/ src / cluster_linearize.h
cluster_linearize.h
   1  // Copyright (c) The Bitcoin Core developers
   2  // Distributed under the MIT software license, see the accompanying
   3  // file COPYING or http://www.opensource.org/licenses/mit-license.php.
   4  
   5  #ifndef BITCOIN_CLUSTER_LINEARIZE_H
   6  #define BITCOIN_CLUSTER_LINEARIZE_H
   7  
   8  #include <algorithm>
   9  #include <cstdint>
  10  #include <numeric>
  11  #include <optional>
  12  #include <utility>
  13  #include <vector>
  14  
  15  #include <attributes.h>
  16  #include <memusage.h>
  17  #include <random.h>
  18  #include <span.h>
  19  #include <util/feefrac.h>
  20  #include <util/vecdeque.h>
  21  
  22  namespace cluster_linearize {
  23  
  24  /** Data type to represent transaction indices in DepGraphs and the clusters they represent. */
  25  using DepGraphIndex = uint32_t;
  26  
  27  /** Data structure that holds a transaction graph's preprocessed data (fee, size, ancestors,
  28   *  descendants). */
  29  template<typename SetType>
  30  class DepGraph
  31  {
  32      /** Information about a single transaction. */
  33      struct Entry
  34      {
  35          /** Fee and size of transaction itself. */
  36          FeeFrac feerate;
  37          /** All ancestors of the transaction (including itself). */
  38          SetType ancestors;
  39          /** All descendants of the transaction (including itself). */
  40          SetType descendants;
  41  
  42          /** Equality operator (primarily for testing purposes). */
  43          friend bool operator==(const Entry&, const Entry&) noexcept = default;
  44  
  45          /** Construct an empty entry. */
  46          Entry() noexcept = default;
  47          /** Construct an entry with a given feerate, ancestor set, descendant set. */
  48          Entry(const FeeFrac& f, const SetType& a, const SetType& d) noexcept : feerate(f), ancestors(a), descendants(d) {}
  49      };
  50  
  51      /** Data for each transaction. */
  52      std::vector<Entry> entries;
  53  
  54      /** Which positions are used. */
  55      SetType m_used;
  56  
  57  public:
  58      /** Equality operator (primarily for testing purposes). */
  59      friend bool operator==(const DepGraph& a, const DepGraph& b) noexcept
  60      {
  61          if (a.m_used != b.m_used) return false;
  62          // Only compare the used positions within the entries vector.
  63          for (auto idx : a.m_used) {
  64              if (a.entries[idx] != b.entries[idx]) return false;
  65          }
  66          return true;
  67      }
  68  
  69      // Default constructors.
  70      DepGraph() noexcept = default;
  71      DepGraph(const DepGraph&) noexcept = default;
  72      DepGraph(DepGraph&&) noexcept = default;
  73      DepGraph& operator=(const DepGraph&) noexcept = default;
  74      DepGraph& operator=(DepGraph&&) noexcept = default;
  75  
  76      /** Construct a DepGraph object given another DepGraph and a mapping from old to new.
  77       *
  78       * @param depgraph   The original DepGraph that is being remapped.
  79       *
  80       * @param mapping    A span such that mapping[i] gives the position in the new DepGraph
  81       *                   for position i in the old depgraph. Its size must be equal to
  82       *                   depgraph.PositionRange(). The value of mapping[i] is ignored if
  83       *                   position i is a hole in depgraph (i.e., if !depgraph.Positions()[i]).
  84       *
  85       * @param pos_range  The PositionRange() for the new DepGraph. It must equal the largest
  86       *                   value in mapping for any used position in depgraph plus 1, or 0 if
  87       *                   depgraph.TxCount() == 0.
  88       *
  89       * Complexity: O(N^2) where N=depgraph.TxCount().
  90       */
  91      DepGraph(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> mapping, DepGraphIndex pos_range) noexcept : entries(pos_range)
  92      {
  93          Assume(mapping.size() == depgraph.PositionRange());
  94          Assume((pos_range == 0) == (depgraph.TxCount() == 0));
  95          for (DepGraphIndex i : depgraph.Positions()) {
  96              auto new_idx = mapping[i];
  97              Assume(new_idx < pos_range);
  98              // Add transaction.
  99              entries[new_idx].ancestors = SetType::Singleton(new_idx);
 100              entries[new_idx].descendants = SetType::Singleton(new_idx);
 101              m_used.Set(new_idx);
 102              // Fill in fee and size.
 103              entries[new_idx].feerate = depgraph.entries[i].feerate;
 104          }
 105          for (DepGraphIndex i : depgraph.Positions()) {
 106              // Fill in dependencies by mapping direct parents.
 107              SetType parents;
 108              for (auto j : depgraph.GetReducedParents(i)) parents.Set(mapping[j]);
 109              AddDependencies(parents, mapping[i]);
 110          }
 111          // Verify that the provided pos_range was correct (no unused positions at the end).
 112          Assume(m_used.None() ? (pos_range == 0) : (pos_range == m_used.Last() + 1));
 113      }
 114  
 115      /** Get the set of transactions positions in use. Complexity: O(1). */
 116      const SetType& Positions() const noexcept { return m_used; }
 117      /** Get the range of positions in this DepGraph. All entries in Positions() are in [0, PositionRange() - 1]. */
 118      DepGraphIndex PositionRange() const noexcept { return entries.size(); }
 119      /** Get the number of transactions in the graph. Complexity: O(1). */
 120      auto TxCount() const noexcept { return m_used.Count(); }
 121      /** Get the feerate of a given transaction i. Complexity: O(1). */
 122      const FeeFrac& FeeRate(DepGraphIndex i) const noexcept { return entries[i].feerate; }
 123      /** Get the mutable feerate of a given transaction i. Complexity: O(1). */
 124      FeeFrac& FeeRate(DepGraphIndex i) noexcept { return entries[i].feerate; }
 125      /** Get the ancestors of a given transaction i. Complexity: O(1). */
 126      const SetType& Ancestors(DepGraphIndex i) const noexcept { return entries[i].ancestors; }
 127      /** Get the descendants of a given transaction i. Complexity: O(1). */
 128      const SetType& Descendants(DepGraphIndex i) const noexcept { return entries[i].descendants; }
 129  
 130      /** Add a new unconnected transaction to this transaction graph (in the first available
 131       *  position), and return its DepGraphIndex.
 132       *
 133       * Complexity: O(1) (amortized, due to resizing of backing vector).
 134       */
 135      DepGraphIndex AddTransaction(const FeeFrac& feefrac) noexcept
 136      {
 137          static constexpr auto ALL_POSITIONS = SetType::Fill(SetType::Size());
 138          auto available = ALL_POSITIONS - m_used;
 139          Assume(available.Any());
 140          DepGraphIndex new_idx = available.First();
 141          if (new_idx == entries.size()) {
 142              entries.emplace_back(feefrac, SetType::Singleton(new_idx), SetType::Singleton(new_idx));
 143          } else {
 144              entries[new_idx] = Entry(feefrac, SetType::Singleton(new_idx), SetType::Singleton(new_idx));
 145          }
 146          m_used.Set(new_idx);
 147          return new_idx;
 148      }
 149  
 150      /** Remove the specified positions from this DepGraph.
 151       *
 152       * The specified positions will no longer be part of Positions(), and dependencies with them are
 153       * removed. Note that due to DepGraph only tracking ancestors/descendants (and not direct
 154       * dependencies), if a parent is removed while a grandparent remains, the grandparent will
 155       * remain an ancestor.
 156       *
 157       * Complexity: O(N) where N=TxCount().
 158       */
 159      void RemoveTransactions(const SetType& del) noexcept
 160      {
 161          m_used -= del;
 162          // Remove now-unused trailing entries.
 163          while (!entries.empty() && !m_used[entries.size() - 1]) {
 164              entries.pop_back();
 165          }
 166          // Remove the deleted transactions from ancestors/descendants of other transactions. Note
 167          // that the deleted positions will retain old feerate and dependency information. This does
 168          // not matter as they will be overwritten by AddTransaction if they get used again.
 169          for (auto& entry : entries) {
 170              entry.ancestors &= m_used;
 171              entry.descendants &= m_used;
 172          }
 173      }
 174  
 175      /** Modify this transaction graph, adding multiple parents to a specified child.
 176       *
 177       * Complexity: O(N) where N=TxCount().
 178       */
 179      void AddDependencies(const SetType& parents, DepGraphIndex child) noexcept
 180      {
 181          Assume(m_used[child]);
 182          Assume(parents.IsSubsetOf(m_used));
 183          // Compute the ancestors of parents that are not already ancestors of child.
 184          SetType par_anc;
 185          for (auto par : parents - Ancestors(child)) {
 186              par_anc |= Ancestors(par);
 187          }
 188          par_anc -= Ancestors(child);
 189          // Bail out if there are no such ancestors.
 190          if (par_anc.None()) return;
 191          // To each such ancestor, add as descendants the descendants of the child.
 192          const auto& chl_des = entries[child].descendants;
 193          for (auto anc_of_par : par_anc) {
 194              entries[anc_of_par].descendants |= chl_des;
 195          }
 196          // To each descendant of the child, add those ancestors.
 197          for (auto dec_of_chl : Descendants(child)) {
 198              entries[dec_of_chl].ancestors |= par_anc;
 199          }
 200      }
 201  
 202      /** Compute the (reduced) set of parents of node i in this graph.
 203       *
 204       * This returns the minimal subset of the parents of i whose ancestors together equal all of
 205       * i's ancestors (unless i is part of a cycle of dependencies). Note that DepGraph does not
 206       * store the set of parents; this information is inferred from the ancestor sets.
 207       *
 208       * Complexity: O(N) where N=Ancestors(i).Count() (which is bounded by TxCount()).
 209       */
 210      SetType GetReducedParents(DepGraphIndex i) const noexcept
 211      {
 212          SetType parents = Ancestors(i);
 213          parents.Reset(i);
 214          for (auto parent : parents) {
 215              if (parents[parent]) {
 216                  parents -= Ancestors(parent);
 217                  parents.Set(parent);
 218              }
 219          }
 220          return parents;
 221      }
 222  
 223      /** Compute the (reduced) set of children of node i in this graph.
 224       *
 225       * This returns the minimal subset of the children of i whose descendants together equal all of
 226       * i's descendants (unless i is part of a cycle of dependencies). Note that DepGraph does not
 227       * store the set of children; this information is inferred from the descendant sets.
 228       *
 229       * Complexity: O(N) where N=Descendants(i).Count() (which is bounded by TxCount()).
 230       */
 231      SetType GetReducedChildren(DepGraphIndex i) const noexcept
 232      {
 233          SetType children = Descendants(i);
 234          children.Reset(i);
 235          for (auto child : children) {
 236              if (children[child]) {
 237                  children -= Descendants(child);
 238                  children.Set(child);
 239              }
 240          }
 241          return children;
 242      }
 243  
 244      /** Compute the aggregate feerate of a set of nodes in this graph.
 245       *
 246       * Complexity: O(N) where N=elems.Count().
 247       **/
 248      FeeFrac FeeRate(const SetType& elems) const noexcept
 249      {
 250          FeeFrac ret;
 251          for (auto pos : elems) ret += entries[pos].feerate;
 252          return ret;
 253      }
 254  
 255      /** Get the connected component within the subset "todo" that contains tx (which must be in
 256       *  todo).
 257       *
 258       * Two transactions are considered connected if they are both in `todo`, and one is an ancestor
 259       * of the other in the entire graph (so not just within `todo`), or transitively there is a
 260       * path of transactions connecting them. This does mean that if `todo` contains a transaction
 261       * and a grandparent, but misses the parent, they will still be part of the same component.
