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diff --git a/src/cluster_linearize.h b/src/cluster_linearize.h new file mode 100644 index 0000000000..07d28a9aa5 --- /dev/null +++ b/src/cluster_linearize.h @@ -0,0 +1,743 @@ +// Copyright (c) The Bitcoin Core developers +// Distributed under the MIT software license, see the accompanying +// file COPYING or http://www.opensource.org/licenses/mit-license.php. + +#ifndef BITCOIN_CLUSTER_LINEARIZE_H +#define BITCOIN_CLUSTER_LINEARIZE_H + +#include <algorithm> +#include <numeric> +#include <optional> +#include <stdint.h> +#include <vector> +#include <utility> + +#include <random.h> +#include <span.h> +#include <util/feefrac.h> +#include <util/vecdeque.h> + +namespace cluster_linearize { + +/** Data type to represent cluster input. + * + * cluster[i].first is tx_i's fee and size. + * cluster[i].second[j] is true iff tx_i spends one or more of tx_j's outputs. + */ +template<typename SetType> +using Cluster = std::vector<std::pair<FeeFrac, SetType>>; + +/** Data type to represent transaction indices in clusters. */ +using ClusterIndex = uint32_t; + +/** Data structure that holds a transaction graph's preprocessed data (fee, size, ancestors, + * descendants). */ +template<typename SetType> +class DepGraph +{ + /** Information about a single transaction. */ + struct Entry + { + /** Fee and size of transaction itself. */ + FeeFrac feerate; + /** All ancestors of the transaction (including itself). */ + SetType ancestors; + /** All descendants of the transaction (including itself). */ + SetType descendants; + + /** Equality operator (primarily for for testing purposes). */ + friend bool operator==(const Entry&, const Entry&) noexcept = default; + + /** Construct an empty entry. */ + Entry() noexcept = default; + /** Construct an entry with a given feerate, ancestor set, descendant set. */ + Entry(const FeeFrac& f, const SetType& a, const SetType& d) noexcept : feerate(f), ancestors(a), descendants(d) {} + }; + + /** Data for each transaction, in the same order as the Cluster it was constructed from. */ + std::vector<Entry> entries; + +public: + /** Equality operator (primarily for testing purposes). */ + friend bool operator==(const DepGraph&, const DepGraph&) noexcept = default; + + // Default constructors. + DepGraph() noexcept = default; + DepGraph(const DepGraph&) noexcept = default; + DepGraph(DepGraph&&) noexcept = default; + DepGraph& operator=(const DepGraph&) noexcept = default; + DepGraph& operator=(DepGraph&&) noexcept = default; + + /** Construct a DepGraph object for ntx transactions, with no dependencies. + * + * Complexity: O(N) where N=ntx. + **/ + explicit DepGraph(ClusterIndex ntx) noexcept + { + Assume(ntx <= SetType::Size()); + entries.resize(ntx); + for (ClusterIndex i = 0; i < ntx; ++i) { + entries[i].ancestors = SetType::Singleton(i); + entries[i].descendants = SetType::Singleton(i); + } + } + + /** Construct a DepGraph object given a cluster. + * + * Complexity: O(N^2) where N=cluster.size(). + */ + explicit DepGraph(const Cluster<SetType>& cluster) noexcept : entries(cluster.size()) + { + for (ClusterIndex i = 0; i < cluster.size(); ++i) { + // Fill in fee and size. + entries[i].feerate = cluster[i].first; + // Fill in direct parents as ancestors. + entries[i].ancestors = cluster[i].second; + // Make sure transactions are ancestors of themselves. + entries[i].ancestors.Set(i); + } + + // Propagate ancestor information. + for (ClusterIndex i = 0; i < entries.size(); ++i) { + // At this point, entries[a].ancestors[b] is true iff b is an ancestor of a and there + // is a path from a to b through the subgraph consisting of {a, b} union + // {0, 1, ..., (i-1)}. + SetType to_merge = entries[i].ancestors; + for (ClusterIndex j = 0; j < entries.size(); ++j) { + if (entries[j].ancestors[i]) { + entries[j].ancestors |= to_merge; + } + } + } + + // Fill in descendant information by transposing the ancestor information. + for (ClusterIndex