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bitcoin/src/cluster_linearize.h
Pieter Wuille 1808b5aaf7 clusterlin: remove unused FixLinearization (cleanup)
2026-01-05 11:48:34 -05:00

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// 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 <cstdint>
#include <numeric>
#include <optional>
#include <utility>
#include <vector>
#include <memusage.h>
#include <random.h>
#include <span.h>
#include <util/feefrac.h>
#include <util/vecdeque.h>
namespace cluster_linearize {
/** Data type to represent transaction indices in DepGraphs and the clusters they represent. */
using DepGraphIndex = 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 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. */
std::vector<Entry> entries;
/** Which positions are used. */
SetType m_used;
public:
/** Equality operator (primarily for testing purposes). */
friend bool operator==(const DepGraph& a, const DepGraph& b) noexcept
{
if (a.m_used != b.m_used) return false;
// Only compare the used positions within the entries vector.
for (auto idx : a.m_used) {
if (a.entries[idx] != b.entries[idx]) return false;
}
return true;
}
// 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 given another DepGraph and a mapping from old to new.
*
* @param depgraph The original DepGraph that is being remapped.
*
* @param mapping A span such that mapping[i] gives the position in the new DepGraph
* for position i in the old depgraph. Its size must be equal to
* depgraph.PositionRange(). The value of mapping[i] is ignored if
* position i is a hole in depgraph (i.e., if !depgraph.Positions()[i]).
*
* @param pos_range The PositionRange() for the new DepGraph. It must equal the largest
* value in mapping for any used position in depgraph plus 1, or 0 if
* depgraph.TxCount() == 0.
*
* Complexity: O(N^2) where N=depgraph.TxCount().
*/
DepGraph(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> mapping, DepGraphIndex pos_range) noexcept : entries(pos_range)
{
Assume(mapping.size() == depgraph.PositionRange());
Assume((pos_range == 0) == (depgraph.TxCount() == 0));
for (DepGraphIndex i : depgraph.Positions()) {
auto new_idx = mapping[i];
Assume(new_idx < pos_range);
// Add transaction.
entries[new_idx].ancestors = SetType::Singleton(new_idx);
entries[new_idx].descendants = SetType::Singleton(new_idx);
m_used.Set(new_idx);
// Fill in fee and size.
entries[new_idx].feerate = depgraph.entries[i].feerate;
}
for (DepGraphIndex i : depgraph.Positions()) {
// Fill in dependencies by mapping direct parents.
SetType parents;
for (auto j : depgraph.GetReducedParents(i)) parents.Set(mapping[j]);
AddDependencies(parents, mapping[i]);
}
// Verify that the provided pos_range was correct (no unused positions at the end).
Assume(m_used.None() ? (pos_range == 0) : (pos_range == m_used.Last() + 1));
}
/** Get the set of transactions positions in use. Complexity: O(1). */
const SetType& Positions() const noexcept { return m_used; }
/** Get the range of positions in this DepGraph. All entries in Positions() are in [0, PositionRange() - 1]. */
DepGraphIndex PositionRange() const noexcept { return entries.size(); }
/** Get the number of transactions in the graph. Complexity: O(1). */
auto TxCount() const noexcept { return m_used.Count(); }
/** Get the feerate of a given transaction i. Complexity: O(1). */
const FeeFrac& FeeRate(DepGraphIndex i) const noexcept { return entries[i].feerate; }
/** Get the mutable feerate of a given transaction i. Complexity: O(1). */
FeeFrac& FeeRate(DepGraphIndex i) noexcept { return entries[i].feerate; }
/** Get the ancestors of a given transaction i. Complexity: O(1). */
const SetType& Ancestors(DepGraphIndex i) const noexcept { return entries[i].ancestors; }
/** Get the descendants of a given transaction i. Complexity: O(1). */
const SetType& Descendants(DepGraphIndex i) const noexcept { return entries[i].descendants; }
/** Add a new unconnected transaction to this transaction graph (in the first available
* position), and return its DepGraphIndex.
*
* Complexity: O(1) (amortized, due to resizing of backing vector).
*/
DepGraphIndex AddTransaction(const FeeFrac& feefrac) noexcept
{
static constexpr auto ALL_POSITIONS = SetType::Fill(SetType::Size());
auto available = ALL_POSITIONS - m_used;
Assume(available.Any());
DepGraphIndex new_idx = available.First();
if (new_idx == entries.size()) {
entries.emplace_back(feefrac, SetType::Singleton(new_idx), SetType::Singleton(new_idx));
} else {
entries[new_idx] = Entry(feefrac, SetType::Singleton(new_idx), SetType::Singleton(new_idx));
}
m_used.Set(new_idx);
return new_idx;
}
/** Remove the specified positions from this DepGraph.
*
* The specified positions will no longer be part of Positions(), and dependencies with them are
* removed. Note that due to DepGraph only tracking ancestors/descendants (and not direct
* dependencies), if a parent is removed while a grandparent remains, the grandparent will
* remain an ancestor.
*
* Complexity: O(N) where N=TxCount().
*/
void RemoveTransactions(const SetType& del) noexcept
{
m_used -= del;
// Remove now-unused trailing entries.
while (!entries.empty() && !m_used[entries.size() - 1]) {
entries.pop_back();
}
// Remove the deleted transactions from ancestors/descendants of other transactions. Note
// that the deleted positions will retain old feerate and dependency information. This does
// not matter as they will be overwritten by AddTransaction if they get used again.
for (auto& entry : entries) {
entry.ancestors &= m_used;
entry.descendants &= m_used;
}
}
/** Modify this transaction graph, adding multiple parents to a specified child.
*
* Complexity: O(N) where N=TxCount().
*/
void AddDependencies(const SetType& parents, DepGraphIndex child) noexcept
{
Assume(m_used[child]);
Assume(parents.IsSubsetOf(m_used));
// Compute the ancestors of parents that are not already ancestors of child.
SetType par_anc;
for (auto par : parents - Ancestors(child)) {
par_anc |= Ancestors(par);
}
par_anc -= Ancestors(child);
// Bail out if there are no such ancestors.
if (par_anc.None()) return;
// To each such ancestor, add as descendants the descendants of the child.
const auto& chl_des = entries[child].descendants;
for (auto anc_of_par : par_anc) {
entries[anc_of_par].descendants |= chl_des;
}
// To each descendant of the child, add those ancestors.
for (auto dec_of_chl : Descendants(child)) {
entries[dec_of_chl].ancestors |= par_anc;
}
}
/** Compute the (reduced) set of parents of node i in this graph.
*
* This returns the minimal subset of the parents of i whose ancestors together equal all of
* i's ancestors (unless i is part of a cycle of dependencies). Note that DepGraph does not
* store the set of parents; this information is inferred from the ancestor sets.
*
* Complexity: O(N) where N=Ancestors(i).Count() (which is bounded by TxCount()).
*/
SetType GetReducedParents(DepGraphIndex i) const noexcept
{
SetType parents = Ancestors(i);
parents.Reset(i);
for (auto parent : parents) {
if (parents[parent]) {
parents -= Ancestors(parent);
parents.Set(parent);
}
}
return parents;
}
/** Compute the (reduced) set of children of node i in this graph.
*
* This returns the minimal subset of the children of i whose descendants together equal all of
* i's descendants (unless i is part of a cycle of dependencies). Note that DepGraph does not
* store the set of children; this information is inferred from the descendant sets.
*
* Complexity: O(N) where N=Descendants(i).Count() (which is bounded by TxCount()).