 262       *
 263       * Complexity: O(ret.Count()).
 264       */
 265      SetType GetConnectedComponent(const SetType& todo, DepGraphIndex tx) const noexcept
 266      {
 267          Assume(todo[tx]);
 268          Assume(todo.IsSubsetOf(m_used));
 269          auto to_add = SetType::Singleton(tx);
 270          SetType ret;
 271          do {
 272              SetType old = ret;
 273              for (auto add : to_add) {
 274                  ret |= Descendants(add);
 275                  ret |= Ancestors(add);
 276              }
 277              ret &= todo;
 278              to_add = ret - old;
 279          } while (to_add.Any());
 280          return ret;
 281      }
 282  
 283      /** Find some connected component within the subset "todo" of this graph.
 284       *
 285       * Specifically, this finds the connected component which contains the first transaction of
 286       * todo (if any).
 287       *
 288       * Complexity: O(ret.Count()).
 289       */
 290      SetType FindConnectedComponent(const SetType& todo) const noexcept
 291      {
 292          if (todo.None()) return todo;
 293          return GetConnectedComponent(todo, todo.First());
 294      }
 295  
 296      /** Determine if a subset is connected.
 297       *
 298       * Complexity: O(subset.Count()).
 299       */
 300      bool IsConnected(const SetType& subset) const noexcept
 301      {
 302          return FindConnectedComponent(subset) == subset;
 303      }
 304  
 305      /** Determine if this entire graph is connected.
 306       *
 307       * Complexity: O(TxCount()).
 308       */
 309      bool IsConnected() const noexcept { return IsConnected(m_used); }
 310  
 311      /** Append the entries of select to list in a topologically valid order.
 312       *
 313       * Complexity: O(select.Count() * log(select.Count())).
 314       */
 315      void AppendTopo(std::vector<DepGraphIndex>& list, const SetType& select) const noexcept
 316      {
 317          DepGraphIndex old_len = list.size();
 318          for (auto i : select) list.push_back(i);
 319          std::sort(list.begin() + old_len, list.end(), [&](DepGraphIndex a, DepGraphIndex b) noexcept {
 320              const auto a_anc_count = entries[a].ancestors.Count();
 321              const auto b_anc_count = entries[b].ancestors.Count();
 322              if (a_anc_count != b_anc_count) return a_anc_count < b_anc_count;
 323              return a < b;
 324          });
 325      }
 326  
 327      /** Check if this graph is acyclic. */
 328      bool IsAcyclic() const noexcept
 329      {
 330          for (auto i : Positions()) {
 331              if ((Ancestors(i) & Descendants(i)) != SetType::Singleton(i)) {
 332                  return false;
 333              }
 334          }
 335          return true;
 336      }
 337  
 338      unsigned CountDependencies() const noexcept
 339      {
 340          unsigned ret = 0;
 341          for (auto i : Positions()) {
 342              ret += GetReducedParents(i).Count();
 343          }
 344          return ret;
 345      }
 346  
 347      /** Reduce memory usage if possible. No observable effect. */
 348      void Compact() noexcept
 349      {
 350          entries.shrink_to_fit();
 351      }
 352  
 353      size_t DynamicMemoryUsage() const noexcept
 354      {
 355          return memusage::DynamicUsage(entries);
 356      }
 357  };
 358  
 359  /** A set of transactions together with their aggregate feerate. */
 360  template<typename SetType>
 361  struct SetInfo
 362  {
 363      /** The transactions in the set. */
 364      SetType transactions;
 365      /** Their combined fee and size. */
 366      FeeFrac feerate;
 367  
 368      /** Construct a SetInfo for the empty set. */
 369      SetInfo() noexcept = default;
 370  
 371      /** Construct a SetInfo for a specified set and feerate. */
 372      SetInfo(const SetType& txn, const FeeFrac& fr) noexcept : transactions(txn), feerate(fr) {}
 373  
 374      /** Construct a SetInfo for a given transaction in a depgraph. */
 375      explicit SetInfo(const DepGraph<SetType>& depgraph, DepGraphIndex pos) noexcept :
 376          transactions(SetType::Singleton(pos)), feerate(depgraph.FeeRate(pos)) {}
 377  
 378      /** Construct a SetInfo for a set of transactions in a depgraph. */
 379      explicit SetInfo(const DepGraph<SetType>& depgraph, const SetType& txn) noexcept :
 380          transactions(txn), feerate(depgraph.FeeRate(txn)) {}
 381  
 382      /** Add a transaction to this SetInfo (which must not yet be in it). */
 383      void Set(const DepGraph<SetType>& depgraph, DepGraphIndex pos) noexcept
 384      {
 385          Assume(!transactions[pos]);
 386          transactions.Set(pos);
 387          feerate += depgraph.FeeRate(pos);
 388      }
 389  
 390      /** Add the transactions of other to this SetInfo (no overlap allowed). */
 391      SetInfo& operator|=(const SetInfo& other) noexcept
 392      {
 393          Assume(!transactions.Overlaps(other.transactions));
 394          transactions |= other.transactions;
 395          feerate += other.feerate;
 396          return *this;
 397      }
 398  
 399      /** Remove the transactions of other from this SetInfo (which must be a subset). */
 400      SetInfo& operator-=(const SetInfo& other) noexcept
 401      {
 402          Assume(other.transactions.IsSubsetOf(transactions));
 403          transactions -= other.transactions;
 404          feerate -= other.feerate;
 405          return *this;
 406      }
 407  
 408      /** Compute the difference between this and other SetInfo (which must be a subset). */
 409      SetInfo operator-(const SetInfo& other) const noexcept
 410      {
 411          Assume(other.transactions.IsSubsetOf(transactions));
 412          return {transactions - other.transactions, feerate - other.feerate};
 413      }
 414  
 415      /** Swap two SetInfo objects. */
 416      friend void swap(SetInfo& a, SetInfo& b) noexcept
 417      {
 418          swap(a.transactions, b.transactions);
 419          swap(a.feerate, b.feerate);
 420      }
 421  
 422      /** Permit equality testing. */
 423      friend bool operator==(const SetInfo&, const SetInfo&) noexcept = default;
 424  };
 425  
 426  /** Compute the chunks of linearization as SetInfos. */
 427  template<typename SetType>
 428  std::vector<SetInfo<SetType>> ChunkLinearizationInfo(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> linearization) noexcept
 429  {
 430      std::vector<SetInfo<SetType>> ret;
 431      for (DepGraphIndex i : linearization) {
 432          /** The new chunk to be added, initially a singleton. */
 433          SetInfo<SetType> new_chunk(depgraph, i);
 434          // As long as the new chunk has a higher feerate than the last chunk so far, absorb it.
 435          while (!ret.empty() && new_chunk.feerate >> ret.back().feerate) {
 436              new_chunk |= ret.back();
 437              ret.pop_back();
 438          }
 439          // Actually move that new chunk into the chunking.
 440          ret.emplace_back(std::move(new_chunk));
 441      }
 442      return ret;
 443  }
 444  
 445  /** Compute the feerates of the chunks of linearization. Identical to ChunkLinearizationInfo, but
 446   *  only returns the chunk feerates, not the corresponding transaction sets. */
 447  template<typename SetType>
 448  std::vector<FeeFrac> ChunkLinearization(const DepGraph<SetType>& depgraph, std::span<const DepGraphIndex> linearization) noexcept
 449  {
 450      std::vector<FeeFrac> ret;
 451      for (DepGraphIndex i : linearization) {
 452          /** The new chunk to be added, initially a singleton. */
 453          auto new_chunk = depgraph.FeeRate(i);
 454          // As long as the new chunk has a higher feerate than the last chunk so far, absorb it.
 455          while (!ret.empty() && new_chunk >> ret.back()) {
 456              new_chunk += ret.back();
 457              ret.pop_back();
 458          }
 459          // Actually move that new chunk into the chunking.
 460          ret.push_back(std::move(new_chunk));
 461      }
 462      return ret;
 463  }
 464  
 465  /** Concept for function objects that return std::strong_ordering when invoked with two Args. */
 466  template<typename F, typename Arg>
 467  concept StrongComparator =
 468      std::regular_invocable<F, Arg, Arg> &&
 469      std::is_same_v<std::invoke_result_t<F, Arg, Arg>, std::strong_ordering>;
 470  
 471  /** Simple default transaction ordering function for SpanningForestState::GetLinearization() and
 472   *  Linearize(), which just sorts by DepGraphIndex. */
 473  using IndexTxOrder = std::compare_three_way;
 474  
 475  /** A default cost model for SFL for SetType=BitSet<64>, based on benchmarks.
 476   *
 477   * The numbers here were obtained in February 2026 by:
 478   * - For a variety of machines:
 479   *   - Running a fixed collection of ~385000 clusters found through random generation and fuzzing,
 480   *     optimizing for difficulty of linearization.
 481   *     - Linearize each ~3000 times, with different random seeds. Sometimes without input
 482   *       linearization, sometimes with a bad one.
 483   *       - Gather cycle counts for each of the operations included in this cost model,
 484   *         broken down by their parameters.
 485   *   - Correct the data by subtracting the runtime of obtaining the cycle count.
 486   *   - Drop the 5% top and bottom samples from each cycle count dataset, and compute the average
 487   *     of the remaining samples.
 488   *   - For each operation, fit a least-squares linear function approximation through the samples.
 489   * - Rescale all machine expressions to make their total time match, as we only care about
 490   *   relative cost of each operation.
 491   * - Take the per-operation average of operation expressions across all machines, to construct
 492   *   expressions for an average machine.
 493   * - Approximate the result with integer coefficients. Each cost unit corresponds to somewhere
 494   *   between 0.5 ns and 2.5 ns, depending on the hardware.
 495   */
 496  class SFLDefaultCostModel
 497  {
 498      uint64_t m_cost{0};
 499  
 500  public:
 501      inline void InitializeBegin() noexcept {}
 502      inline void InitializeEnd(int num_txns, int num_deps) noexcept
 503      {
 504           // Cost of initialization.
 505           m_cost += 39 * num_txns;
 506           // Cost of producing linearization at the end.
 507           m_cost += 48 * num_txns + 4 * num_deps;
 508      }
 509      inline void GetLinearizationBegin() noexcept {}
 510      inline void GetLinearizationEnd(int num_txns, int num_deps) noexcept
 511      {
 512          // Note that we account for the cost of the final linearization at the beginning (see
 513          // InitializeEnd), because the cost budget decision needs to be made before calling
 514          // GetLinearization.
 515          // This function exists here to allow overriding it easily for benchmark purposes.