i = 0; i < entries.size(); ++i) { + for (auto j : entries[i].ancestors) { + entries[j].descendants.Set(i); + } + } + } + + /** Get the number of transactions in the graph. Complexity: O(1). */ + auto TxCount() const noexcept { return entries.size(); } + /** Get the feerate of a given transaction i. Complexity: O(1). */ + const FeeFrac& FeeRate(ClusterIndex i) const noexcept { return entries[i].feerate; } + /** Get the ancestors of a given transaction i. Complexity: O(1). */ + const SetType& Ancestors(ClusterIndex i) const noexcept { return entries[i].ancestors; } + /** Get the descendants of a given transaction i. Complexity: O(1). */ + const SetType& Descendants(ClusterIndex i) const noexcept { return entries[i].descendants; } + + /** Add a new unconnected transaction to this transaction graph (at the end), and return its + * ClusterIndex. + * + * Complexity: O(1) (amortized, due to resizing of backing vector). + */ + ClusterIndex AddTransaction(const FeeFrac& feefrac) noexcept + { + Assume(TxCount() < SetType::Size()); + ClusterIndex new_idx = TxCount(); + entries.emplace_back(feefrac, SetType::Singleton(new_idx), SetType::Singleton(new_idx)); + return new_idx; + } + + /** Modify this transaction graph, adding a dependency between a specified parent and child. + * + * Complexity: O(N) where N=TxCount(). + **/ + void AddDependency(ClusterIndex parent, ClusterIndex child) noexcept + { + // Bail out if dependency is already implied. + if (entries[child].ancestors[parent]) return; + // To each ancestor of the parent, add as descendants the descendants of the child. + const auto& chl_des = entries[child].descendants; + for (auto anc_of_par : Ancestors(parent)) { + entries[anc_of_par].descendants |= chl_des; + } + // To each descendant of the child, add as ancestors the ancestors of the parent. + const auto& par_anc = entries[parent].ancestors; + for (auto dec_of_chl : Descendants(child)) { + entries[dec_of_chl].ancestors |= par_anc; + } + } + + /** Compute the aggregate feerate of a set of nodes in this graph. + * + * Complexity: O(N) where N=elems.Count(). + **/ + FeeFrac FeeRate(const SetType& elems) const noexcept + { + FeeFrac ret; + for (auto pos : elems) ret += entries[pos].feerate; + return ret; + } + + /** Append the entries of select to list in a topologically valid order. + * + * Complexity: O(select.Count() * log(select.Count())). + */ + void AppendTopo(std::vector<ClusterIndex>& list, const SetType& select) const noexcept + { + ClusterIndex old_len = list.size(); + for (auto i : select) list.push_back(i); + std::sort(list.begin() + old_len, list.end(), [&](ClusterIndex a, ClusterIndex b) noexcept { + const auto a_anc_count = entries[a].ancestors.Count(); + const auto b_anc_count = entries[b].ancestors.Count(); + if (a_anc_count != b_anc_count) return a_anc_count < b_anc_count; + return a < b; + }); + } +}; + +/** A set of transactions together with their aggregate feerate. */ +template<typename SetType> +struct SetInfo +{ + /** The transactions in the set. */ + SetType transactions; + /** Their combined fee and size. */ + FeeFrac feerate; + + /** Construct a SetInfo for the empty set. */ + SetInfo() noexcept = default; + + /** Construct a SetInfo for a specified set and feerate. */ + SetInfo(const SetType& txn, const FeeFrac& fr) noexcept : transactions(txn), feerate(fr) {} + + /** Construct a SetInfo for a given transaction in a depgraph. */ + explicit SetInfo(const DepGraph<SetType>& depgraph, ClusterIndex pos) noexcept : + transactions(SetType::Singleton(pos)), feerate(depgraph.FeeRate(pos)) {} + + /** Construct a SetInfo for a set of transactions in a depgraph. */ + explicit SetInfo(const DepGraph<SetType>& depgraph, const SetType& txn) noexcept : + transactions(txn), feerate(depgraph.FeeRate(txn)) {} + + /** Add the transactions of other to this SetInfo (no overlap allowed). */ + SetInfo& operator|=(const SetInfo& other) noexcept + { + Assume(!transactions.Overlaps(other.transactions)); + transactions |= other.transactions; + feerate += other.feerate; + return *this; + } + + /** Construct a new SetInfo equal to this, with more transactions added (which may overlap + * with the existing transactions in the SetInfo). */ + [[nodiscard]] SetInfo Add(const DepGraph<SetType>& depgraph, const SetType& txn) const noexcept + { + return {transactions | txn, feerate + depgraph.FeeRate(txn - transactions)}; + } + + /** Swap two SetInfo objects. */ + friend void swap(SetInfo& a, SetInfo& b) noexcept + { + swap(a.transactions, b.transactions); + swap(a.feerate, b.feerate); + } + + /** Permit equality testing. */ + friend bool operator==(const SetInfo&, const SetInfo&) noexcept = default; +}; + +/** Compute the feerates of the chunks of linearization. */ +template<typename SetType> +std::vector<FeeFrac> ChunkLinearization(const DepGraph<SetType>& depgraph, Span<const ClusterIndex> linearization) noexcept +{ + std::vector<FeeFrac> ret; + for (ClusterIndex i : linearization) { + /** The new chunk to be added, initially a singleton. */ + auto new_chunk = depgraph.FeeRate(i); + // As long as the new chunk has a higher feerate than the last chunk so far, absorb it. + while (!ret.empty() && new_chunk >> ret.back()) { + new_chunk += ret.back(); + ret.pop_back(); + } + // Actually move that new chunk into the chunking. + ret.push_back(std::move(new_chunk)); + } + return ret; +} + +/** Data structure encapsulating the chunking of a linearization, permitting removal of subsets. */ +template<typename SetType> +class LinearizationChunking +{ + /** The depgraph this linearization is for. */ + const DepGraph<SetType>& m_depgraph; + + /** The linearization we started from. */ + Span<const ClusterIndex> m_linearization; + + /** Chunk sets and their feerates, of what remains of the linearization. */ + std::vector<SetInfo<SetType>> m_chunks; + + /** Which transactions remain in the linearization. */ + SetType m_todo; + + /** Fill the m_chunks variable. */ + void BuildChunks() noexcept + { + // Caller must clear m_chunks. + Assume(m_chunks.empty()); + + // Iterate over the entries in m_linearization. This is effectively the same + // algorithm as ChunkLinearization, but supports skipping parts of the linearization and + // keeps track of the sets themselves instead of just their feerates. + for (auto idx : m_linearization) { + if (!m_todo[idx]) continue; + // Start with an initial chunk containing just element idx. + SetInfo add(m_depgraph, idx); + // Absorb existing final chunks into add while they have lower feerate. + while (!m_chunks.empty() && add.feerate >> m_chunks.back().feerate) { + add |= m_chunks.back(); + m_chunks.pop_back(); + } + // Remember new chunk. + m_chunks.push_back(std::move(add)); + } + } + +public: + /** Initialize a LinearizationSubset object for a given length of linearization. */ + explicit LinearizationChunking(const DepGraph<SetType>& depgraph LIFETIMEBOUND, Span<const ClusterIndex> lin LIFETIMEBOUND) noexcept : + m_depgraph(depgraph), m_linearization(lin) + { + // Mark everything in lin as todo still. + for (auto i : m_linearization) m_todo.Set(i); + // Compute the initial chunking. + m_chunks.reserve(depgraph.TxCount()); + BuildChunks(); + } + + /** Determine how many chunks remain in the linearization. */ + ClusterIndex NumChunksLeft() const noexcept { return m_chunks.size(); } + + /** Access a chunk. Chunk 0 is the highest-feerate prefix of what remains. */ + const SetInfo<SetType>& GetChunk(ClusterIndex n) const noexcept + { + Assume(n < m_chunks.size()); + return m_chunks[n]; + } + + /** Remove some subset of transactions from the linearization. */ + void MarkDone(SetType subset) noexcept + { + Assume(subset.Any()); + Assume(subset.IsSubsetOf(m_todo)); + m_todo -= subset; + // Rechunk what remains of m_linearization. + m_chunks.clear(); + BuildChunks(); + } + + /** Find the shortest intersection between subset and the prefixes of remaining chunks + * of the