count rather than on the budget, which is not visible here: a dive to a leaf costs at most one node per candidate, so the floor is that depth times a constant. 200 was the best single value over 42 fixtures at three budgets and the metric is not sharply peaked around it. Wallet track, against the plain dive, eps=0.1: 10 ms -0.48% 2 better, 0 worse 100 ms -3.81% 5 better, 0 worse exhausted 28 -> 31 of 42 1000 ms -3.89% 5 better, 1 worse exhausted 31 -> 33 of 42 `subsidizing_ancestry_50` reaches the optimum of 4,508 after a 10,001-node dive and 8 passes. Peak RSS stays at 3.6 MB. The default path is untouched: no flag, no behaviour change, byte-identical to the parent commit on all 42 fixtures. The one regression is opportunity cost, not a lost incumbent: handing over ends the dive, so against a dive that keeps the whole budget the hybrid can come out behind. It cannot come out behind a dive given the same dive budget. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01HLiTkESMktypGJhFag2ZBM

evanlinjin and others added 26 commits August 14, 2026 04:52

bench: restore capped BnB frontier coverage

28c5455

Separate deterministic solution-finding cases from larger pools expected to exhaust the fixed round cap. Assert each fixture's expected search outcome before measuring it so benchmark comparisons cannot silently time different paths.

docs: polish ancestor-aware API guidance

7e965cf

fixup! perf: search branch and bound with in-place DFS

7d48f88

evanlinjin mentioned this pull request Aug 16, 2026

perf!: store per-candidate ancestor sets sparsely #75

Draft

Navigation Menu

Uh oh!

feat: iterative deepening on the bound, dived first - #74

feat: iterative deepening on the bound, dived first#74
evanlinjin wants to merge 26 commits into
bitcoindevkit:masterfrom
evanlinjin:experiment/iterative-deepening

evanlinjin commented Aug 16, 2026

Uh oh!

Reviewers

Assignees

Labels

Projects

Milestone

Development

Uh oh!

1 participant

Uh oh!

Conversation

evanlinjin commented Aug 16, 2026

What this adds

Results

Correctness

What a reviewer should push back on

Uh oh!

Reviewers

Assignees

Labels

Projects

Milestone

Development

Uh oh!

1 participant