 516      }
 517      inline void MakeTopologicalBegin() noexcept {}
 518      inline void MakeTopologicalEnd(int num_chunks, int num_steps) noexcept
 519      {
 520          m_cost += 20 * num_chunks + 28 * num_steps;
 521      }
 522      inline void StartOptimizingBegin() noexcept {}
 523      inline void StartOptimizingEnd(int num_chunks) noexcept { m_cost += 13 * num_chunks; }
 524      inline void ActivateBegin() noexcept {}
 525      inline void ActivateEnd(int num_deps) noexcept { m_cost += 10 * num_deps + 1; }
 526      inline void DeactivateBegin() noexcept {}
 527      inline void DeactivateEnd(int num_deps) noexcept { m_cost += 11 * num_deps + 8; }
 528      inline void MergeChunksBegin() noexcept {}
 529      inline void MergeChunksMid(int num_txns) noexcept { m_cost += 2 * num_txns; }
 530      inline void MergeChunksEnd(int num_steps) noexcept { m_cost += 3 * num_steps + 5; }
 531      inline void PickMergeCandidateBegin() noexcept {}
 532      inline void PickMergeCandidateEnd(int num_steps) noexcept { m_cost += 8 * num_steps; }
 533      inline void PickChunkToOptimizeBegin() noexcept {}
 534      inline void PickChunkToOptimizeEnd(int num_steps) noexcept { m_cost += num_steps + 4; }
 535      inline void PickDependencyToSplitBegin() noexcept {}
 536      inline void PickDependencyToSplitEnd(int num_txns) noexcept { m_cost += 8 * num_txns + 9; }
 537      inline void StartMinimizingBegin() noexcept {}
 538      inline void StartMinimizingEnd(int num_chunks) noexcept { m_cost += 18 * num_chunks; }
 539      inline void MinimizeStepBegin() noexcept {}
 540      inline void MinimizeStepMid(int num_txns) noexcept { m_cost += 11 * num_txns + 11; }
 541      inline void MinimizeStepEnd(bool split) noexcept { m_cost += 17 * split + 7; }
 542  
 543      inline uint64_t GetCost() const noexcept { return m_cost; }
 544  };
 545  
 546  /** Class to represent the internal state of the spanning-forest linearization (SFL) algorithm.
 547   *
 548   * At all times, each dependency is marked as either "active" or "inactive". The subset of active
 549   * dependencies is the state of the SFL algorithm. The implementation maintains several other
 550   * values to speed up operations, but everything is ultimately a function of what that subset of
 551   * active dependencies is.
 552   *
 553   * Given such a subset, define a chunk as the set of transactions that are connected through active
 554   * dependencies (ignoring their parent/child direction). Thus, every state implies a particular
 555   * partitioning of the graph into chunks (including potential singletons). In the extreme, each
 556   * transaction may be in its own chunk, or in the other extreme all transactions may form a single
 557   * chunk. A chunk's feerate is its total fee divided by its total size.
 558   *
 559   * The algorithm consists of switching dependencies between active and inactive. The final
 560   * linearization that is produced at the end consists of these chunks, sorted from high to low
 561   * feerate, each individually sorted in an arbitrary but topological (= no child before parent)
 562   * way.
 563   *
 564   * We define four quality properties the state can have:
 565   *
 566   * - acyclic: The state is acyclic whenever no cycle of active dependencies exists within the
 567   *            graph, ignoring the parent/child direction. This is equivalent to saying that within
 568   *            each chunk the set of active dependencies form a tree, and thus the overall set of
 569   *            active dependencies in the graph form a spanning forest, giving the algorithm its
 570   *            name. Being acyclic is also equivalent to every chunk of N transactions having
 571   *            exactly N-1 active dependencies.
 572   *
 573   *            For example in a diamond graph, D->{B,C}->A, the 4 dependencies cannot be
 574   *            simultaneously active. If at least one is inactive, the state is acyclic.
 575   *
 576   *            The algorithm maintains an acyclic state at *all* times as an invariant. This implies
 577   *            that activating a dependency always corresponds to merging two chunks, and that
 578   *            deactivating one always corresponds to splitting two chunks.
 579   *
 580   * - topological: We say the state is topological whenever it is acyclic and no inactive dependency
 581   *                exists between two distinct chunks such that the child chunk has higher or equal
 582   *                feerate than the parent chunk.
 583   *
 584   *                The relevance is that whenever the state is topological, the produced output
 585   *                linearization will be topological too (i.e., not have children before parents).
 586   *                Note that the "or equal" part of the definition matters: if not, one can end up
 587   *                in a situation with mutually-dependent equal-feerate chunks that cannot be
 588   *                linearized. For example C->{A,B} and D->{A,B}, with C->A and D->B active. The AC
 589   *                chunk depends on DB through C->B, and the BD chunk depends on AC through D->A.
 590   *                Merging them into a single ABCD chunk fixes this.
 591   *
 592   *                The algorithm attempts to keep the state topological as much as possible, so it
 593   *                can be interrupted to produce an output whenever, but will sometimes need to
 594   *                temporarily deviate from it when improving the state.
 595   *
 596   * - optimal: For every active dependency, define its top and bottom set as the set of transactions
 597   *            in the chunks that would result if the dependency were deactivated; the top being the
 598   *            one with the dependency's parent, and the bottom being the one with the child. Note
 599   *            that due to acyclicity, every deactivation splits a chunk exactly in two.
 600   *
 601   *            We say the state is optimal whenever it is topological and it has no active
 602   *            dependency whose top feerate is strictly higher than its bottom feerate. The
 603   *            relevance is that it can be proven that whenever the state is optimal, the produced
 604   *            linearization will also be optimal (in the convexified feerate diagram sense). It can
 605   *            also be proven that for every graph at least one optimal state exists.
 606   *
 607   *            Note that it is possible for the SFL state to not be optimal, but the produced
 608   *            linearization to still be optimal. This happens when the chunks of a state are
 609   *            identical to those of an optimal state, but the exact set of active dependencies
 610   *            within a chunk differ in such a way that the state optimality condition is not
 611   *            satisfied. Thus, the state being optimal is more a "the eventual output is *known*
 612   *            to be optimal".
 613   *
 614   * - minimal: We say the state is minimal when it is:
 615   *            - acyclic
 616   *            - topological, except that inactive dependencies between equal-feerate chunks are
 617   *              allowed as long as they do not form a loop.
 618   *            - like optimal, no active dependencies whose top feerate is strictly higher than
 619   *              the bottom feerate are allowed.
 620   *            - no chunk contains a proper non-empty subset which includes all its own in-chunk
 621   *              dependencies of the same feerate as the chunk itself.
 622   *
 623   *            A minimal state effectively corresponds to an optimal state, where every chunk has
 624   *            been split into its minimal equal-feerate components.
 625   *
 626   *            The algorithm terminates whenever a minimal state is reached.
 627   *
 628   *
 629   * This leads to the following high-level algorithm:
 630   * - Start with all dependencies inactive, and thus all transactions in their own chunk. This is
 631   *   definitely acyclic.
 632   * - Activate dependencies (merging chunks) until the state is topological.
 633   * - Loop until optimal (no dependencies with higher-feerate top than bottom), or time runs out:
 634   *   - Deactivate a violating dependency, potentially making the state non-topological.
 635   *   - Activate other dependencies to make the state topological again.
 636   * - If there is time left and the state is optimal:
 637   *   - Attempt to split chunks into equal-feerate parts without mutual dependencies between them.
 638   *     When this succeeds, recurse into them.
 639   *   - If no such chunks can be found, the state is minimal.
 640   * - Output the chunks from high to low feerate, each internally sorted topologically.
 641   *
 642   * When merging, we always either:
 643   * - Merge upwards: merge a chunk with the lowest-feerate other chunk it depends on, among those
 644   *                  with lower or equal feerate than itself.
 645   * - Merge downwards: merge a chunk with the highest-feerate other chunk that depends on it, among
 646   *                    those with higher or equal feerate than itself.
 647   *
 648   * Using these strategies in the improvement loop above guarantees that the output linearization
 649   * after a deactivate + merge step is never worse or incomparable (in the convexified feerate
 650   * diagram sense) than the output linearization that would be produced before the step. With that,
 651   * we can refine the high-level algorithm to:
 652   * - Start with all dependencies inactive.
 653   * - Perform merges as described until none are possible anymore, making the state topological.
 654   * - Loop until optimal or time runs out:
 655   *   - Pick a dependency D to deactivate among those with higher feerate top than bottom.
 656   *   - Deactivate D, causing the chunk it is in to split into top T and bottom B.
 657   *   - Do an upwards merge of T, if possible. If so, repeat the same with the merged result.
 658   *   - Do a downwards merge of B, if possible. If so, repeat the same with the merged result.
 659   * - Split chunks further to obtain a minimal state, see below.
 660   * - Output the chunks from high to low feerate, each internally sorted topologically.
 661   *
 662   * Instead of performing merges arbitrarily to make the initial state topological, it is possible
 663   * to do so guided by an existing linearization. This has the advantage that the state's would-be
 664   * output linearization is immediately as good as the existing linearization it was based on:
 665   * - Start with all dependencies inactive.
 666   * - For each transaction t in the existing linearization:
 667   *   - Find the chunk C that transaction is in (which will be singleton).
 668   *   - Do an upwards merge of C, if possible. If so, repeat the same with the merged result.
 669   * No downwards merges are needed in this case.
 670   *
 671   * After reaching an optimal state, it can be transformed into a minimal state by attempting to
 672   * split chunks further into equal-feerate parts. To do so, pick a specific transaction in each
 673   * chunk (the pivot), and rerun the above split-then-merge procedure again:
 674   * - first, while pretending the pivot transaction has an infinitesimally higher (or lower) fee
 675   *   than it really has. If a split exists with the pivot in the top part (or bottom part), this
 676   *   will find it.
 677   * - if that fails to split, repeat while pretending the pivot transaction has an infinitesimally
 678   *   lower (or higher) fee. If a split exists with the pivot in the bottom part (or top part), this
 679   *   will find it.
 680   * - if either succeeds, repeat the procedure for the newly found chunks to split them further.
 681   *   If not, the chunk is already minimal.
 682   * If the chunk can be split into equal-feerate parts, then the pivot must exist in either the top
 683   * or bottom part of that potential split. By trying both with the same pivot, if a split exists,
 684   * it will be found.
 685   *
 686   * What remains to be specified are a number of heuristics:
 687   *
 688   * - How to decide which chunks to merge:
 689   *   - The merge upwards and downward rules specify that the lowest-feerate respectively
 690   *     highest-feerate candidate chunk is merged with, but if there are multiple equal-feerate
 691   *     candidates, a uniformly random one among them is picked.
 692   *
 693   * - How to decide what dependency to activate (when merging chunks):
 694   *   - After picking two chunks to be merged (see above), a uniformly random dependency between the
 695   *     two chunks is activated.
 696   *
 697   * - How to decide which chunk to find a dependency to split in:
 698   *   - A round-robin queue of chunks to improve is maintained. The initial ordering of this queue
 699   *     is uniformly randomly permuted.
 700   *
 701   * - How to decide what dependency to deactivate (when splitting chunks):
 702   *   - Inside the selected chunk (see above), among the dependencies whose top feerate is strictly
 703   *     higher than its bottom feerate in the selected chunk, if any, a uniformly random dependency
 704   *     is deactivated.
 705   *   - After every split, it is possible that the top and the bottom chunk merge with each other
 706   *     again in the merge sequence (through a top->bottom dependency, not through the deactivated
 707   *     one, which was bottom->top). Call this a self-merge. If a self-merge does not occur after
 708   *     a split, the resulting linearization is strictly improved (the area under the convexified
 709   *     feerate diagram increases by at least gain/2), while self-merges do not change it.
 710   *
 711   * - How to decide the exact output linearization:
 712   *   - When there are multiple equal-feerate chunks with no dependencies between them, pick the
 713   *     smallest one first. If there are multiple smallest ones, pick the one that contains the
 714   *     last transaction (according to the provided fallback order) last (note that this is not the
 715   *     same as picking the chunk with the first transaction first).
 716   *   - Within chunks, pick among all transactions without missing dependencies the one with the
 717   *     highest individual feerate. If there are multiple ones with the same individual feerate,
 718   *     pick the smallest first. If there are multiple with the same fee and size, pick the one
 719   *     that sorts first according to the fallback order first.