linearization that has a feerate not below subset's. + * + * This is a crucial operation in guaranteeing improvements to linearizations. If subset has + * a feerate not below GetChunk(0)'s, then moving Intersect(subset) to the front of (what + * remains of) the linearization is guaranteed not to make it worse at any point. + * + * See https://delvingbitcoin.org/t/introduction-to-cluster-linearization/1032 for background. + */ + SetInfo<SetType> Intersect(const SetInfo<SetType>& subset) const noexcept + { + Assume(subset.transactions.IsSubsetOf(m_todo)); + SetInfo<SetType> accumulator; + // Iterate over all chunks of the remaining linearization. + for (ClusterIndex i = 0; i < NumChunksLeft(); ++i) { + // Find what (if any) intersection the chunk has with subset. + const SetType to_add = GetChunk(i).transactions & subset.transactions; + if (to_add.Any()) { + // If adding that to accumulator makes us hit all of subset, we are done as no + // shorter intersection with higher/equal feerate exists. + accumulator.transactions |= to_add; + if (accumulator.transactions == subset.transactions) break; + // Otherwise update the accumulator feerate. + accumulator.feerate += m_depgraph.FeeRate(to_add); + // If that does result in something better, or something with the same feerate but + // smaller, return that. Even if a longer, higher-feerate intersection exists, it + // does not hurt to return the shorter one (the remainder of the longer intersection + // will generally be found in the next call to Intersect, but even if not, it is not + // required for the improvement guarantee this function makes). + if (!(accumulator.feerate << subset.feerate)) return accumulator; + } + } + return subset; + } +}; + +/** Class encapsulating the state needed to find the best remaining ancestor set. + * + * It is initialized for an entire DepGraph, and parts of the graph can be dropped by calling + * MarkDone. + * + * As long as any part of the graph remains, FindCandidateSet() can be called which will return a + * SetInfo with the highest-feerate ancestor set that remains (an ancestor set is a single + * transaction together with all its remaining ancestors). + */ +template<typename SetType> +class AncestorCandidateFinder +{ + /** Internal dependency graph. */ + const DepGraph<SetType>& m_depgraph; + /** Which transaction are left to include. */ + SetType m_todo; + /** Precomputed ancestor-set feerates (only kept up-to-date for indices in m_todo). */ + std::vector<FeeFrac> m_ancestor_set_feerates; + +public: + /** Construct an AncestorCandidateFinder for a given cluster. + * + * Complexity: O(N^2) where N=depgraph.TxCount(). + */ + AncestorCandidateFinder(const DepGraph<SetType>& depgraph LIFETIMEBOUND) noexcept : + m_depgraph(depgraph), + m_todo{SetType::Fill(depgraph.TxCount())}, + m_ancestor_set_feerates(depgraph.TxCount()) + { + // Precompute ancestor-set feerates. + for (ClusterIndex i = 0; i < depgraph.TxCount(); ++i) { + /** The remaining ancestors for transaction i. */ + SetType anc_to_add = m_depgraph.Ancestors(i); + FeeFrac anc_feerate; + // Reuse accumulated feerate from first ancestor, if usable. + Assume(anc_to_add.Any()); + ClusterIndex first = anc_to_add.First(); + if (first < i) { + anc_feerate = m_ancestor_set_feerates[first]; + Assume(!anc_feerate.IsEmpty()); + anc_to_add -= m_depgraph.Ancestors(first); + } + // Add in other ancestors (which necessarily include i itself). + Assume(anc_to_add[i]); + anc_feerate += m_depgraph.FeeRate(anc_to_add); + // Store the result. + m_ancestor_set_feerates[i] = anc_feerate; + } + } + + /** Remove a set of transactions from the set of to-be-linearized ones. + * + * The same transaction may not be MarkDone()'d twice. + * + * Complexity: O(N*M) where N=depgraph.TxCount(), M=select.Count(). + */ + void MarkDone(SetType select) noexcept + { + Assume(select.Any()); + Assume(select.IsSubsetOf(m_todo)); + m_todo -= select; + for (auto i : select) { + auto feerate = m_depgraph.FeeRate(i); + for (auto j : m_depgraph.Descendants(i) & m_todo) { + m_ancestor_set_feerates[j] -= feerate; + } + } + } + + /** Check whether any unlinearized transactions remain. */ + bool AllDone() const noexcept + { + return m_todo.None(); + } + + /** Find the best (highest-feerate, smallest among those in case of a tie) ancestor set + * among the remaining transactions. Requires !AllDone(). + * + * Complexity: O(N) where N=depgraph.TxCount(); + */ + SetInfo<SetType> FindCandidateSet() const noexcept + { + Assume(!AllDone()); + std::optional<ClusterIndex> best; + for (auto i : m_todo) { + if (best.has_value()) { + Assume(!m_ancestor_set_feerates[i].IsEmpty()); + if (!(m_ancestor_set_feerates[i] > m_ancestor_set_feerates[*best])) continue; + } + best = i; + } + Assume(best.has_value()); + return {m_depgraph.Ancestors(*best) & m_todo, m_ancestor_set_feerates[*best]}; + } +}; + +/** Class encapsulating the state needed to perform search for good candidate sets. + * + * It is initialized for an entire DepGraph, and parts of the graph can be dropped by calling + * MarkDone(). + * + * As long as any part of the graph remains, FindCandidateSet() can be called to perform a search + * over the set of topologically-valid subsets of that remainder, with a limit on how many + * combinations are tried. + */ +template<typename SetType> +class SearchCandidateFinder +{ + /** Internal RNG. */ + InsecureRandomContext m_rng; + /** Internal dependency graph for the cluster. */ + const DepGraph<SetType>& m_depgraph; + /** Which transactions are left to do (sorted indices). */ + SetType m_todo; + +public: + /** Construct a candidate finder for a graph. + * + * @param[in] depgraph Dependency graph for the to-be-linearized cluster. + * @param[in] rng_seed A random seed to control the search order. + * + * Complexity: O(1). + */ + SearchCandidateFinder(const DepGraph<SetType>& depgraph LIFETIMEBOUND, uint64_t rng_seed) noexcept : + m_rng(rng_seed), + m_depgraph(depgraph), + m_todo(SetType::Fill(depgraph.TxCount())) {} + + /** Check whether any unlinearized transactions remain. */ + bool AllDone() const noexcept + { + return m_todo.None(); + } + + /** Find a high-feerate topologically-valid subset of what remains of the cluster. + * Requires !AllDone(). + * + * @param[in] max_iterations The maximum number of optimization steps that will be performed. + * @param[in] best A set/feerate pair with an already-known good candidate. This may + * be empty. + * @return A pair of: + * - The best (highest feerate, smallest size as tiebreaker) + * topologically valid subset (and its feerate) that was + * encountered during search. It will be at least as good as the + * best passed in (if not empty). + * - The number of optimization steps that were performed. This will + * be <= max_iterations. If strictly < max_iterations, the + * returned subset is optimal. + * + * Complexity: O(N * min(max_iterations, 2^N)) where N=depgraph.TxCount(). + */ + std::pair<SetInfo<SetType>, uint64_t> FindCandidateSet(uint64_t max_iterations, SetInfo<SetType> best) noexcept + { + Assume(!AllDone()); + + /** Type for work queue items. */ + struct WorkItem + { + /** Set of transactions definitely included (and its feerate). This must be a subset + * of m_todo, and be topologically valid (includes all in-m_todo ancestors of + * itself). */ + SetInfo<SetType> inc; + /** Set of undecided transactions. This must be a subset of m_todo, and have no overlap + * with inc. The set (inc | und) must be topologically valid. */ + SetType und; + + /** Construct a new work item. */ + WorkItem(SetInfo<SetType>&& i, SetType&& u) noexcept : + inc(std::move(i)), und(std::move(u)) {} + + /** Swap two WorkItems. */ + void Swap(WorkItem& other) noexcept + { + swap(inc, other.inc); + swap(und, other.und); + } + }; + + /** The queue of work items. */ + VecDeque<WorkItem> queue; + queue.reserve(std::max<size_t>(256, 2 * m_todo.Count())); + + // Create an initial entry with