*/
SetType GetReducedChildren(DepGraphIndex i) const noexcept
{
SetType children = Descendants(i);
children.Reset(i);
for (auto child : children) {
if (children[child]) {
children -= Descendants(child);
children.Set(child);
}
}
return children;
}
/** 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;
}
/** Get the connected component within the subset "todo" that contains tx (which must be in
* todo).
*
* Two transactions are considered connected if they are both in `todo`, and one is an ancestor
* of the other in the entire graph (so not just within `todo`), or transitively there is a
* path of transactions connecting them. This does mean that if `todo` contains a transaction
* and a grandparent, but misses the parent, they will still be part of the same component.
*
* Complexity: O(ret.Count()).
*/
SetType GetConnectedComponent(const SetType& todo, DepGraphIndex tx) const noexcept
{
Assume(todo[tx]);
Assume(todo.IsSubsetOf(m_used));
auto to_add = SetType::Singleton(tx);
SetType ret;
do {
SetType old = ret;
for (auto add : to_add) {
ret |= Descendants(add);
ret |= Ancestors(add);
}
ret &= todo;
to_add = ret - old;
} while (to_add.Any());
return ret;
}
/** Find some connected component within the subset "todo" of this graph.
*
* Specifically, this finds the connected component which contains the first transaction of
* todo (if any).
*
* Complexity: O(ret.Count()).
*/
SetType FindConnectedComponent(const SetType& todo) const noexcept
{
if (todo.None()) return todo;
return GetConnectedComponent(todo, todo.First());
}
/** Determine if a subset is connected.
*
* Complexity: O(subset.Count()).
*/
bool IsConnected(const SetType& subset) const noexcept
{
return FindConnectedComponent(subset) == subset;
}
/** Determine if this entire graph is connected.
*
* Complexity: O(TxCount()).
*/
bool IsConnected() const noexcept { return IsConnected(m_used); }
/** Append the entries of select to list in a topologically valid order.
*
* Complexity: O(select.Count() * log(select.Count())).
*/
void AppendTopo(std::vector<DepGraphIndex>& list, const SetType& select) const noexcept
{
DepGraphIndex old_len = list.size();
for (auto i : select) list.push_back(i);
std::sort(list.begin() + old_len, list.end(), [&](DepGraphIndex a, DepGraphIndex 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;
});
}
/** Check if this graph is acyclic. */
bool IsAcyclic() const noexcept
{
for (auto i : Positions()) {
if ((Ancestors(i) & Descendants(i)) != SetType::Singleton(i)) {
return false;
}
}
return true;
}
unsigned CountDependencies() const noexcept
{
unsigned ret = 0;
for (auto i : Positions()) {
ret += GetReducedParents(i).Count();
}
return ret;
}
/** Reduce memory usage if possible. No observable effect. */
void Compact() noexcept
{
entries.shrink_to_fit();
}
size_t DynamicMemoryUsage() const noexcept
{
return memusage::DynamicUsage(entries);
}
};
/** 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, DepGraphIndex 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 a transaction to this SetInfo (which must not yet be in it). */
void Set(const DepGraph<SetType>& depgraph, DepGraphIndex pos) noexcept
{
Assume(!transactions[pos]);
transactions.Set(pos);
feerate += depgraph.FeeRate(pos);
}
/** 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;
}
/** Remove the transactions of other from this SetInfo (which must be a subset). */
SetInfo& operator-=(const SetInfo& other) noexcept
{
Assume(other.transactions.IsSubsetOf(transactions));
transactions -= other.transactions;
feerate -= other.feerate;
return *this;
}
/** Compute the difference between this and other SetInfo (which must be a subset). */
SetInfo operator-(const SetInfo& other) const noexcept
{
Assume(other.transactions.IsSubsetOf(transactions));
return {transactions - other.transactions, feerate - other.feerate};
}
/** 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 chunks of linearization as SetInfos. */
template<typename SetType>
std::vector<SetInfo<SetType>> ChunkLinearizationInfo(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> linearization) noexcept
{
std::vector<SetInfo<SetType>> ret;
for (DepGraphIndex i : linearization) {
/** The new chunk to be added, initially a singleton. */
SetInfo<SetType> new_chunk(depgraph, i);
// As long as the new chunk has a higher feerate than the last chunk so far, absorb it.
while (!ret.empty() && new_chunk.feerate >> ret.back().feerate) {
new_chunk |= ret.back();
ret.pop_back();
}
// Actually move that new chunk into the chunking.
ret.emplace_back(std::move(new_chunk));
}
return ret;
}
/** Compute the feerates of the chunks of linearization. Identical to ChunkLinearizationInfo, but
* only returns the chunk feerates, not the corresponding transaction sets. */
template<typename SetType>
std::vector<FeeFrac> ChunkLinearization(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> linearization) noexcept
{
std::vector<FeeFrac> ret;
for (DepGraphIndex 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;
}
/** Class to represent the internal state of the spanning-forest linearization (SFL) algorithm.
*
* At all times, each dependency is marked as either "active" or "inactive". The subset of active
* dependencies is the state of the SFL algorithm. The implementation maintains several other
* values to speed up operations, but everything is ultimately a function of what that subset of
* active dependencies is.
*
* Given such a subset, define a chunk as the set of transactions that are connected through active
* dependencies (ignoring their parent/child direction). Thus, every state implies a particular
* partitioning of the graph into chunks (including potential singletons). In the extreme, each
* transaction may be in its own chunk, or in the other extreme all transactions may form a single
* chunk. A chunk's feerate is its total fee divided by its total size.
*
* The algorithm consists of switching dependencies between active and inactive. The final
* linearization that is produced at the end consists of these chunks, sorted from high to low
* feerate, each individually sorted in an arbitrary but topological (= no child before parent)
* way.
*
* We define three quality properties the state can have, each being stronger than the previous:
*
* - acyclic: The state is acyclic whenever no cycle of active dependencies exists within the
* graph, ignoring the parent/child direction. This is equivalent to saying that within
* each chunk the set of active dependencies form a tree, and thus the overall set of
* active dependencies in the graph form a spanning forest, giving the algorithm its
* name. Being acyclic is also equivalent to every chunk of N transactions having
* exactly N-1 active dependencies.
*
* For example in a diamond graph, D->{B,C}->A, the 4 dependencies cannot be
* simultaneously active. If at least one is inactive, the state is acyclic.
*
* The algorithm maintains an acyclic state at *all* times as an invariant. This implies
* that activating a dependency always corresponds to merging two chunks, and that
* deactivating one always corresponds to splitting two chunks.
*
* - topological: We say the state is topological whenever it is acyclic and no inactive dependency
* exists between two distinct chunks such that the child chunk has higher or equal
* feerate than the parent chunk.
*
* The relevance is that whenever the state is topological, the produced output
* linearization will be topological too (i.e., not have children before parents).
* Note that the "or equal" part of the definition matters: if not, one can end up
* in a situation with mutually-dependent equal-feerate chunks that cannot be
* linearized. For example C->{A,B} and D->{A,B}, with C->A and D->B active. The AC
* chunk depends on DB through C->B, and the BD chunk depends on AC through D->A.
* Merging them into a single ABCD chunk fixes this.
*
* The algorithm attempts to keep the state topological as much as possible, so it
* can be interrupted to produce an output whenever, but will sometimes need to
* temporarily deviate from it when improving the state.
*
* - optimal: For every active dependency, define its top and bottom set as the set of transactions
* in the chunks that would result if the dependency were deactivated; the top being the
* one with the dependency's parent, and the bottom being the one with the child. Note
* that due to acyclicity, every deactivation splits a chunk exactly in two.
*
* We say the state is optimal whenever it is topological and it has no active
* dependency whose top feerate is strictly higher than its bottom feerate. The
* relevance is that it can be proven that whenever the state is optimal, the produced
* linearization will also be optimal (in the convexified feerate diagram sense). It can
* also be proven that for every graph at least one optimal state exists.