 720   */
 721  template<typename SetType, typename CostModel = SFLDefaultCostModel>
 722  class SpanningForestState
 723  {
 724  private:
 725      /** Internal RNG. */
 726      InsecureRandomContext m_rng;
 727  
 728      /** Data type to represent indexing into m_tx_data. */
 729      using TxIdx = DepGraphIndex;
 730      /** Data type to represent indexing into m_set_info. Use the smallest type possible to improve
 731       *  cache locality. */
 732      using SetIdx = std::conditional_t<(SetType::Size() <= 0xff),
 733                                        uint8_t,
 734                                        std::conditional_t<(SetType::Size() <= 0xffff),
 735                                                           uint16_t,
 736                                                           uint32_t>>;
 737      /** An invalid SetIdx. */
 738      static constexpr SetIdx INVALID_SET_IDX = SetIdx(-1);
 739  
 740      /** Structure with information about a single transaction. */
 741      struct TxData {
 742          /** The top set for every active child dependency this transaction has, indexed by child
 743           *  TxIdx. Only defined for indexes in active_children. */
 744          std::array<SetIdx, SetType::Size()> dep_top_idx;
 745          /** The set of parent transactions of this transaction. Immutable after construction. */
 746          SetType parents;
 747          /** The set of child transactions of this transaction. Immutable after construction. */
 748          SetType children;
 749          /** The set of child transactions reachable through an active dependency. */
 750          SetType active_children;
 751          /** Which chunk this transaction belongs to. */
 752          SetIdx chunk_idx;
 753      };
 754  
 755      /** The set of all TxIdx's of transactions in the cluster indexing into m_tx_data. */
 756      SetType m_transaction_idxs;
 757      /** The set of all chunk SetIdx's. This excludes the SetIdxs that refer to active
 758       *  dependencies' tops. */
 759      SetType m_chunk_idxs;
 760      /** The set of all SetIdx's that appear in m_suboptimal_chunks. Note that they do not need to
 761       *  be chunks: some of these sets may have been converted to a dependency's top set since being
 762       *  added to m_suboptimal_chunks. */
 763      SetType m_suboptimal_idxs;
 764      /** Information about each transaction (and chunks). Keeps the "holes" from DepGraph during
 765       *  construction. Indexed by TxIdx. */
 766      std::vector<TxData> m_tx_data;
 767      /** Information about each set (chunk, or active dependency top set). Indexed by SetIdx. */
 768      std::vector<SetInfo<SetType>> m_set_info;
 769      /** For each chunk, indexed by SetIdx, the set of out-of-chunk reachable transactions, in the
 770       *  upwards (.first) and downwards (.second) direction. */
 771      std::vector<std::pair<SetType, SetType>> m_reachable;
 772      /** A FIFO of chunk SetIdxs for chunks that may be improved still. */
 773      VecDeque<SetIdx> m_suboptimal_chunks;
 774      /** A FIFO of chunk indexes with a pivot transaction in them, and a flag to indicate their
 775       *  status:
 776       *  - bit 1: currently attempting to move the pivot down, rather than up.
 777       *  - bit 2: this is the second stage, so we have already tried moving the pivot in the other
 778       *           direction.
 779       */
 780      VecDeque<std::tuple<SetIdx, TxIdx, unsigned>> m_nonminimal_chunks;
 781  
 782      /** The DepGraph we are trying to linearize. */
 783      const DepGraph<SetType>& m_depgraph;
 784  
 785      /** Accounting for the cost of this computation. */
 786      CostModel m_cost;
 787  
 788      /** Pick a random transaction within a set (which must be non-empty). */
 789      TxIdx PickRandomTx(const SetType& tx_idxs) noexcept
 790      {
 791          Assume(tx_idxs.Any());
 792          unsigned pos = m_rng.randrange<unsigned>(tx_idxs.Count());
 793          for (auto tx_idx : tx_idxs) {
 794              if (pos == 0) return tx_idx;
 795              --pos;
 796          }
 797          Assume(false);
 798          return TxIdx(-1);
 799      }
 800  
 801      /** Find the set of out-of-chunk transactions reachable from tx_idxs, both in upwards and
 802       *  downwards direction. Only used by SanityCheck to verify the precomputed reachable sets in
 803       *  m_reachable that are maintained by Activate/Deactivate. */
 804      std::pair<SetType, SetType> GetReachable(const SetType& tx_idxs) const noexcept
 805      {
 806          SetType parents, children;
 807          for (auto tx_idx : tx_idxs) {
 808              const auto& tx_data = m_tx_data[tx_idx];
 809              parents |= tx_data.parents;
 810              children |= tx_data.children;
 811          }
 812          return {parents - tx_idxs, children - tx_idxs};
 813      }
 814  
 815      /** Make the inactive dependency from child to parent, which must not be in the same chunk
 816       *  already, active. Returns the merged chunk idx. */
 817      SetIdx Activate(TxIdx parent_idx, TxIdx child_idx) noexcept
 818      {
 819          m_cost.ActivateBegin();
 820          // Gather and check information about the parent and child transactions.
 821          auto& parent_data = m_tx_data[parent_idx];
 822          auto& child_data = m_tx_data[child_idx];
 823          Assume(parent_data.children[child_idx]);
 824          Assume(!parent_data.active_children[child_idx]);
 825          // Get the set index of the chunks the parent and child are currently in. The parent chunk
 826          // will become the top set of the newly activated dependency, while the child chunk will be
 827          // grown to become the merged chunk.
 828          auto parent_chunk_idx = parent_data.chunk_idx;
 829          auto child_chunk_idx = child_data.chunk_idx;
 830          Assume(parent_chunk_idx != child_chunk_idx);
 831          Assume(m_chunk_idxs[parent_chunk_idx]);
 832          Assume(m_chunk_idxs[child_chunk_idx]);
 833          auto& top_info = m_set_info[parent_chunk_idx];
 834          auto& bottom_info = m_set_info[child_chunk_idx];
 835  
 836          // Consider the following example:
 837          //
 838          //    A           A     There are two chunks, ABC and DEF, and the inactive E->C dependency
 839          //   / \         / \    is activated, resulting in a single chunk ABCDEF.
 840          //  B   C       B   C
 841          //      :  ==>      |   Dependency | top set before | top set after | change
 842          //  D   E       D   E   B->A       | AC             | ACDEF         | +DEF
 843          //   \ /         \ /    C->A       | AB             | AB            |
 844          //    F           F     F->D       | D              | D             |
 845          //                      F->E       | E              | ABCE          | +ABC
 846          //
 847          // The common pattern here is that any dependency which has the parent or child of the
 848          // dependency being activated (E->C here) in its top set, will have the opposite part added
 849          // to it. This is true for B->A and F->E, but not for C->A and F->D.
 850          //
 851          // Traverse the old parent chunk top_info (ABC in example), and add bottom_info (DEF) to
 852          // every dependency's top set which has the parent (C) in it. At the same time, change the
 853          // chunk_idx for each to be child_chunk_idx, which becomes the set for the merged chunk.
 854          for (auto tx_idx : top_info.transactions) {
 855              auto& tx_data = m_tx_data[tx_idx];
 856              tx_data.chunk_idx = child_chunk_idx;
 857              for (auto dep_child_idx : tx_data.active_children) {
 858                  auto& dep_top_info = m_set_info[tx_data.dep_top_idx[dep_child_idx]];
 859                  if (dep_top_info.transactions[parent_idx]) dep_top_info |= bottom_info;
 860              }
 861          }
 862          // Traverse the old child chunk bottom_info (DEF in example), and add top_info (ABC) to
 863          // every dependency's top set which has the child (E) in it.
 864          for (auto tx_idx : bottom_info.transactions) {
 865              auto& tx_data = m_tx_data[tx_idx];
 866              for (auto dep_child_idx : tx_data.active_children) {
 867                  auto& dep_top_info = m_set_info[tx_data.dep_top_idx[dep_child_idx]];
 868                  if (dep_top_info.transactions[child_idx]) dep_top_info |= top_info;
 869              }
 870          }
 871          // Merge top_info into bottom_info, which becomes the merged chunk.
 872          bottom_info |= top_info;
 873          // Compute merged sets of reachable transactions from the new chunk, based on the input
 874          // chunks' reachable sets.
 875          m_reachable[child_chunk_idx].first |= m_reachable[parent_chunk_idx].first;
 876          m_reachable[child_chunk_idx].second |= m_reachable[parent_chunk_idx].second;
 877          m_reachable[child_chunk_idx].first -= bottom_info.transactions;
 878          m_reachable[child_chunk_idx].second -= bottom_info.transactions;
 879          // Make parent chunk the set for the new active dependency.
 880          parent_data.dep_top_idx[child_idx] = parent_chunk_idx;
 881          parent_data.active_children.Set(child_idx);
 882          m_chunk_idxs.Reset(parent_chunk_idx);
 883          // Return the newly merged chunk.
 884          m_cost.ActivateEnd(/*num_deps=*/bottom_info.transactions.Count() - 1);
 885          return child_chunk_idx;
 886      }
 887  
 888      /** Make a specified active dependency inactive. Returns the created parent and child chunk
 889       *  indexes. */
 890      std::pair<SetIdx, SetIdx> Deactivate(TxIdx parent_idx, TxIdx child_idx) noexcept
 891      {
 892          m_cost.DeactivateBegin();
 893          // Gather and check information about the parent transactions.
 894          auto& parent_data = m_tx_data[parent_idx];
 895          Assume(parent_data.children[child_idx]);
 896          Assume(parent_data.active_children[child_idx]);
 897          // Get the top set of the active dependency (which will become the parent chunk) and the
 898          // chunk set the transactions are currently in (which will become the bottom chunk).
 899          auto parent_chunk_idx = parent_data.dep_top_idx[child_idx];
 900          auto child_chunk_idx = parent_data.chunk_idx;
 901          Assume(parent_chunk_idx != child_chunk_idx);
 902          Assume(m_chunk_idxs[child_chunk_idx]);
 903          Assume(!m_chunk_idxs[parent_chunk_idx]); // top set, not a chunk
 904          auto& top_info = m_set_info[parent_chunk_idx];
 905          auto& bottom_info = m_set_info[child_chunk_idx];
 906  
 907          // Remove the active dependency.
 908          parent_data.active_children.Reset(child_idx);
 909          m_chunk_idxs.Set(parent_chunk_idx);
 910          auto ntx = bottom_info.transactions.Count();
 911          // Subtract the top_info from the bottom_info, as it will become the child chunk.
 912          bottom_info -= top_info;
 913          // See the comment above in Activate(). We perform the opposite operations here, removing
 914          // instead of adding. Simultaneously, aggregate the top/bottom's union of parents/children.
 915          SetType top_parents, top_children;
 916          for (auto tx_idx : top_info.transactions) {
 917              auto& tx_data = m_tx_data[tx_idx];
 918              tx_data.chunk_idx = parent_chunk_idx;
 919              top_parents |= tx_data.parents;
 920              top_children |= tx_data.children;
 921              for (auto dep_child_idx : tx_data.active_children) {
 922                  auto& dep_top_info = m_set_info[tx_data.dep_top_idx[dep_child_idx]];
 923                  if (dep_top_info.transactions[parent_idx]) dep_top_info -= bottom_info;
 924              }
 925          }
 926          SetType bottom_parents, bottom_children;
 927          for (auto tx_idx : bottom_info.transactions) {
 928              auto& tx_data = m_tx_data[tx_idx];
 929              bottom_parents |= tx_data.parents;
 930              bottom_children |= tx_data.children;
 931              for (auto dep_child_idx : tx_data.active_children) {
 932                  auto& dep_top_info = m_set_info[tx_data.dep_top_idx[dep_child_idx]];
 933                  if (dep_top_info.transactions[child_idx]) dep_top_info -= top_info;
 934              }
 935          }
 936          // Compute the new sets of reachable transactions for each new chunk, based on the
 937          // top/bottom parents and children computed above.