m_todo as undecided. Also use it as best if not provided, + // so that during the work processing loop below, and during the add_fn/split_fn calls, we + // do not need to deal with the best=empty case. + if (best.feerate.IsEmpty()) best = SetInfo(m_depgraph, m_todo); + queue.emplace_back(SetInfo<SetType>{}, SetType{m_todo}); + + /** Local copy of the iteration limit. */ + uint64_t iterations_left = max_iterations; + + /** Internal function to add an item to the queue of elements to explore if there are any + * transactions left to split on, and to update best. + * + * - inc: the "inc" value for the new work item (must be topological). + * - und: the "und" value for the new work item ((inc | und) must be topological). + */ + auto add_fn = [&](SetInfo<SetType> inc, SetType und) noexcept { + if (!inc.feerate.IsEmpty()) { + // If inc's feerate is better than best's, remember it as our new best. + if (inc.feerate > best.feerate) { + best = inc; + } + } else { + Assume(inc.transactions.None()); + } + + // Make sure there are undecided transactions left to split on. + if (und.None()) return; + + // Actually construct a new work item on the queue. Due to the switch to DFS when queue + // space runs out (see below), we know that no reallocation of the queue should ever + // occur. + Assume(queue.size() < queue.capacity()); + queue.emplace_back(std::move(inc), std::move(und)); + }; + + /** Internal process function. It takes an existing work item, and splits it in two: one + * with a particular transaction (and its ancestors) included, and one with that + * transaction (and its descendants) excluded. */ + auto split_fn = [&](WorkItem&& elem) noexcept { + // Any queue element must have undecided transactions left, otherwise there is nothing + // to explore anymore. + Assume(elem.und.Any()); + // The included and undecided set are all subsets of m_todo. + Assume(elem.inc.transactions.IsSubsetOf(m_todo) && elem.und.IsSubsetOf(m_todo)); + // Included transactions cannot be undecided. + Assume(!elem.inc.transactions.Overlaps(elem.und)); + + // Pick the first undecided transaction as the one to split on. + const ClusterIndex split = elem.und.First(); + + // Add a work item corresponding to exclusion of the split transaction. + const auto& desc = m_depgraph.Descendants(split); + add_fn(/*inc=*/elem.inc, + /*und=*/elem.und - desc); + + // Add a work item corresponding to inclusion of the split transaction. + const auto anc = m_depgraph.Ancestors(split) & m_todo; + add_fn(/*inc=*/elem.inc.Add(m_depgraph, anc), + /*und=*/elem.und - anc); + + // Account for the performed split. + --iterations_left; + }; + + // Work processing loop. + // + // New work items are always added at the back of the queue, but items to process use a + // hybrid approach where they can be taken from the front or the back. + // + // Depth-first search (DFS) corresponds to always taking from the back of the queue. This + // is very memory-efficient (linear in the number of transactions). Breadth-first search + // (BFS) corresponds to always taking from the front, which potentially uses more memory + // (up to exponential in the transaction count), but seems to work better in practice. + // + // The approach here combines the two: use BFS (plus random swapping) until the queue grows + // too large, at which point we temporarily switch to DFS until the size shrinks again. + while (!queue.empty()) { + // Randomly swap the first two items to randomize the search order. + if (queue.size() > 1 && m_rng.randbool()) { + queue[0].Swap(queue[1]); + } + + // Processing the first queue item, and then using DFS for everything it gives rise to, + // may increase the queue size by the number of undecided elements in there, minus 1 + // for the first queue item being removed. Thus, only when that pushes the queue over + // its capacity can we not process from the front (BFS), and should we use DFS. + while (queue.size() - 1 + queue.front().und.Count() > queue.capacity()) { + if (!iterations_left) break; + auto elem = queue.back(); + queue.pop_back(); + split_fn(std::move(elem)); + } + + // Process one entry from the front of the queue (BFS exploration) + if (!iterations_left) break; + auto elem = queue.front(); + queue.pop_front(); + split_fn(std::move(elem)); + } + + // Return the found best set and the number of iterations performed. + return {std::move(best), max_iterations - iterations_left}; + } + + /** Remove a subset of transactions from the cluster being linearized. + * + * Complexity: O(N) where N=done.Count(). + */ + void MarkDone(const SetType& done) noexcept + { + Assume(done.Any()); + Assume(done.IsSubsetOf(m_todo)); + m_todo -= done; + } +}; + +/** Find or improve a linearization for a cluster. + * + * @param[in] depgraph Dependency graph of the cluster to be linearized. + * @param[in] max_iterations Upper bound on the number of optimization steps that will be done. + * @param[in] rng_seed A random number seed to control search order. This prevents peers + * from predicting exactly which clusters would be hard for us to + * linearize. + * @param[in] old_linearization An existing linearization for the cluster (which must be + * topologically valid), or empty. + * @return A pair of: + * - The resulting linearization. It is guaranteed to be at least as + * good (in the feerate diagram sense) as old_linearization. + * - A boolean indicating whether the result is guaranteed to be + * optimal. + * + * Complexity: O(N * min(max_iterations + N, 2^N)) where N=depgraph.TxCount(). + */ +template<typename SetType> +std::pair<std::vector<ClusterIndex>, bool> Linearize(const DepGraph<SetType>& depgraph, uint64_t max_iterations, uint64_t rng_seed, Span<const ClusterIndex> old_linearization = {}) noexcept +{ + Assume(old_linearization.empty() || old_linearization.size() == depgraph.TxCount()); + if (depgraph.TxCount() == 0) return {{}, true}; + + uint64_t iterations_left = max_iterations; + std::vector<ClusterIndex> linearization; + + AncestorCandidateFinder anc_finder(depgraph); + SearchCandidateFinder src_finder(depgraph, rng_seed); + linearization.reserve(depgraph.TxCount()); + bool optimal = true; + + /** Chunking of what remains of the old linearization. */ + LinearizationChunking old_chunking(depgraph, old_linearization); + + while (true) { + // Find the highest-feerate prefix of the remainder of old_linearization. + SetInfo<SetType> best_prefix; + if (old_chunking.NumChunksLeft()) best_prefix = old_chunking.GetChunk(0); + + // Then initialize best to be either the best remaining ancestor set, or the first chunk. + auto best = anc_finder.FindCandidateSet(); + if (!best_prefix.feerate.IsEmpty() && best_prefix.feerate >= best.feerate) best = best_prefix; + + // Invoke bounded search to update best, with up to half of our remaining iterations as + // limit. + uint64_t max_iterations_now = (iterations_left + 1) / 2; + uint64_t iterations_done_now = 0; + std::tie(best, iterations_done_now) = src_finder.FindCandidateSet(max_iterations_now, best); + iterations_left -= iterations_done_now; + + if (iterations_done_now == max_iterations_now) { + optimal = false; + // If the search result is not (guaranteed to be) optimal, run intersections to make + // sure we don't pick something that makes us unable to reach further diagram points + // of the old linearization. + if (old_chunking.NumChunksLeft() > 0) { + best = old_chunking.Intersect(best); + } + } + + // Add to output in topological order. + depgraph.AppendTopo(linearization, best.transactions); + + // Update state to reflect best is no longer to be linearized. + anc_finder.MarkDone(best.transactions); + if (anc_finder.AllDone()) break; + src_finder.MarkDone(best.transactions); + if (old_chunking.NumChunksLeft() > 0) { + old_chunking.MarkDone(best.transactions); + } + } + + return {std::move(linearization), optimal}; +} + +} // namespace cluster_linearize + +#endif // BITCOIN_CLUSTER_LINEARIZE_H |