*
* Note that it is possible for the SFL state to not be optimal, but the produced
* linearization to still be optimal. This happens when the chunks of a state are
* identical to those of an optimal state, but the exact set of active dependencies
* within a chunk differ in such a way that the state optimality condition is not
* satisfied. Thus, the state being optimal is more a "the eventual output is *known*
* to be optimal".
*
* The algorithm terminates whenever an optimal state is reached.
*
*
* This leads to the following high-level algorithm:
* - Start with all dependencies inactive, and thus all transactions in their own chunk. This is
* definitely acyclic.
* - Activate dependencies (merging chunks) until the state is topological.
* - Loop until optimal (no dependencies with higher-feerate top than bottom), or time runs out:
* - Deactivate a violating dependency, potentially making the state non-topological.
* - Activate other dependencies to make the state topological again.
* - Output the chunks from high to low feerate, each internally sorted topologically.
*
* When merging, we always either:
* - Merge upwards: merge a chunk with the lowest-feerate other chunk it depends on, among those
* with lower or equal feerate than itself.
* - Merge downwards: merge a chunk with the highest-feerate other chunk that depends on it, among
* those with higher or equal feerate than itself.
*
* Using these strategies in the improvement loop above guarantees that the output linearization
* after a deactivate + merge step is never worse or incomparable (in the convexified feerate
* diagram sense) than the output linearization that would be produced before the step. With that,
* we can refine the high-level algorithm to:
* - Start with all dependencies inactive.
* - Perform merges as described until none are possible anymore, making the state topological.
* - Loop until optimal or time runs out:
* - Pick a dependency D to deactivate among those with higher feerate top than bottom.
* - Deactivate D, causing the chunk it is in to split into top T and bottom B.
* - Do an upwards merge of T, if possible. If so, repeat the same with the merged result.
* - Do a downwards merge of B, if possible. If so, repeat the same with the merged result.
* - Output the chunks from high to low feerate, each internally sorted topologically.
*
* Instead of performing merges arbitrarily to make the initial state topological, it is possible
* to do so guided by an existing linearization. This has the advantage that the state's would-be
* output linearization is immediately as good as the existing linearization it was based on:
* - Start with all dependencies inactive.
* - For each transaction t in the existing linearization:
* - Find the chunk C that transaction is in (which will be singleton).
* - Do an upwards merge of C, if possible. If so, repeat the same with the merged result.
* No downwards merges are needed in this case.
*
* What remains to be specified are a number of heuristics:
*
* - How to decide which chunks to merge:
* - The merge upwards and downward rules specify that the lowest-feerate respectively
* highest-feerate candidate chunk is merged with, but if there are multiple equal-feerate
* candidates, a uniformly random one among them is picked.
*
* - How to decide what dependency to activate (when merging chunks):
* - After picking two chunks to be merged (see above), a uniformly random dependency between the
* two chunks is activated.
*
* - How to decide which chunk to find a dependency to split in:
* - A round-robin queue of chunks to improve is maintained. The initial ordering of this queue
* is uniformly randomly permuted.
*
* - How to decide what dependency to deactivate (when splitting chunks):
* - Inside the selected chunk (see above), among the dependencies whose top feerate is strictly
* higher than its bottom feerate in the selected chunk, if any, a uniformly random dependency
* is deactivated.
*
* - How to decide the exact output linearization:
* - When there are multiple equal-feerate chunks with no dependencies between them, output a
* uniformly random one among the ones with no missing dependent chunks first.
* - Within chunks, repeatedly pick a uniformly random transaction among those with no missing
* dependencies.
*/
template<typename SetType>
class SpanningForestState
{
private:
/** Internal RNG. */
InsecureRandomContext m_rng;
/** Data type to represent indexing into m_tx_data. */
using TxIdx = uint32_t;
/** Data type to represent indexing into m_dep_data. */
using DepIdx = uint32_t;
/** Structure with information about a single transaction. For transactions that are the
* representative for the chunk they are in, this also stores chunk information. */
struct TxData {
/** The dependencies to children of this transaction. Immutable after construction. */
std::vector<DepIdx> child_deps;
/** The set of parent transactions of this transaction. Immutable after construction. */
SetType parents;
/** The set of child transactions of this transaction. Immutable after construction. */
SetType children;
/** Which transaction holds the chunk_setinfo for the chunk this transaction is in
* (the representative for the chunk). */
TxIdx chunk_rep;
/** (Only if this transaction is the representative for the chunk it is in) the total
* chunk set and feerate. */
SetInfo<SetType> chunk_setinfo;
};
/** Structure with information about a single dependency. */
struct DepData {
/** Whether this dependency is active. */
bool active;
/** What the parent and child transactions are. Immutable after construction. */
TxIdx parent, child;
/** (Only if this dependency is active) the would-be top chunk and its feerate that would
* be formed if this dependency were to be deactivated. */
SetInfo<SetType> top_setinfo;
};
/** The set of all TxIdx's of transactions in the cluster indexing into m_tx_data. */
SetType m_transaction_idxs;
/** Information about each transaction (and chunks). Keeps the "holes" from DepGraph during
* construction. Indexed by TxIdx. */
std::vector<TxData> m_tx_data;
/** Information about each dependency. Indexed by DepIdx. */
std::vector<DepData> m_dep_data;
/** A FIFO of chunk representatives of chunks that may be improved still. */
VecDeque<TxIdx> m_suboptimal_chunks;
/** The number of updated transactions in activations/deactivations. */
uint64_t m_cost{0};
/** Update a chunk:
* - All transactions have their chunk representative set to `chunk_rep`.
* - All dependencies which have `query` in their top_setinfo get `dep_change` added to it
* (if `!Subtract`) or removed from it (if `Subtract`).
*/
template<bool Subtract>
void UpdateChunk(const SetType& chunk, TxIdx query, TxIdx chunk_rep, const SetInfo<SetType>& dep_change) noexcept
{
// Iterate over all the chunk's transactions.
for (auto tx_idx : chunk) {
auto& tx_data = m_tx_data[tx_idx];
// Update the chunk representative.
tx_data.chunk_rep = chunk_rep;
// Iterate over all active dependencies with tx_idx as parent. Combined with the outer
// loop this iterates over all internal active dependencies of the chunk.
auto child_deps = std::span{tx_data.child_deps};
for (auto dep_idx : child_deps) {
auto& dep_entry = m_dep_data[dep_idx];
Assume(dep_entry.parent == tx_idx);
// Skip inactive dependencies.
if (!dep_entry.active) continue;
// If this dependency's top_setinfo contains query, update it to add/remove
// dep_change.
if (dep_entry.top_setinfo.transactions[query]) {
if constexpr (Subtract) {
dep_entry.top_setinfo -= dep_change;
} else {
dep_entry.top_setinfo |= dep_change;
}
}
}
}
}
/** Make a specified inactive dependency active. Returns the merged chunk representative. */
TxIdx Activate(DepIdx dep_idx) noexcept
{
auto& dep_data = m_dep_data[dep_idx];
Assume(!dep_data.active);
auto& child_tx_data = m_tx_data[dep_data.child];
auto& parent_tx_data = m_tx_data[dep_data.parent];
// Gather information about the parent and child chunks.