 938          m_reachable[parent_chunk_idx].first = top_parents - top_info.transactions;
 939          m_reachable[parent_chunk_idx].second = top_children - top_info.transactions;
 940          m_reachable[child_chunk_idx].first = bottom_parents - bottom_info.transactions;
 941          m_reachable[child_chunk_idx].second = bottom_children - bottom_info.transactions;
 942          // Return the two new set idxs.
 943          m_cost.DeactivateEnd(/*num_deps=*/ntx - 1);
 944          return {parent_chunk_idx, child_chunk_idx};
 945      }
 946  
 947      /** Activate a dependency from the bottom set to the top set, which must exist. Return the
 948       *  index of the merged chunk. */
 949      SetIdx MergeChunks(SetIdx top_idx, SetIdx bottom_idx) noexcept
 950      {
 951          m_cost.MergeChunksBegin();
 952          Assume(m_chunk_idxs[top_idx]);
 953          Assume(m_chunk_idxs[bottom_idx]);
 954          auto& top_chunk_info = m_set_info[top_idx];
 955          auto& bottom_chunk_info = m_set_info[bottom_idx];
 956          // Count the number of dependencies between bottom_chunk and top_chunk.
 957          unsigned num_deps{0};
 958          for (auto tx_idx : top_chunk_info.transactions) {
 959              auto& tx_data = m_tx_data[tx_idx];
 960              num_deps += (tx_data.children & bottom_chunk_info.transactions).Count();
 961          }
 962          m_cost.MergeChunksMid(/*num_txns=*/top_chunk_info.transactions.Count());
 963          Assume(num_deps > 0);
 964          // Uniformly randomly pick one of them and activate it.
 965          unsigned pick = m_rng.randrange(num_deps);
 966          unsigned num_steps = 0;
 967          for (auto tx_idx : top_chunk_info.transactions) {
 968              ++num_steps;
 969              auto& tx_data = m_tx_data[tx_idx];
 970              auto intersect = tx_data.children & bottom_chunk_info.transactions;
 971              auto count = intersect.Count();
 972              if (pick < count) {
 973                  for (auto child_idx : intersect) {
 974                      if (pick == 0) {
 975                          m_cost.MergeChunksEnd(/*num_steps=*/num_steps);
 976                          return Activate(tx_idx, child_idx);
 977                      }
 978                      --pick;
 979                  }
 980                  Assume(false);
 981                  break;
 982              }
 983              pick -= count;
 984          }
 985          Assume(false);
 986          return INVALID_SET_IDX;
 987      }
 988  
 989      /** Activate a dependency from chunk_idx to merge_chunk_idx (if !DownWard), or a dependency
 990       *  from merge_chunk_idx to chunk_idx (if DownWard). Return the index of the merged chunk. */
 991      template<bool DownWard>
 992      SetIdx MergeChunksDirected(SetIdx chunk_idx, SetIdx merge_chunk_idx) noexcept
 993      {
 994          if constexpr (DownWard) {
 995              return MergeChunks(chunk_idx, merge_chunk_idx);
 996          } else {
 997              return MergeChunks(merge_chunk_idx, chunk_idx);
 998          }
 999      }
1000  
1001      /** Determine which chunk to merge chunk_idx with, or INVALID_SET_IDX if none. */
1002      template<bool DownWard>
1003      SetIdx PickMergeCandidate(SetIdx chunk_idx) noexcept
1004      {
1005          m_cost.PickMergeCandidateBegin();
1006          /** Information about the chunk. */
1007          Assume(m_chunk_idxs[chunk_idx]);
1008          auto& chunk_info = m_set_info[chunk_idx];
1009          // Iterate over all chunks reachable from this one. For those depended-on chunks,
1010          // remember the highest-feerate (if DownWard) or lowest-feerate (if !DownWard) one.
1011          // If multiple equal-feerate candidate chunks to merge with exist, pick a random one
1012          // among them.
1013  
1014          /** The minimum feerate (if downward) or maximum feerate (if upward) to consider when
1015           *  looking for candidate chunks to merge with. Initially, this is the original chunk's
1016           *  feerate, but is updated to be the current best candidate whenever one is found. */
1017          FeeFrac best_other_chunk_feerate = chunk_info.feerate;
1018          /** The chunk index for the best candidate chunk to merge with. INVALID_SET_IDX if none. */
1019          SetIdx best_other_chunk_idx = INVALID_SET_IDX;
1020          /** We generate random tiebreak values to pick between equal-feerate candidate chunks.
1021           *  This variable stores the tiebreak of the current best candidate. */
1022          uint64_t best_other_chunk_tiebreak{0};
1023  
1024          /** Which parent/child transactions we still need to process the chunks for. */
1025          auto todo = DownWard ? m_reachable[chunk_idx].second : m_reachable[chunk_idx].first;
1026          unsigned steps = 0;
1027          while (todo.Any()) {
1028              ++steps;
1029              // Find a chunk for a transaction in todo, and remove all its transactions from todo.
1030              auto reached_chunk_idx = m_tx_data[todo.First()].chunk_idx;
1031              auto& reached_chunk_info = m_set_info[reached_chunk_idx];
1032              todo -= reached_chunk_info.transactions;
1033              // See if it has an acceptable feerate.
1034              auto cmp = DownWard ? FeeRateCompare(best_other_chunk_feerate, reached_chunk_info.feerate)
1035                                  : FeeRateCompare(reached_chunk_info.feerate, best_other_chunk_feerate);
1036              if (cmp > 0) continue;
1037              uint64_t tiebreak = m_rng.rand64();
1038              if (cmp < 0 || tiebreak >= best_other_chunk_tiebreak) {
1039                  best_other_chunk_feerate = reached_chunk_info.feerate;
1040                  best_other_chunk_idx = reached_chunk_idx;
1041                  best_other_chunk_tiebreak = tiebreak;
1042              }
1043          }
1044          Assume(steps <= m_set_info.size());
1045  
1046          m_cost.PickMergeCandidateEnd(/*num_steps=*/steps);
1047          return best_other_chunk_idx;
1048      }
1049  
1050      /** Perform an upward or downward merge step, on the specified chunk. Returns the merged chunk,
1051       *  or INVALID_SET_IDX if no merge took place. */
1052      template<bool DownWard>
1053      SetIdx MergeStep(SetIdx chunk_idx) noexcept
1054      {
1055          auto merge_chunk_idx = PickMergeCandidate<DownWard>(chunk_idx);
1056          if (merge_chunk_idx == INVALID_SET_IDX) return INVALID_SET_IDX;
1057          chunk_idx = MergeChunksDirected<DownWard>(chunk_idx, merge_chunk_idx);
1058          Assume(chunk_idx != INVALID_SET_IDX);
1059          return chunk_idx;
1060      }
1061  
1062      /** Perform an upward or downward merge sequence on the specified chunk. */
1063      template<bool DownWard>
1064      void MergeSequence(SetIdx chunk_idx) noexcept
1065      {
1066          Assume(m_chunk_idxs[chunk_idx]);
1067          while (true) {
1068              auto merged_chunk_idx = MergeStep<DownWard>(chunk_idx);
1069              if (merged_chunk_idx == INVALID_SET_IDX) break;
1070              chunk_idx = merged_chunk_idx;
1071          }
1072          // Add the chunk to the queue of improvable chunks, if it wasn't already there.
1073          if (!m_suboptimal_idxs[chunk_idx]) {
1074              m_suboptimal_idxs.Set(chunk_idx);
1075              m_suboptimal_chunks.push_back(chunk_idx);
1076          }
1077      }
1078  
1079      /** Split a chunk, and then merge the resulting two chunks to make the graph topological
1080       *  again. */
1081      void Improve(TxIdx parent_idx, TxIdx child_idx) noexcept
1082      {
1083          // Deactivate the specified dependency, splitting it into two new chunks: a top containing
1084          // the parent, and a bottom containing the child. The top should have a higher feerate.
1085          auto [parent_chunk_idx, child_chunk_idx] = Deactivate(parent_idx, child_idx);
1086  
1087          // At this point we have exactly two chunks which may violate topology constraints (the
1088          // parent chunk and child chunk that were produced by deactivation). We can fix
1089          // these using just merge sequences, one upwards and one downwards, avoiding the need for a
1090          // full MakeTopological.
1091          const auto& parent_reachable = m_reachable[parent_chunk_idx].first;
1092          const auto& child_chunk_txn = m_set_info[child_chunk_idx].transactions;
1093          if (parent_reachable.Overlaps(child_chunk_txn)) {
1094              // The parent chunk has a dependency on a transaction in the child chunk. In this case,
1095              // the parent needs to merge back with the child chunk (a self-merge), and no other
1096              // merges are needed. Special-case this, so the overhead of PickMergeCandidate and
1097              // MergeSequence can be avoided.
1098  
1099              // In the self-merge, the roles reverse: the parent chunk (from the split) depends
1100              // on the child chunk, so child_chunk_idx is the "top" and parent_chunk_idx is the
1101              // "bottom" for MergeChunks.
1102              auto merged_chunk_idx = MergeChunks(child_chunk_idx, parent_chunk_idx);
1103              if (!m_suboptimal_idxs[merged_chunk_idx]) {
1104                  m_suboptimal_idxs.Set(merged_chunk_idx);
1105                  m_suboptimal_chunks.push_back(merged_chunk_idx);
1106              }
1107          } else {
1108              // Merge the top chunk with lower-feerate chunks it depends on.
1109              MergeSequence<false>(parent_chunk_idx);
1110              // Merge the bottom chunk with higher-feerate chunks that depend on it.
1111              MergeSequence<true>(child_chunk_idx);
1112          }
1113      }
1114  
1115      /** Determine the next chunk to optimize, or INVALID_SET_IDX if none. */
1116      SetIdx PickChunkToOptimize() noexcept
1117      {
1118          m_cost.PickChunkToOptimizeBegin();
1119          unsigned steps{0};
1120          while (!m_suboptimal_chunks.empty()) {
1121              ++steps;
1122              // Pop an entry from the potentially-suboptimal chunk queue.
1123              SetIdx chunk_idx = m_suboptimal_chunks.front();
1124              Assume(m_suboptimal_idxs[chunk_idx]);
1125              m_suboptimal_idxs.Reset(chunk_idx);
1126              m_suboptimal_chunks.pop_front();
1127              if (m_chunk_idxs[chunk_idx]) {
1128                  m_cost.PickChunkToOptimizeEnd(/*num_steps=*/steps);
1129                  return chunk_idx;
1130              }
1131              // If what was popped is not currently a chunk, continue. This may
1132              // happen when a split chunk merges in Improve() with one or more existing chunks that
1133              // are themselves on the suboptimal queue already.
1134          }
1135          m_cost.PickChunkToOptimizeEnd(/*num_steps=*/steps);
1136          return INVALID_SET_IDX;
1137      }
1138  
1139      /** Find a (parent, child) dependency to deactivate in chunk_idx, or (-1, -1) if none. */
1140      std::pair<TxIdx, TxIdx> PickDependencyToSplit(SetIdx chunk_idx) noexcept
1141      {
1142          m_cost.PickDependencyToSplitBegin();
1143          Assume(m_chunk_idxs[chunk_idx]);
1144          auto& chunk_info = m_set_info[chunk_idx];
1145  
1146          // Remember the best dependency {par, chl} seen so far.
1147          std::pair<TxIdx, TxIdx> candidate_dep = {TxIdx(-1), TxIdx(-1)};
1148          uint64_t candidate_tiebreak = 0;
1149          // Iterate over all transactions.