Assume(parent_tx_data.chunk_rep != child_tx_data.chunk_rep);
auto& par_chunk_data = m_tx_data[parent_tx_data.chunk_rep];
auto& chl_chunk_data = m_tx_data[child_tx_data.chunk_rep];
TxIdx top_rep = parent_tx_data.chunk_rep;
auto top_part = par_chunk_data.chunk_setinfo;
auto bottom_part = chl_chunk_data.chunk_setinfo;
// Update the parent chunk to also contain the child.
par_chunk_data.chunk_setinfo |= bottom_part;
m_cost += par_chunk_data.chunk_setinfo.transactions.Count();
// Consider the following example:
//
// A A There are two chunks, ABC and DEF, and the inactive E->C dependency
// / \ / \ is activated, resulting in a single chunk ABCDEF.
// B C B C
// : ==> | Dependency | top set before | top set after | change
// D E D E B->A | AC | ACDEF | +DEF
// \ / \ / C->A | AB | AB |
// F F F->D | D | D |
// F->E | E | ABCE | +ABC
//
// The common pattern here is that any dependency which has the parent or child of the
// dependency being activated (E->C here) in its top set, will have the opposite part added
// to it. This is true for B->A and F->E, but not for C->A and F->D.
//
// Let UpdateChunk traverse the old parent chunk top_part (ABC in example), and add
// bottom_part (DEF) to every dependency's top_set which has the parent (C) in it. The
// representative of each of these transactions was already top_rep, so that is not being
// changed here.
UpdateChunk<false>(/*chunk=*/top_part.transactions, /*query=*/dep_data.parent,
/*chunk_rep=*/top_rep, /*dep_change=*/bottom_part);
// Let UpdateChunk traverse the old child chunk bottom_part (DEF in example), and add
// top_part (ABC) to every dependency's top_set which has the child (E) in it. At the same
// time, change the representative of each of these transactions to be top_rep, which
// becomes the representative for the merged chunk.
UpdateChunk<false>(/*chunk=*/bottom_part.transactions, /*query=*/dep_data.child,
/*chunk_rep=*/top_rep, /*dep_change=*/top_part);
// Make active.
dep_data.active = true;
dep_data.top_setinfo = top_part;
return top_rep;
}
/** Make a specified active dependency inactive. */
void Deactivate(DepIdx dep_idx) noexcept
{
auto& dep_data = m_dep_data[dep_idx];
Assume(dep_data.active);
auto& parent_tx_data = m_tx_data[dep_data.parent];
// Make inactive.
dep_data.active = false;
// Update representatives.
auto& chunk_data = m_tx_data[parent_tx_data.chunk_rep];
m_cost += chunk_data.chunk_setinfo.transactions.Count();
auto top_part = dep_data.top_setinfo;
auto bottom_part = chunk_data.chunk_setinfo - top_part;
TxIdx bottom_rep = dep_data.child;
auto& bottom_chunk_data = m_tx_data[bottom_rep];
bottom_chunk_data.chunk_setinfo = bottom_part;
TxIdx top_rep = dep_data.parent;
auto& top_chunk_data = m_tx_data[top_rep];
top_chunk_data.chunk_setinfo = top_part;
// See the comment above in Activate(). We perform the opposite operations here,
// removing instead of adding.
//
// Let UpdateChunk traverse the old parent chunk top_part, and remove bottom_part from
// every dependency's top_set which has the parent in it. At the same time, change the
// representative of each of these transactions to be top_rep.
UpdateChunk<true>(/*chunk=*/top_part.transactions, /*query=*/dep_data.parent,
/*chunk_rep=*/top_rep, /*dep_change=*/bottom_part);
// Let UpdateChunk traverse the old child chunk bottom_part, and remove top_part from every
// dependency's top_set which has the child in it. At the same time, change the
// representative of each of these transactions to be bottom_rep.
UpdateChunk<true>(/*chunk=*/bottom_part.transactions, /*query=*/dep_data.child,
/*chunk_rep=*/bottom_rep, /*dep_change=*/top_part);
}
/** Activate a dependency from the chunk represented by bottom_rep to the chunk represented by
* top_rep, which must exist. Return the representative of the merged chunk. */
TxIdx MergeChunks(TxIdx top_rep, TxIdx bottom_rep) noexcept
{
auto& top_chunk = m_tx_data[top_rep];
Assume(top_chunk.chunk_rep == top_rep);
auto& bottom_chunk = m_tx_data[bottom_rep];
Assume(bottom_chunk.chunk_rep == bottom_rep);
// Count the number of dependencies between bottom_chunk and top_chunk.
TxIdx num_deps{0};
for (auto tx : top_chunk.chunk_setinfo.transactions) {
auto& tx_data = m_tx_data[tx];
num_deps += (tx_data.children & bottom_chunk.chunk_setinfo.transactions).Count();
}
Assume(num_deps > 0);
// Uniformly randomly pick one of them and activate it.
TxIdx pick = m_rng.randrange(num_deps);
for (auto tx : top_chunk.chunk_setinfo.transactions) {
auto& tx_data = m_tx_data[tx];
auto intersect = tx_data.children & bottom_chunk.chunk_setinfo.transactions;
auto count = intersect.Count();
if (pick < count) {
for (auto dep : tx_data.child_deps) {
auto& dep_data = m_dep_data[dep];
if (bottom_chunk.chunk_setinfo.transactions[dep_data.child]) {
if (pick == 0) return Activate(dep);
--pick;
}
}
break;
}
pick -= count;
}
Assume(false);
return TxIdx(-1);
}
/** Perform an upward or downward merge step, on the specified chunk representative. Returns
* the representative of the merged chunk, or TxIdx(-1) if no merge took place. */
template<bool DownWard>
TxIdx MergeStep(TxIdx chunk_rep) noexcept
{
/** Information about the chunk that tx_idx is currently in. */
auto& chunk_data = m_tx_data[chunk_rep];
SetType chunk_txn = chunk_data.chunk_setinfo.transactions;
// Iterate over all transactions in the chunk, figuring out which other chunk each
// depends on, but only testing each other chunk once. For those depended-on chunks,
// remember the highest-feerate (if DownWard) or lowest-feerate (if !DownWard) one.
// If multiple equal-feerate candidate chunks to merge with exist, pick a random one
// among them.
/** Which transactions have been reached from this chunk already. Initialize with the
* chunk itself, so internal dependencies within the chunk are ignored. */
SetType explored = chunk_txn;
/** The minimum feerate (if downward) or maximum feerate (if upward) to consider when
* looking for candidate chunks to merge with. Initially, this is the original chunk's
* feerate, but is updated to be the current best candidate whenever one is found. */
FeeFrac best_other_chunk_feerate = chunk_data.chunk_setinfo.feerate;
/** The representative for the best candidate chunk to merge with. -1 if none. */
TxIdx best_other_chunk_rep = TxIdx(-1);
/** We generate random tiebreak values to pick between equal-feerate candidate chunks.
* This variable stores the tiebreak of the current best candidate. */
uint64_t best_other_chunk_tiebreak{0};
for (auto tx : chunk_txn) {
auto& tx_data = m_tx_data[tx];
/** The transactions reached by following dependencies from tx that have not been
* explored before. */
auto newly_reached = (DownWard ? tx_data.children : tx_data.parents) - explored;
explored |= newly_reached;
while (newly_reached.Any()) {
// Find a chunk inside newly_reached, and remove it from newly_reached.
auto reached_chunk_rep = m_tx_data[newly_reached.First()].chunk_rep;
auto& reached_chunk = m_tx_data[reached_chunk_rep].chunk_setinfo;
newly_reached -= reached_chunk.transactions;
// See if it has an acceptable feerate.
auto cmp = DownWard ? FeeRateCompare(best_other_chunk_feerate, reached_chunk.feerate)
: FeeRateCompare(reached_chunk.feerate, best_other_chunk_feerate);
if (cmp > 0) continue;
uint64_t tiebreak = m_rng.rand64();
if (cmp < 0 || tiebreak >= best_other_chunk_tiebreak) {
best_other_chunk_feerate = reached_chunk.feerate;
best_other_chunk_rep = reached_chunk_rep;
best_other_chunk_tiebreak = tiebreak;
}
}
}
// Stop if there are no candidate chunks to merge with.
if (best_other_chunk_rep == TxIdx(-1)) return TxIdx(-1);
if constexpr (DownWard) {
chunk_rep = MergeChunks(chunk_rep, best_other_chunk_rep);
} else {
chunk_rep = MergeChunks(best_other_chunk_rep, chunk_rep);
}
Assume(chunk_rep != TxIdx(-1));
return chunk_rep;
}
/** Perform an upward or downward merge sequence on the specified transaction. */
template<bool DownWard>
void MergeSequence(TxIdx tx_idx) noexcept
{
auto chunk_rep = m_tx_data[tx_idx].chunk_rep;
while (true) {
auto merged_rep = MergeStep<DownWard>(chunk_rep);
if (merged_rep == TxIdx(-1)) break;
chunk_rep = merged_rep;
}
// Add the chunk to the queue of improvable chunks.
m_suboptimal_chunks.push_back(chunk_rep);
}
/** Split a chunk, and then merge the resulting two chunks to make the graph topological
* again. */
void Improve(DepIdx dep_idx) noexcept
{
auto& dep_data = m_dep_data[dep_idx];
Assume(dep_data.active);
// Deactivate the specified dependency, splitting it into two new chunks: a top containing
// the parent, and a bottom containing the child. The top should have a higher feerate.
Deactivate(dep_idx);
// At this point we have exactly two chunks which may violate topology constraints (the
// parent chunk and child chunk that were produced by deactivating dep_idx). We can fix
// these using just merge sequences, one upwards and one downwards, avoiding the need for a
// full MakeTopological.
// Merge the top chunk with lower-feerate chunks it depends on (which may be the bottom it
// was just split from, or other pre-existing chunks).
MergeSequence<false>(dep_data.parent);
// Merge the bottom chunk with higher-feerate chunks that depend on it.
MergeSequence<true>(dep_data.child);
}
public:
/** Construct a spanning forest for the given DepGraph, with every transaction in its own chunk
* (not topological). */
explicit SpanningForestState(const DepGraph<SetType>& depgraph, uint64_t rng_seed) noexcept : m_rng(rng_seed)
{
m_transaction_idxs = depgraph.Positions();
auto num_transactions = m_transaction_idxs.Count();
m_tx_data.resize(depgraph.PositionRange());
// Reserve the maximum number of (reserved) dependencies the cluster can have, so
// m_dep_data won't need any reallocations during construction. For a cluster with N
// transactions, the worst case consists of two sets of transactions, the parents and the
// children, where each child depends on each parent and nothing else. For even N, both
// sets can be sized N/2, which means N^2/4 dependencies. For odd N, one can be (N + 1)/2
// and the other can be (N - 1)/2, meaning (N^2 - 1)/4 dependencies. Because N^2 is odd in
// this case, N^2/4 (with rounding-down division) is the correct value in both cases.
m_dep_data.reserve((num_transactions * num_transactions) / 4);
for (auto tx : m_transaction_idxs) {
// Fill in transaction data.
auto& tx_data = m_tx_data[tx];
tx_data.chunk_rep = tx;
tx_data.chunk_setinfo.transactions = SetType::Singleton(tx);
tx_data.chunk_setinfo.feerate = depgraph.FeeRate(tx);
// Add its dependencies.
SetType parents = depgraph.GetReducedParents(tx);
for (auto par : parents) {
auto& par_tx_data = m_tx_data[par];
auto dep_idx = m_dep_data.size();
// Construct new dependency.
auto& dep = m_dep_data.emplace_back();
dep.active = false;
dep.parent = par;
dep.child = tx;
// Add it as parent of the child.
tx_data.parents.Set(par);
// Add it as child of the parent.
par_tx_data.child_deps.push_back(dep_idx);
par_tx_data.children.Set(tx);
}
}
}
/** Load an existing linearization. Must be called immediately after constructor. The result is
* topological if the linearization is valid. Otherwise, MakeTopological still needs to be
* called. */
void LoadLinearization(std::span<const DepGraphIndex> old_linearization) noexcept
{
// Add transactions one by one, in order of existing linearization.
for (DepGraphIndex tx : old_linearization) {
auto chunk_rep = m_tx_data[tx].chunk_rep;
// Merge the chunk upwards, as long as merging succeeds.
while (true) {
chunk_rep = MergeStep<false>(chunk_rep);
if (chunk_rep == TxIdx(-1)) break;
}
}
}
/** Make state topological. Can be called after constructing, or after LoadLinearization. */
void MakeTopological() noexcept
{
for (auto tx : m_transaction_idxs) {
auto& tx_data = m_tx_data[tx];
if (tx_data.chunk_rep == tx) {
m_suboptimal_chunks.emplace_back(tx);
// Randomize the initial order of suboptimal chunks in the queue.
TxIdx j = m_rng.randrange<TxIdx>(m_suboptimal_chunks.size());
if (j != m_suboptimal_chunks.size() - 1) {
std::swap(m_suboptimal_chunks.back(), m_suboptimal_chunks[j]);
}
}
}
while (!m_suboptimal_chunks.empty()) {
// Pop an entry from the potentially-suboptimal chunk queue.
TxIdx chunk = m_suboptimal_chunks.front();
m_suboptimal_chunks.pop_front();
auto& chunk_data = m_tx_data[chunk];
// If what was popped is not currently a chunk representative, continue. This may
// happen when it was merged with something else since being added.
if (chunk_data.chunk_rep != chunk) continue;
int flip = m_rng.randbool();
for (int i = 0; i < 2; ++i) {
if (i ^ flip) {
// Attempt to merge the chunk upwards.
auto result_up = MergeStep<false>(chunk);
if (result_up != TxIdx(-1)) {
m_suboptimal_chunks.push_back(result_up);
break;
}
} else {
// Attempt to merge the chunk downwards.
auto result_down = MergeStep<true>(chunk);
if (result_down != TxIdx(-1)) {
m_suboptimal_chunks.push_back(result_down);
break;
}
}
}
}
}
/** Initialize the data structure for optimization. It must be topological already. */
void StartOptimizing() noexcept
{
// Mark chunks suboptimal.
for (auto tx : m_transaction_idxs) {
auto& tx_data = m_tx_data[tx];
if (tx_data.chunk_rep == tx) {
m_suboptimal_chunks.push_back(tx);
// Randomize the initial order of suboptimal chunks in the queue.
TxIdx j = m_rng.randrange<TxIdx>(m_suboptimal_chunks.size());
if (j != m_suboptimal_chunks.size() - 1) {
std::swap(m_suboptimal_chunks.back(), m_suboptimal_chunks[j]);
}
}
}
}
/** Try to improve the forest. Returns false if it is optimal, true otherwise. */
bool OptimizeStep() noexcept
{
while (!m_suboptimal_chunks.empty()) {
// Pop an entry from the potentially-suboptimal chunk queue.
TxIdx chunk = m_suboptimal_chunks.front();
m_suboptimal_chunks.pop_front();
auto& chunk_data = m_tx_data[chunk];
// If what was popped is not currently a chunk representative, continue. This may
// happen when a split chunk merges in Improve() with one or more existing chunks that
// are themselves on the suboptimal queue already.
if (chunk_data.chunk_rep != chunk) continue;
// Remember the best dependency seen so far.