1150          for (auto tx_idx : chunk_info.transactions) {
1151              const auto& tx_data = m_tx_data[tx_idx];
1152              // Iterate over all active child dependencies of the transaction.
1153              for (auto child_idx : tx_data.active_children) {
1154                  auto& dep_top_info = m_set_info[tx_data.dep_top_idx[child_idx]];
1155                  // Skip if this dependency is ineligible (the top chunk that would be created
1156                  // does not have higher feerate than the chunk it is currently part of).
1157                  auto cmp = FeeRateCompare(dep_top_info.feerate, chunk_info.feerate);
1158                  if (cmp <= 0) continue;
1159                  // Generate a random tiebreak for this dependency, and reject it if its tiebreak
1160                  // is worse than the best so far. This means that among all eligible
1161                  // dependencies, a uniformly random one will be chosen.
1162                  uint64_t tiebreak = m_rng.rand64();
1163                  if (tiebreak < candidate_tiebreak) continue;
1164                  // Remember this as our (new) candidate dependency.
1165                  candidate_dep = {tx_idx, child_idx};
1166                  candidate_tiebreak = tiebreak;
1167              }
1168          }
1169          m_cost.PickDependencyToSplitEnd(/*num_txns=*/chunk_info.transactions.Count());
1170          return candidate_dep;
1171      }
1172  
1173  public:
1174      /** Construct a spanning forest for the given DepGraph, with every transaction in its own chunk
1175       *  (not topological). */
1176      explicit SpanningForestState(const DepGraph<SetType>& depgraph LIFETIMEBOUND, uint64_t rng_seed, const CostModel& cost = CostModel{}) noexcept :
1177          m_rng(rng_seed), m_depgraph(depgraph), m_cost(cost)
1178      {
1179          m_cost.InitializeBegin();
1180          m_transaction_idxs = depgraph.Positions();
1181          auto num_transactions = m_transaction_idxs.Count();
1182          m_tx_data.resize(depgraph.PositionRange());
1183          m_set_info.resize(num_transactions);
1184          m_reachable.resize(num_transactions);
1185          size_t num_chunks = 0;
1186          size_t num_deps = 0;
1187          for (auto tx_idx : m_transaction_idxs) {
1188              // Fill in transaction data.
1189              auto& tx_data = m_tx_data[tx_idx];
1190              tx_data.parents = depgraph.GetReducedParents(tx_idx);
1191              for (auto parent_idx : tx_data.parents) {
1192                  m_tx_data[parent_idx].children.Set(tx_idx);
1193              }
1194              num_deps += tx_data.parents.Count();
1195              // Create a singleton chunk for it.
1196              tx_data.chunk_idx = num_chunks;
1197              m_set_info[num_chunks++] = SetInfo(depgraph, tx_idx);
1198          }
1199          // Set the reachable transactions for each chunk to the transactions' parents and children.
1200          for (SetIdx chunk_idx = 0; chunk_idx < num_transactions; ++chunk_idx) {
1201              auto& tx_data = m_tx_data[m_set_info[chunk_idx].transactions.First()];
1202              m_reachable[chunk_idx].first = tx_data.parents;
1203              m_reachable[chunk_idx].second = tx_data.children;
1204          }
1205          Assume(num_chunks == num_transactions);
1206          // Mark all chunk sets as chunks.
1207          m_chunk_idxs = SetType::Fill(num_chunks);
1208          m_cost.InitializeEnd(/*num_txns=*/num_chunks, /*num_deps=*/num_deps);
1209      }
1210  
1211      /** Load an existing linearization. Must be called immediately after constructor. The result is
1212       *  topological if the linearization is valid. Otherwise, MakeTopological still needs to be
1213       *  called. */
1214      void LoadLinearization(std::span<const DepGraphIndex> old_linearization) noexcept
1215      {
1216          // Add transactions one by one, in order of existing linearization.
1217          for (DepGraphIndex tx_idx : old_linearization) {
1218              auto chunk_idx = m_tx_data[tx_idx].chunk_idx;
1219              // Merge the chunk upwards, as long as merging succeeds.
1220              while (true) {
1221                  chunk_idx = MergeStep<false>(chunk_idx);
1222                  if (chunk_idx == INVALID_SET_IDX) break;
1223              }
1224          }
1225      }
1226  
1227      /** Make state topological. Can be called after constructing, or after LoadLinearization. */
1228      void MakeTopological() noexcept
1229      {
1230          m_cost.MakeTopologicalBegin();
1231          Assume(m_suboptimal_chunks.empty());
1232          /** What direction to initially merge chunks in; one of the two directions is enough. This
1233           *  is sufficient because if a non-topological inactive dependency exists between two
1234           *  chunks, at least one of the two chunks will eventually be processed in a direction that
1235           *  discovers it - either the lower chunk tries upward, or the upper chunk tries downward.
1236           *  Chunks that are the result of the merging are always tried in both directions. */
1237          unsigned init_dir = m_rng.randbool();
1238          /** Which chunks are the result of merging, and thus need merge attempts in both
1239           *  directions. */
1240          SetType merged_chunks;
1241          // Mark chunks as suboptimal.
1242          m_suboptimal_idxs = m_chunk_idxs;
1243          for (auto chunk_idx : m_chunk_idxs) {
1244              m_suboptimal_chunks.emplace_back(chunk_idx);
1245              // Randomize the initial order of suboptimal chunks in the queue.
1246              SetIdx j = m_rng.randrange<SetIdx>(m_suboptimal_chunks.size());
1247              if (j != m_suboptimal_chunks.size() - 1) {
1248                  std::swap(m_suboptimal_chunks.back(), m_suboptimal_chunks[j]);
1249              }
1250          }
1251          unsigned chunks = m_chunk_idxs.Count();
1252          unsigned steps = 0;
1253          while (!m_suboptimal_chunks.empty()) {
1254              ++steps;
1255              // Pop an entry from the potentially-suboptimal chunk queue.
1256              SetIdx chunk_idx = m_suboptimal_chunks.front();
1257              m_suboptimal_chunks.pop_front();
1258              Assume(m_suboptimal_idxs[chunk_idx]);
1259              m_suboptimal_idxs.Reset(chunk_idx);
1260              // If what was popped is not currently a chunk, continue. This may
1261              // happen when it was merged with something else since being added.
1262              if (!m_chunk_idxs[chunk_idx]) continue;
1263              /** What direction(s) to attempt merging in. 1=up, 2=down, 3=both. */
1264              unsigned direction = merged_chunks[chunk_idx] ? 3 : init_dir + 1;
1265              int flip = m_rng.randbool();
1266              for (int i = 0; i < 2; ++i) {
1267                  if (i ^ flip) {
1268                      if (!(direction & 1)) continue;
1269                      // Attempt to merge the chunk upwards.
1270                      auto result_up = MergeStep<false>(chunk_idx);
1271                      if (result_up != INVALID_SET_IDX) {
1272                          if (!m_suboptimal_idxs[result_up]) {
1273                              m_suboptimal_idxs.Set(result_up);
1274                              m_suboptimal_chunks.push_back(result_up);
1275                          }
1276                          merged_chunks.Set(result_up);
1277                          break;
1278                      }
1279                  } else {
1280                      if (!(direction & 2)) continue;
1281                      // Attempt to merge the chunk downwards.
1282                      auto result_down = MergeStep<true>(chunk_idx);
1283                      if (result_down != INVALID_SET_IDX) {
1284                          if (!m_suboptimal_idxs[result_down]) {
1285                              m_suboptimal_idxs.Set(result_down);
1286                              m_suboptimal_chunks.push_back(result_down);
1287                          }
1288                          merged_chunks.Set(result_down);
1289                          break;
1290                      }
1291                  }
1292              }
1293          }
1294          m_cost.MakeTopologicalEnd(/*num_chunks=*/chunks, /*num_steps=*/steps);
1295      }
1296  
1297      /** Initialize the data structure for optimization. It must be topological already. */
1298      void StartOptimizing() noexcept
1299      {
1300          m_cost.StartOptimizingBegin();
1301          Assume(m_suboptimal_chunks.empty());
1302          // Mark chunks suboptimal.
1303          m_suboptimal_idxs = m_chunk_idxs;
1304          for (auto chunk_idx : m_chunk_idxs) {
1305              m_suboptimal_chunks.push_back(chunk_idx);
1306              // Randomize the initial order of suboptimal chunks in the queue.
1307              SetIdx j = m_rng.randrange<SetIdx>(m_suboptimal_chunks.size());
1308              if (j != m_suboptimal_chunks.size() - 1) {
1309                  std::swap(m_suboptimal_chunks.back(), m_suboptimal_chunks[j]);
1310              }
1311          }
1312          m_cost.StartOptimizingEnd(/*num_chunks=*/m_suboptimal_chunks.size());
1313      }
1314  
1315      /** Try to improve the forest. Returns false if it is optimal, true otherwise. */
1316      bool OptimizeStep() noexcept
1317      {
1318          auto chunk_idx = PickChunkToOptimize();
1319          if (chunk_idx == INVALID_SET_IDX) {
1320              // No improvable chunk was found, we are done.
1321              return false;
1322          }
1323          auto [parent_idx, child_idx] = PickDependencyToSplit(chunk_idx);
1324          if (parent_idx == TxIdx(-1)) {
1325              // Nothing to improve in chunk_idx. Need to continue with other chunks, if any.
1326              return !m_suboptimal_chunks.empty();
1327          }
1328          // Deactivate the found dependency and then make the state topological again with a
1329          // sequence of merges.
1330          Improve(parent_idx, child_idx);
1331          return true;
1332      }
1333  
1334      /** Initialize data structure for minimizing the chunks. Can only be called if state is known
1335       *  to be optimal. OptimizeStep() cannot be called anymore afterwards. */
1336      void StartMinimizing() noexcept
1337      {
1338          m_cost.StartMinimizingBegin();
1339          m_nonminimal_chunks.clear();
1340          m_nonminimal_chunks.reserve(m_transaction_idxs.Count());
1341          // Gather all chunks, and for each, add it with a random pivot in it, and a random initial
1342          // direction, to m_nonminimal_chunks.
1343          for (auto chunk_idx : m_chunk_idxs) {
1344              TxIdx pivot_idx = PickRandomTx(m_set_info[chunk_idx].transactions);
1345              m_nonminimal_chunks.emplace_back(chunk_idx, pivot_idx, m_rng.randbits<1>());
1346              // Randomize the initial order of nonminimal chunks in the queue.
1347              SetIdx j = m_rng.randrange<SetIdx>(m_nonminimal_chunks.size());
1348              if (j != m_nonminimal_chunks.size() - 1) {
1349                  std::swap(m_nonminimal_chunks.back(), m_nonminimal_chunks[j]);
1350              }
1351          }
1352          m_cost.StartMinimizingEnd(/*num_chunks=*/m_nonminimal_chunks.size());
1353      }
1354  
1355      /** Try to reduce a chunk's size. Returns false if all chunks are minimal, true otherwise. */
1356      bool MinimizeStep() noexcept
1357      {
1358          // If the queue of potentially-non-minimal chunks is empty, we are done.
1359          if (m_nonminimal_chunks.empty()) return false;
1360          m_cost.MinimizeStepBegin();
1361          // Pop an entry from the potentially-non-minimal chunk queue.