DepIdx candidate_dep = DepIdx(-1);
uint64_t candidate_tiebreak = 0;
// Iterate over all transactions.
for (auto tx : chunk_data.chunk_setinfo.transactions) {
const auto& tx_data = m_tx_data[tx];
// Iterate over all active child dependencies of the transaction.
const auto children = std::span{tx_data.child_deps};
for (DepIdx dep_idx : children) {
const auto& dep_data = m_dep_data[dep_idx];
if (!dep_data.active) continue;
// Skip if this dependency is ineligible (the top chunk that would be created
// does not have higher feerate than the chunk it is currently part of).
auto cmp = FeeRateCompare(dep_data.top_setinfo.feerate, chunk_data.chunk_setinfo.feerate);
if (cmp <= 0) continue;
// Generate a random tiebreak for this dependency, and reject it if its tiebreak
// is worse than the best so far. This means that among all eligible
// dependencies, a uniformly random one will be chosen.
uint64_t tiebreak = m_rng.rand64();
if (tiebreak < candidate_tiebreak) continue;
// Remember this as our (new) candidate dependency.
candidate_dep = dep_idx;
candidate_tiebreak = tiebreak;
}
}
// If a candidate with positive gain was found, deactivate it and then make the state
// topological again with a sequence of merges.
if (candidate_dep != DepIdx(-1)) Improve(candidate_dep);
// Stop processing for now, even if nothing was activated, as the loop above may have
// had a nontrivial cost.
return !m_suboptimal_chunks.empty();
}
// No improvable chunk was found, we are done.
return false;
}
/** Construct a topologically-valid linearization from the current forest state. Must be
* topological. */
std::vector<DepGraphIndex> GetLinearization() noexcept
{
/** The output linearization. */
std::vector<DepGraphIndex> ret;
ret.reserve(m_transaction_idxs.Count());
/** A heap with all chunks (by representative) that can currently be included, sorted by
* chunk feerate and a random tie-breaker. */
std::vector<std::pair<TxIdx, uint64_t>> ready_chunks;
/** Information about chunks:
* - The first value is only used for chunk representatives, and counts the number of
* unmet dependencies this chunk has on other chunks (not including dependencies within
* the chunk itself).
* - The second value is the number of unmet dependencies overall.
*/
std::vector<std::pair<TxIdx, TxIdx>> chunk_deps(m_tx_data.size(), {0, 0});
/** The set of all chunk representatives. */
SetType chunk_reps;
/** A list with all transactions within the current chunk that can be included. */
std::vector<TxIdx> ready_tx;
// Populate chunk_deps[c] with the number of {out-of-chunk dependencies, dependencies} the
// child has.
for (TxIdx chl_idx : m_transaction_idxs) {
const auto& chl_data = m_tx_data[chl_idx];
chunk_deps[chl_idx].second = chl_data.parents.Count();
auto chl_chunk_rep = chl_data.chunk_rep;
chunk_reps.Set(chl_chunk_rep);
for (auto par_idx : chl_data.parents) {
auto par_chunk_rep = m_tx_data[par_idx].chunk_rep;
chunk_deps[chl_chunk_rep].first += (par_chunk_rep != chl_chunk_rep);
}
}
// Construct a heap with all chunks that have no out-of-chunk dependencies.
/** Comparison function for the heap. */
auto chunk_cmp_fn = [&](const std::pair<TxIdx, uint64_t>& a, const std::pair<TxIdx, uint64_t>& b) noexcept {
auto& chunk_a = m_tx_data[a.first];
auto& chunk_b = m_tx_data[b.first];
Assume(chunk_a.chunk_rep == a.first);
Assume(chunk_b.chunk_rep == b.first);
// First sort by chunk feerate.
if (chunk_a.chunk_setinfo.feerate != chunk_b.chunk_setinfo.feerate) {
return chunk_a.chunk_setinfo.feerate < chunk_b.chunk_setinfo.feerate;
}
// Tie-break randomly.
if (a.second != b.second) return a.second < b.second;
// Lastly, tie-break by chunk representative.
return a.first < b.first;
};
for (TxIdx chunk_rep : chunk_reps) {
if (chunk_deps[chunk_rep].first == 0) ready_chunks.emplace_back(chunk_rep, m_rng.rand64());
}
std::make_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
// Pop chunks off the heap, highest-feerate ones first.
while (!ready_chunks.empty()) {
auto [chunk_rep, _rnd] = ready_chunks.front();
std::pop_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
ready_chunks.pop_back();
Assume(m_tx_data[chunk_rep].chunk_rep == chunk_rep);
Assume(chunk_deps[chunk_rep].first == 0);
const auto& chunk_txn = m_tx_data[chunk_rep].chunk_setinfo.transactions;
// Build heap of all includable transactions in chunk.
for (TxIdx tx_idx : chunk_txn) {
if (chunk_deps[tx_idx].second == 0) {
ready_tx.push_back(tx_idx);
}
}
Assume(!ready_tx.empty());
// Pick transactions from the ready queue, append them to linearization, and decrement
// dependency counts.
while (!ready_tx.empty()) {
// Move a random queue element to the back.
auto pos = m_rng.randrange(ready_tx.size());
if (pos != ready_tx.size() - 1) std::swap(ready_tx.back(), ready_tx[pos]);
// Pop from the back.
auto tx_idx = ready_tx.back();
Assume(chunk_txn[tx_idx]);
ready_tx.pop_back();
// Append to linearization.
ret.push_back(tx_idx);
// Decrement dependency counts.
auto& tx_data = m_tx_data[tx_idx];
for (TxIdx chl_idx : tx_data.children) {
auto& chl_data = m_tx_data[chl_idx];
// Decrement tx dependency count.
Assume(chunk_deps[chl_idx].second > 0);
if (--chunk_deps[chl_idx].second == 0 && chunk_txn[chl_idx]) {
// Child tx has no dependencies left, and is in this chunk. Add it to the tx queue.
ready_tx.push_back(chl_idx);
}
// Decrement chunk dependency count if this is out-of-chunk dependency.
if (chl_data.chunk_rep != chunk_rep) {
Assume(chunk_deps[chl_data.chunk_rep].first > 0);
if (--chunk_deps[chl_data.chunk_rep].first == 0) {
// Child chunk has no dependencies left. Add it to the chunk heap.
ready_chunks.emplace_back(chl_data.chunk_rep, m_rng.rand64());
std::push_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
}
}
}
}
}
Assume(ret.size() == m_transaction_idxs.Count());
return ret;
}
/** Get the diagram for the current state, which must be topological. Test-only.
*
* The linearization produced by GetLinearization() is always at least as good (in the
* CompareChunks() sense) as this diagram, but may be better.
*
* After an OptimizeStep(), the diagram will always be at least as good as before. Once
* OptimizeStep() returns false, the diagram will be equivalent to that produced by
* GetLinearization(), and optimal.
*/
std::vector<FeeFrac> GetDiagram() const noexcept
{
std::vector<FeeFrac> ret;
for (auto tx : m_transaction_idxs) {
if (m_tx_data[tx].chunk_rep == tx) {
ret.push_back(m_tx_data[tx].chunk_setinfo.feerate);
}
}
std::sort(ret.begin(), ret.end(), std::greater{});
return ret;
}
/** Determine how much work was performed so far. */
uint64_t GetCost() const noexcept { return m_cost; }
/** Verify internal consistency of the data structure. */
void SanityCheck(const DepGraph<SetType>& depgraph) const
{
//
// Verify dependency parent/child information, and build list of (active) dependencies.