1362          auto [chunk_idx, pivot_idx, flags] = m_nonminimal_chunks.front();
1363          m_nonminimal_chunks.pop_front();
1364          auto& chunk_info = m_set_info[chunk_idx];
1365          /** Whether to move the pivot down rather than up. */
1366          bool move_pivot_down = flags & 1;
1367          /** Whether this is already the second stage. */
1368          bool second_stage = flags & 2;
1369  
1370          // Find a random dependency whose top and bottom set feerates are equal, and which has
1371          // pivot in bottom set (if move_pivot_down) or in top set (if !move_pivot_down).
1372          std::pair<TxIdx, TxIdx> candidate_dep;
1373          uint64_t candidate_tiebreak{0};
1374          bool have_any = false;
1375          // Iterate over all transactions.
1376          for (auto tx_idx : chunk_info.transactions) {
1377              const auto& tx_data = m_tx_data[tx_idx];
1378              // Iterate over all active child dependencies of the transaction.
1379              for (auto child_idx : tx_data.active_children) {
1380                  const auto& dep_top_info = m_set_info[tx_data.dep_top_idx[child_idx]];
1381                  // Skip if this dependency does not have equal top and bottom set feerates. Note
1382                  // that the top cannot have higher feerate than the bottom, or OptimizeSteps would
1383                  // have dealt with it.
1384                  if (dep_top_info.feerate << chunk_info.feerate) continue;
1385                  have_any = true;
1386                  // Skip if this dependency does not have pivot in the right place.
1387                  if (move_pivot_down == dep_top_info.transactions[pivot_idx]) continue;
1388                  // Remember this as our chosen dependency if it has a better tiebreak.
1389                  uint64_t tiebreak = m_rng.rand64() | 1;
1390                  if (tiebreak > candidate_tiebreak) {
1391                      candidate_tiebreak = tiebreak;
1392                      candidate_dep = {tx_idx, child_idx};
1393                  }
1394              }
1395          }
1396          m_cost.MinimizeStepMid(/*num_txns=*/chunk_info.transactions.Count());
1397          // If no dependencies have equal top and bottom set feerate, this chunk is minimal.
1398          if (!have_any) return true;
1399          // If all found dependencies have the pivot in the wrong place, try moving it in the other
1400          // direction. If this was the second stage already, we are done.
1401          if (candidate_tiebreak == 0) {
1402              // Switch to other direction, and to second phase.
1403              flags ^= 3;
1404              if (!second_stage) m_nonminimal_chunks.emplace_back(chunk_idx, pivot_idx, flags);
1405              return true;
1406          }
1407  
1408          // Otherwise, deactivate the dependency that was found.
1409          auto [parent_chunk_idx, child_chunk_idx] = Deactivate(candidate_dep.first, candidate_dep.second);
1410          // Determine if there is a dependency from the new bottom to the new top (opposite from the
1411          // dependency that was just deactivated).
1412          auto& parent_reachable = m_reachable[parent_chunk_idx].first;
1413          auto& child_chunk_txn = m_set_info[child_chunk_idx].transactions;
1414          if (parent_reachable.Overlaps(child_chunk_txn)) {
1415              // A self-merge is needed. Note that the child_chunk_idx is the top, and
1416              // parent_chunk_idx is the bottom, because we activate a dependency in the reverse
1417              // direction compared to the deactivation above.
1418              auto merged_chunk_idx = MergeChunks(child_chunk_idx, parent_chunk_idx);
1419              // Re-insert the chunk into the queue, in the same direction. Note that the chunk_idx
1420              // will have changed.
1421              m_nonminimal_chunks.emplace_back(merged_chunk_idx, pivot_idx, flags);
1422              m_cost.MinimizeStepEnd(/*split=*/false);
1423          } else {
1424              // No self-merge happens, and thus we have found a way to split the chunk. Create two
1425              // smaller chunks, and add them to the queue. The one that contains the current pivot
1426              // gets to continue with it in the same direction, to minimize the number of times we
1427              // alternate direction. If we were in the second phase already, the newly created chunk
1428              // inherits that too, because we know no split with the pivot on the other side is
1429              // possible already. The new chunk without the current pivot gets a new randomly-chosen
1430              // one.
1431              if (move_pivot_down) {
1432                  auto parent_pivot_idx = PickRandomTx(m_set_info[parent_chunk_idx].transactions);
1433                  m_nonminimal_chunks.emplace_back(parent_chunk_idx, parent_pivot_idx, m_rng.randbits<1>());
1434                  m_nonminimal_chunks.emplace_back(child_chunk_idx, pivot_idx, flags);
1435              } else {
1436                  auto child_pivot_idx = PickRandomTx(m_set_info[child_chunk_idx].transactions);
1437                  m_nonminimal_chunks.emplace_back(parent_chunk_idx, pivot_idx, flags);
1438                  m_nonminimal_chunks.emplace_back(child_chunk_idx, child_pivot_idx, m_rng.randbits<1>());
1439              }
1440              if (m_rng.randbool()) {
1441                  std::swap(m_nonminimal_chunks.back(), m_nonminimal_chunks[m_nonminimal_chunks.size() - 2]);
1442              }
1443              m_cost.MinimizeStepEnd(/*split=*/true);
1444          }
1445          return true;
1446      }
1447  
1448      /** Construct a topologically-valid linearization from the current forest state. Must be
1449       *  topological. fallback_order is a comparator that defines a strong order for DepGraphIndexes
1450       *  in this cluster, used to order equal-feerate transactions and chunks.
1451       *
1452       * Specifically, the resulting order consists of:
1453       * - The chunks of the current SFL state, sorted by (in decreasing order of priority):
1454       *   - topology (parents before children)
1455       *   - highest chunk feerate first
1456       *   - smallest chunk size first
1457       *   - the chunk with the lowest maximum transaction, by fallback_order, first
1458       * - The transactions within a chunk, sorted by (in decreasing order of priority):
1459       *   - topology (parents before children)
1460       *   - highest tx feerate first
1461       *   - smallest tx size first
1462       *   - the lowest transaction, by fallback_order, first
1463       */
1464      std::vector<DepGraphIndex> GetLinearization(const StrongComparator<DepGraphIndex> auto& fallback_order) noexcept
1465      {
1466          m_cost.GetLinearizationBegin();
1467          /** The output linearization. */
1468          std::vector<DepGraphIndex> ret;
1469          ret.reserve(m_set_info.size());
1470          /** A heap with all chunks (by set index) that can currently be included, sorted by
1471           *  chunk feerate (high to low), chunk size (small to large), and by least maximum element
1472           *  according to the fallback order (which is the second pair element). */
1473          std::vector<std::pair<SetIdx, TxIdx>> ready_chunks;
1474          /** For every chunk, indexed by SetIdx, the number of unmet dependencies the chunk has on
1475           *  other chunks (not including dependencies within the chunk itself). */
1476          std::vector<TxIdx> chunk_deps(m_set_info.size(), 0);
1477          /** For every transaction, indexed by TxIdx, the number of unmet dependencies the
1478           *  transaction has. */
1479          std::vector<TxIdx> tx_deps(m_tx_data.size(), 0);
1480          /** A heap with all transactions within the current chunk that can be included, sorted by
1481           *  tx feerate (high to low), tx size (small to large), and fallback order. */
1482          std::vector<TxIdx> ready_tx;
1483          // Populate chunk_deps and tx_deps.
1484          unsigned num_deps{0};
1485          for (TxIdx chl_idx : m_transaction_idxs) {
1486              const auto& chl_data = m_tx_data[chl_idx];
1487              tx_deps[chl_idx] = chl_data.parents.Count();
1488              num_deps += tx_deps[chl_idx];
1489              auto chl_chunk_idx = chl_data.chunk_idx;
1490              auto& chl_chunk_info = m_set_info[chl_chunk_idx];
1491              chunk_deps[chl_chunk_idx] += (chl_data.parents - chl_chunk_info.transactions).Count();
1492          }
1493          /** Function to compute the highest element of a chunk, by fallback_order. */
1494          auto max_fallback_fn = [&](SetIdx chunk_idx) noexcept {
1495              auto& chunk = m_set_info[chunk_idx].transactions;
1496              auto it = chunk.begin();
1497              DepGraphIndex ret = *it;
1498              ++it;
1499              while (it != chunk.end()) {
1500                  if (fallback_order(*it, ret) > 0) ret = *it;
1501                  ++it;
1502              }
1503              return ret;
1504          };
1505          /** Comparison function for the transaction heap. Note that it is a max-heap, so
1506           *  tx_cmp_fn(a, b) == true means "a appears after b in the linearization". */
1507          auto tx_cmp_fn = [&](const auto& a, const auto& b) noexcept {
1508              // Bail out for identical transactions.
1509              if (a == b) return false;
1510              // First sort by increasing transaction feerate.
1511              auto& a_feerate = m_depgraph.FeeRate(a);
1512              auto& b_feerate = m_depgraph.FeeRate(b);
1513              auto feerate_cmp = FeeRateCompare(a_feerate, b_feerate);
1514              if (feerate_cmp != 0) return feerate_cmp < 0;
1515              // Then by decreasing transaction size.
1516              if (a_feerate.size != b_feerate.size) {
1517                  return a_feerate.size > b_feerate.size;
1518              }
1519              // Tie-break by decreasing fallback_order.
1520              auto fallback_cmp = fallback_order(a, b);
1521              if (fallback_cmp != 0) return fallback_cmp > 0;
1522              // This should not be hit, because fallback_order defines a strong ordering.
1523              Assume(false);
1524              return a < b;
1525          };
1526          // Construct a heap with all chunks that have no out-of-chunk dependencies.
1527          /** Comparison function for the chunk heap. Note that it is a max-heap, so
1528           *  chunk_cmp_fn(a, b) == true means "a appears after b in the linearization". */
1529          auto chunk_cmp_fn = [&](const auto& a, const auto& b) noexcept {
1530              // Bail out for identical chunks.
1531              if (a.first == b.first) return false;
1532              // First sort by increasing chunk feerate.
1533              auto& chunk_feerate_a = m_set_info[a.first].feerate;
1534              auto& chunk_feerate_b = m_set_info[b.first].feerate;
1535              auto feerate_cmp = FeeRateCompare(chunk_feerate_a, chunk_feerate_b);
1536              if (feerate_cmp != 0) return feerate_cmp < 0;
1537              // Then by decreasing chunk size.
1538              if (chunk_feerate_a.size != chunk_feerate_b.size) {
1539                  return chunk_feerate_a.size > chunk_feerate_b.size;
1540              }
1541              // Tie-break by decreasing fallback_order.
1542              auto fallback_cmp = fallback_order(a.second, b.second);
1543              if (fallback_cmp != 0) return fallback_cmp > 0;
1544              // This should not be hit, because fallback_order defines a strong ordering.
1545              Assume(false);
1546              return a.second < b.second;
1547          };
1548          // Construct a heap with all chunks that have no out-of-chunk dependencies.
1549          for (SetIdx chunk_idx : m_chunk_idxs) {
1550              if (chunk_deps[chunk_idx] == 0) {
1551                  ready_chunks.emplace_back(chunk_idx, max_fallback_fn(chunk_idx));
1552              }
1553          }
1554          std::make_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
1555          // Pop chunks off the heap.
1556          while (!ready_chunks.empty()) {
1557              auto [chunk_idx, _rnd] = ready_chunks.front();
1558              std::pop_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
1559              ready_chunks.pop_back();
1560              Assume(chunk_deps[chunk_idx] == 0);
1561              const auto& chunk_txn = m_set_info[chunk_idx].transactions;
1562              // Build heap of all includable transactions in chunk.