//
std::vector<std::pair<TxIdx, TxIdx>> expected_dependencies;
std::vector<std::tuple<TxIdx, TxIdx, DepIdx>> all_dependencies;
std::vector<std::tuple<TxIdx, TxIdx, DepIdx>> active_dependencies;
for (auto parent_idx : depgraph.Positions()) {
for (auto child_idx : depgraph.GetReducedChildren(parent_idx)) {
expected_dependencies.emplace_back(parent_idx, child_idx);
}
}
for (DepIdx dep_idx = 0; dep_idx < m_dep_data.size(); ++dep_idx) {
const auto& dep_data = m_dep_data[dep_idx];
all_dependencies.emplace_back(dep_data.parent, dep_data.child, dep_idx);
// Also add to active_dependencies if it is active.
if (m_dep_data[dep_idx].active) {
active_dependencies.emplace_back(dep_data.parent, dep_data.child, dep_idx);
}
}
std::sort(expected_dependencies.begin(), expected_dependencies.end());
std::sort(all_dependencies.begin(), all_dependencies.end());
assert(expected_dependencies.size() == all_dependencies.size());
for (size_t i = 0; i < expected_dependencies.size(); ++i) {
assert(expected_dependencies[i] ==
std::make_pair(std::get<0>(all_dependencies[i]),
std::get<1>(all_dependencies[i])));
}
//
// Verify the chunks against the list of active dependencies
//
for (auto tx_idx: depgraph.Positions()) {
// Only process chunks for now.
if (m_tx_data[tx_idx].chunk_rep == tx_idx) {
const auto& chunk_data = m_tx_data[tx_idx];
// Verify that transactions in the chunk point back to it. This guarantees
// that chunks are non-overlapping.
for (auto chunk_tx : chunk_data.chunk_setinfo.transactions) {
assert(m_tx_data[chunk_tx].chunk_rep == tx_idx);
}
// Verify the chunk's transaction set: it must contain the representative, and for
// every active dependency, if it contains the parent or child, it must contain
// both. It must have exactly N-1 active dependencies in it, guaranteeing it is
// acyclic.
SetType expected_chunk = SetType::Singleton(tx_idx);
while (true) {
auto old = expected_chunk;
size_t active_dep_count{0};
for (const auto& [par, chl, _dep] : active_dependencies) {
if (expected_chunk[par] || expected_chunk[chl]) {
expected_chunk.Set(par);
expected_chunk.Set(chl);
++active_dep_count;
}
}
if (old == expected_chunk) {
assert(expected_chunk.Count() == active_dep_count + 1);
break;
}
}
assert(chunk_data.chunk_setinfo.transactions == expected_chunk);
// Verify the chunk's feerate.
assert(chunk_data.chunk_setinfo.feerate ==
depgraph.FeeRate(chunk_data.chunk_setinfo.transactions));
}
}
//
// Verify other transaction data.
//
assert(m_transaction_idxs == depgraph.Positions());
for (auto tx_idx : m_transaction_idxs) {
const auto& tx_data = m_tx_data[tx_idx];
// Verify it has a valid chunk representative, and that chunk includes this
// transaction.
assert(m_tx_data[tx_data.chunk_rep].chunk_rep == tx_data.chunk_rep);
assert(m_tx_data[tx_data.chunk_rep].chunk_setinfo.transactions[tx_idx]);
// Verify parents/children.
assert(tx_data.parents == depgraph.GetReducedParents(tx_idx));
assert(tx_data.children == depgraph.GetReducedChildren(tx_idx));
// Verify list of child dependencies.
std::vector<DepIdx> expected_child_deps;
for (const auto& [par_idx, chl_idx, dep_idx] : all_dependencies) {
if (tx_idx == par_idx) {
assert(tx_data.children[chl_idx]);
expected_child_deps.push_back(dep_idx);
}
}
std::sort(expected_child_deps.begin(), expected_child_deps.end());
auto child_deps_copy = tx_data.child_deps;
std::sort(child_deps_copy.begin(), child_deps_copy.end());
assert(expected_child_deps == child_deps_copy);
}
//
// Verify active dependencies' top_setinfo.
//
for (const auto& [par_idx, chl_idx, dep_idx] : active_dependencies) {
const auto& dep_data = m_dep_data[dep_idx];
// Verify the top_info's transactions: it must contain the parent, and for every
// active dependency, except dep_idx itself, if it contains the parent or child, it
// must contain both.
SetType expected_top = SetType::Singleton(par_idx);
while (true) {
auto old = expected_top;
for (const auto& [par2_idx, chl2_idx, dep2_idx] : active_dependencies) {
if (dep2_idx != dep_idx && (expected_top[par2_idx] || expected_top[chl2_idx])) {
expected_top.Set(par2_idx);
expected_top.Set(chl2_idx);
}
}
if (old == expected_top) break;
}
assert(!expected_top[chl_idx]);
assert(dep_data.top_setinfo.transactions == expected_top);
// Verify the top_info's feerate.
assert(dep_data.top_setinfo.feerate ==
depgraph.FeeRate(dep_data.top_setinfo.transactions));
}
//
// Verify m_suboptimal_chunks.
//
for (size_t i = 0; i < m_suboptimal_chunks.size(); ++i) {
auto tx_idx = m_suboptimal_chunks[i];
assert(m_transaction_idxs[tx_idx]);
}
}
};
/** 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 amount of work 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, or empty.
* @param[in] is_topological (Only relevant if old_linearization is not empty) Whether
* old_linearization is topologically valid.
* @return A tuple 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.
* - How many optimization steps were actually performed.
*/
template<typename SetType>
std::tuple<std::vector<DepGraphIndex>, bool, uint64_t> Linearize(const DepGraph<SetType>& depgraph, uint64_t max_iterations, uint64_t rng_seed, std::span<const DepGraphIndex> old_linearization = {}, bool is_topological = true) noexcept
{
/** Initialize a spanning forest data structure for this cluster. */
SpanningForestState forest(depgraph, rng_seed);
if (!old_linearization.empty()) {
forest.LoadLinearization(old_linearization);
if (!is_topological) forest.MakeTopological();
} else {
forest.MakeTopological();
}
// Make improvement steps to it until we hit the max_iterations limit, or an optimal result
// is found.
bool optimal = false;
if (forest.GetCost() < max_iterations) {
forest.StartOptimizing();
do {
if (!forest.OptimizeStep()) {
optimal = true;
break;
}
} while (forest.GetCost() < max_iterations);
}
return {forest.GetLinearization(), optimal, forest.GetCost()};
}
/** Improve a given linearization.
*
* @param[in] depgraph Dependency graph of the cluster being linearized.
* @param[in,out] linearization On input, an existing linearization for depgraph. On output, a
* potentially better linearization for the same graph.
*
* Postlinearization guarantees:
* - The resulting chunks are connected.
* - If the input has a tree shape (either all transactions have at most one child, or all
* transactions have at most one parent), the result is optimal.
* - Given a linearization L1 and a leaf transaction T in it. Let L2 be L1 with T moved to the end,
* optionally with its fee increased. Let L3 be the postlinearization of L2. L3 will be at least
* as good as L1. This means that replacing transactions with same-size higher-fee transactions
* will not worsen linearizations through a "drop conflicts, append new transactions,
* postlinearize" process.
*/
template<typename SetType>
void PostLinearize(const DepGraph<SetType>& depgraph, std::span<DepGraphIndex> linearization)
{
// This algorithm performs a number of passes (currently 2); the even ones operate from back to
// front, the odd ones from front to back. Each results in an equal-or-better linearization
// than the one started from.
// - One pass in either direction guarantees that the resulting chunks are connected.
// - Each direction corresponds to one shape of tree being linearized optimally (forward passes
// guarantee this for graphs where each transaction has at most one child; backward passes
// guarantee this for graphs where each transaction has at most one parent).
// - Starting with a backward pass guarantees the moved-tree property.
//
// During an odd (forward) pass, the high-level operation is:
// - Start with an empty list of groups L=[].
// - For every transaction i in the old linearization, from front to back:
// - Append a new group C=[i], containing just i, to the back of L.
// - While L has at least one group before C, and the group immediately before C has feerate
// lower than C:
// - If C depends on P:
// - Merge P into C, making C the concatenation of P+C, continuing with the combined C.
// - Otherwise:
// - Swap P with C, continuing with the now-moved C.
// - The output linearization is the concatenation of the groups in L.
//
// During even (backward) passes, i iterates from the back to the front of the existing
// linearization, and new groups are prepended instead of appended to the list L. To enable
// more code reuse, both passes append groups, but during even passes the meanings of
// parent/child, and of high/low feerate are reversed, and the final concatenation is reversed
// on output.
//
// In the implementation below, the groups are represented by singly-linked lists (pointing
// from the back to the front), which are themselves organized in a singly-linked circular
// list (each group pointing to its predecessor, with a special sentinel group at the front
// that points back to the last group).
//
// Information about transaction t is stored in entries[t + 1], while the sentinel is in
// entries[0].
/** Index of the sentinel in the entries array below. */
static constexpr DepGraphIndex SENTINEL{0};
/** Indicator that a group has no previous transaction. */
static constexpr DepGraphIndex NO_PREV_TX{0};
/** Data structure per transaction entry. */
struct TxEntry
{
/** The index of the previous transaction in this group; NO_PREV_TX if this is the first
* entry of a group. */
DepGraphIndex prev_tx;
// The fields below are only used for transactions that are the last one in a group
// (referred to as tail transactions below).
/** Index of the first transaction in this group, possibly itself. */
DepGraphIndex first_tx;
/** Index of the last transaction in the previous group. The first group (the sentinel)
* points back to the last group here, making it a singly-linked circular list. */
DepGraphIndex prev_group;
/** All transactions in the group. Empty for the sentinel. */
SetType group;
/** All dependencies of the group (descendants in even passes; ancestors in odd ones). */
SetType deps;
/** The combined fee/size of transactions in the group. Fee is negated in even passes. */
FeeFrac feerate;
};
// As an example, consider the state corresponding to the linearization [1,0,3,2], with
// groups [1,0,3] and [2], in an odd pass. The linked lists would be:
//
// +-----+
// 0<-P-- | 0 S | ---\ Legend:
// +-----+ |
// ^ | - digit in box: entries index
// /--------------F---------+ G | (note: one more than tx value)
// v \ | | - S: sentinel group
// +-----+ +-----+ +-----+ | (empty feerate)
// 0<-P-- | 2 | <--P-- | 1 | <--P-- | 4 T | | - T: tail transaction, contains
// +-----+ +-----+ +-----+ | fields beyond prev_tv.
// ^ | - P: prev_tx reference
// G G - F: first_tx reference
// | | - G: prev_group reference
// +-----+ |
// 0<-P-- | 3 T | <--/
// +-----+
// ^ |
// \-F-/
//
// During an even pass, the diagram above would correspond to linearization [2,3,0,1], with
// groups [2] and [3,0,1].
std::vector<TxEntry> entries(depgraph.PositionRange() + 1);
// Perform two passes over the linearization.
for (int pass = 0; pass < 2; ++pass) {
int rev = !(pass & 1);
// Construct a sentinel group, identifying the start of the list.
entries[SENTINEL].prev_group = SENTINEL;
Assume(entries[SENTINEL].feerate.IsEmpty());
// Iterate over all elements in the existing linearization.
for (DepGraphIndex i = 0; i < linearization.size(); ++i) {
// Even passes are from back to front; odd passes from front to back.
DepGraphIndex idx = linearization[rev ? linearization.size() - 1 - i : i];
// Construct a new group containing just idx. In even passes, the meaning of
// parent/child and high/low feerate are swapped.
DepGraphIndex cur_group = idx + 1;
entries[cur_group].group = SetType::Singleton(idx);
entries[cur_group].deps = rev ? depgraph.Descendants(idx): depgraph.Ancestors(idx);
entries[cur_group].feerate = depgraph.FeeRate(idx);
if (rev) entries[cur_group].feerate.fee = -entries[cur_group].feerate.fee;
entries[cur_group].prev_tx = NO_PREV_TX; // No previous transaction in group.
entries[cur_group].first_tx = cur_group; // Transaction itself is first of group.
// Insert the new group at the back of the groups linked list.
entries[cur_group].prev_group = entries[SENTINEL].prev_group;
entries[SENTINEL].prev_group = cur_group;
// Start merge/swap cycle.
DepGraphIndex next_group = SENTINEL; // We inserted at the end, so next group is sentinel.
DepGraphIndex prev_group = entries[cur_group].prev_group;
// Continue as long as the current group has higher feerate than the previous one.
while (entries[cur_group].feerate >> entries[prev_group].feerate) {
// prev_group/cur_group/next_group refer to (the last transactions of) 3
// consecutive entries in groups list.
Assume(cur_group == entries[next_group].prev_group);
Assume(prev_group == entries[cur_group].prev_group);
// The sentinel has empty feerate, which is neither higher or lower than other
// feerates. Thus, the while loop we are in here guarantees that cur_group and
// prev_group are not the sentinel.
Assume(cur_group != SENTINEL);
Assume(prev_group != SENTINEL);
if (entries[cur_group].deps.Overlaps(entries[prev_group].group)) {
// There is a dependency between cur_group and prev_group; merge prev_group
// into cur_group. The group/deps/feerate fields of prev_group remain unchanged
// but become unused.
entries[cur_group].group |= entries[prev_group].group;
entries[cur_group].deps |= entries[prev_group].deps;
entries[cur_group].feerate += entries[prev_group].feerate;
// Make the first of the current group point to the tail of the previous group.
entries[entries[cur_group].first_tx].prev_tx = prev_group;
// The first of the previous group becomes the first of the newly-merged group.
entries[cur_group].first_tx = entries[prev_group].first_tx;
// The previous group becomes whatever group was before the former one.
prev_group = entries[prev_group].prev_group;
entries[cur_group].prev_group = prev_group;
} else {
// There is no dependency between cur_group and prev_group; swap them.
DepGraphIndex preprev_group = entries[prev_group].prev_group;
// If PP, P, C, N were the old preprev, prev, cur, next groups, then the new
// layout becomes [PP, C, P, N]. Update prev_groups to reflect that order.
entries[next_group].prev_group = prev_group;
entries[prev_group].prev_group = cur_group;
entries[cur_group].prev_group = preprev_group;
// The current group remains the same, but the groups before/after it have
// changed.
next_group = prev_group;
prev_group = preprev_group;
}
}
}
// Convert the entries back to linearization (overwriting the existing one).
DepGraphIndex cur_group = entries[0].prev_group;
DepGraphIndex done = 0;
while (cur_group != SENTINEL) {
DepGraphIndex cur_tx = cur_group;
// Traverse the transactions of cur_group (from back to front), and write them in the
// same order during odd passes, and reversed (front to back) in even passes.
if (rev) {
do {
*(linearization.begin() + (done++)) = cur_tx - 1;
cur_tx = entries[cur_tx].prev_tx;
} while (cur_tx != NO_PREV_TX);
} else {
do {
*(linearization.end() - (++done)) = cur_tx - 1;
cur_tx = entries[cur_tx].prev_tx;
} while (cur_tx != NO_PREV_TX);
}
cur_group = entries[cur_group].prev_group;
}
Assume(done == linearization.size());
}
}
} // namespace cluster_linearize
#endif // BITCOIN_CLUSTER_LINEARIZE_H
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