1563              Assume(ready_tx.empty());
1564              for (TxIdx tx_idx : chunk_txn) {
1565                  if (tx_deps[tx_idx] == 0) ready_tx.push_back(tx_idx);
1566              }
1567              Assume(!ready_tx.empty());
1568              std::make_heap(ready_tx.begin(), ready_tx.end(), tx_cmp_fn);
1569              // Pick transactions from the ready heap, append them to linearization, and decrement
1570              // dependency counts.
1571              while (!ready_tx.empty()) {
1572                  // Pop an element from the tx_ready heap.
1573                  auto tx_idx = ready_tx.front();
1574                  std::pop_heap(ready_tx.begin(), ready_tx.end(), tx_cmp_fn);
1575                  ready_tx.pop_back();
1576                  // Append to linearization.
1577                  ret.push_back(tx_idx);
1578                  // Decrement dependency counts.
1579                  auto& tx_data = m_tx_data[tx_idx];
1580                  for (TxIdx chl_idx : tx_data.children) {
1581                      auto& chl_data = m_tx_data[chl_idx];
1582                      // Decrement tx dependency count.
1583                      Assume(tx_deps[chl_idx] > 0);
1584                      if (--tx_deps[chl_idx] == 0 && chunk_txn[chl_idx]) {
1585                          // Child tx has no dependencies left, and is in this chunk. Add it to the tx heap.
1586                          ready_tx.push_back(chl_idx);
1587                          std::push_heap(ready_tx.begin(), ready_tx.end(), tx_cmp_fn);
1588                      }
1589                      // Decrement chunk dependency count if this is out-of-chunk dependency.
1590                      if (chl_data.chunk_idx != chunk_idx) {
1591                          Assume(chunk_deps[chl_data.chunk_idx] > 0);
1592                          if (--chunk_deps[chl_data.chunk_idx] == 0) {
1593                              // Child chunk has no dependencies left. Add it to the chunk heap.
1594                              ready_chunks.emplace_back(chl_data.chunk_idx, max_fallback_fn(chl_data.chunk_idx));
1595                              std::push_heap(ready_chunks.begin(), ready_chunks.end(), chunk_cmp_fn);
1596                          }
1597                      }
1598                  }
1599              }
1600          }
1601          Assume(ret.size() == m_set_info.size());
1602          m_cost.GetLinearizationEnd(/*num_txns=*/m_set_info.size(), /*num_deps=*/num_deps);
1603          return ret;
1604      }
1605  
1606      /** Get the diagram for the current state, which must be topological. Test-only.
1607       *
1608       * The linearization produced by GetLinearization() is always at least as good (in the
1609       * CompareChunks() sense) as this diagram, but may be better.
1610       *
1611       * After an OptimizeStep(), the diagram will always be at least as good as before. Once
1612       * OptimizeStep() returns false, the diagram will be equivalent to that produced by
1613       * GetLinearization(), and optimal.
1614       *
1615       * After a MinimizeStep(), the diagram cannot change anymore (in the CompareChunks() sense),
1616       * but its number of segments can increase still. Once MinimizeStep() returns false, the number
1617       * of chunks of the produced linearization will match the number of segments in the diagram.
1618       */
1619      std::vector<FeeFrac> GetDiagram() const noexcept
1620      {
1621          std::vector<FeeFrac> ret;
1622          for (auto chunk_idx : m_chunk_idxs) {
1623              ret.push_back(m_set_info[chunk_idx].feerate);
1624          }
1625          std::sort(ret.begin(), ret.end(), std::greater{});
1626          return ret;
1627      }
1628  
1629      /** Determine how much work was performed so far. */
1630      uint64_t GetCost() const noexcept { return m_cost.GetCost(); }
1631  
1632      /** Verify internal consistency of the data structure. */
1633      void SanityCheck() const
1634      {
1635          //
1636          // Verify dependency parent/child information, and build list of (active) dependencies.
1637          //
1638          std::vector<std::pair<TxIdx, TxIdx>> expected_dependencies;
1639          std::vector<std::pair<TxIdx, TxIdx>> all_dependencies;
1640          std::vector<std::pair<TxIdx, TxIdx>> active_dependencies;
1641          for (auto parent_idx : m_depgraph.Positions()) {
1642              for (auto child_idx : m_depgraph.GetReducedChildren(parent_idx)) {
1643                  expected_dependencies.emplace_back(parent_idx, child_idx);
1644              }
1645          }
1646          for (auto tx_idx : m_transaction_idxs) {
1647              for (auto child_idx : m_tx_data[tx_idx].children) {
1648                  all_dependencies.emplace_back(tx_idx, child_idx);
1649                  if (m_tx_data[tx_idx].active_children[child_idx]) {
1650                      active_dependencies.emplace_back(tx_idx, child_idx);
1651                  }
1652              }
1653          }
1654          std::sort(expected_dependencies.begin(), expected_dependencies.end());
1655          std::sort(all_dependencies.begin(), all_dependencies.end());
1656          assert(expected_dependencies == all_dependencies);
1657  
1658          //
1659          // Verify the chunks against the list of active dependencies
1660          //
1661          SetType chunk_cover;
1662          for (auto chunk_idx : m_chunk_idxs) {
1663              const auto& chunk_info = m_set_info[chunk_idx];
1664              // Verify that transactions in the chunk point back to it. This guarantees
1665              // that chunks are non-overlapping.
1666              for (auto tx_idx : chunk_info.transactions) {
1667                  assert(m_tx_data[tx_idx].chunk_idx == chunk_idx);
1668              }
1669              assert(!chunk_cover.Overlaps(chunk_info.transactions));
1670              chunk_cover |= chunk_info.transactions;
1671              // Verify the chunk's transaction set: start from an arbitrary chunk transaction,
1672              // and for every active dependency, if it contains the parent or child, add the
1673              // other. It must have exactly N-1 active dependencies in it, guaranteeing it is
1674              // acyclic.
1675              assert(chunk_info.transactions.Any());
1676              SetType expected_chunk = SetType::Singleton(chunk_info.transactions.First());
1677              while (true) {
1678                  auto old = expected_chunk;
1679                  size_t active_dep_count{0};
1680                  for (const auto& [par, chl] : active_dependencies) {
1681                      if (expected_chunk[par] || expected_chunk[chl]) {
1682                          expected_chunk.Set(par);
1683                          expected_chunk.Set(chl);
1684                          ++active_dep_count;
1685                      }
1686                  }
1687                  if (old == expected_chunk) {
1688                      assert(expected_chunk.Count() == active_dep_count + 1);
1689                      break;
1690                  }
1691              }
1692              assert(chunk_info.transactions == expected_chunk);
1693              // Verify the chunk's feerate.
1694              assert(chunk_info.feerate == m_depgraph.FeeRate(chunk_info.transactions));
1695              // Verify the chunk's reachable transactions.
1696              assert(m_reachable[chunk_idx] == GetReachable(expected_chunk));
1697              // Verify that the chunk's reachable transactions don't include its own transactions.
1698              assert(!m_reachable[chunk_idx].first.Overlaps(chunk_info.transactions));
1699              assert(!m_reachable[chunk_idx].second.Overlaps(chunk_info.transactions));
1700          }
1701          // Verify that together, the chunks cover all transactions.
1702          assert(chunk_cover == m_depgraph.Positions());
1703  
1704          //
1705          // Verify transaction data.
1706          //
1707          assert(m_transaction_idxs == m_depgraph.Positions());
1708          for (auto tx_idx : m_transaction_idxs) {
1709              const auto& tx_data = m_tx_data[tx_idx];
1710              // Verify it has a valid chunk index, and that chunk includes this transaction.
1711              assert(m_chunk_idxs[tx_data.chunk_idx]);
1712              assert(m_set_info[tx_data.chunk_idx].transactions[tx_idx]);
1713              // Verify parents/children.
1714              assert(tx_data.parents == m_depgraph.GetReducedParents(tx_idx));
1715              assert(tx_data.children == m_depgraph.GetReducedChildren(tx_idx));
1716              // Verify active_children is a subset of children.
1717              assert(tx_data.active_children.IsSubsetOf(tx_data.children));
1718              // Verify each active child's dep_top_idx points to a valid non-chunk set.
1719              for (auto child_idx : tx_data.active_children) {
1720                  assert(tx_data.dep_top_idx[child_idx] < m_set_info.size());
1721                  assert(!m_chunk_idxs[tx_data.dep_top_idx[child_idx]]);
1722              }
1723          }
1724  
1725          //
1726          // Verify active dependencies' top sets.
1727          //
1728          for (const auto& [par_idx, chl_idx] : active_dependencies) {
1729              // Verify the top set's transactions: it must contain the parent, and for every
1730              // active dependency, except the chl_idx->par_idx dependency itself, if it contains the
1731              // parent or child, it must contain both. It must have exactly N-1 active dependencies
1732              // in it, guaranteeing it is acyclic.
1733              SetType expected_top = SetType::Singleton(par_idx);
1734              while (true) {
1735                  auto old = expected_top;
1736                  size_t active_dep_count{0};
1737                  for (const auto& [par2_idx, chl2_idx] : active_dependencies) {
1738                      if (par_idx == par2_idx && chl_idx == chl2_idx) continue;
1739                      if (expected_top[par2_idx] || expected_top[chl2_idx]) {
1740                          expected_top.Set(par2_idx);
1741                          expected_top.Set(chl2_idx);
1742                          ++active_dep_count;
1743                      }
1744                  }
1745                  if (old == expected_top) {
1746                      assert(expected_top.Count() == active_dep_count + 1);
1747                      break;
1748                  }
1749              }
1750              assert(!expected_top[chl_idx]);
1751              auto& dep_top_info = m_set_info[m_tx_data[par_idx].dep_top_idx[chl_idx]];
1752              assert(dep_top_info.transactions == expected_top);
1753              // Verify the top set's feerate.
1754              assert(dep_top_info.feerate == m_depgraph.FeeRate(dep_top_info.transactions));
1755          }
1756  
1757          //
1758          // Verify m_suboptimal_chunks.
1759          //
1760          SetType suboptimal_idxs;
1761          for (size_t i = 0; i < m_suboptimal_chunks.size(); ++i) {
1762              auto chunk_idx = m_suboptimal_chunks[i];
1763              assert(!suboptimal_idxs[chunk_idx]);
1764              suboptimal_idxs.Set(chunk_idx);
1765          }
1766          assert(m_suboptimal_idxs == suboptimal_idxs);
1767  
1768          //
1769          // Verify m_nonminimal_chunks.
1770          //
1771          SetType nonminimal_idxs;
1772          for (size_t i = 0; i < m_nonminimal_chunks.size(); ++i) {
1773              auto [chunk_idx, pivot, flags] = m_nonminimal_chunks[i];
1774              assert(m_tx_data[pivot].chunk_idx == chunk_idx);
1775              assert(!nonminimal_idxs[chunk_idx]);
1776              nonminimal_idxs.Set(chunk_idx);
1777          }
1778          assert(nonminimal_idxs.IsSubsetOf(m_chunk_idxs));
1779      }
1780  };
1781  
1782  /** Find or improve a linearization for a cluster.
1783   *
1784   * @param[in] depgraph            Dependency graph of the cluster to be linearized.
1785   * @param[in] max_cost            Upper bound on the amount of work that will be done.
1786   * @param[in] rng_seed            A random number seed to control search order. This prevents peers
1787   *                                from predicting exactly which clusters would be hard for us to
1788   *                                linearize.
1789   * @param[in] fallback_order      A comparator to order transactions, used to sort equal-feerate
1790   *                                chunks and transactions. See SpanningForestState::GetLinearization
1791   *                                for details.
1792   * @param[in] old_linearization   An existing linearization for the cluster, or empty.
1793   * @param[in] is_topological      (Only relevant if old_linearization is not empty) Whether
1794   *                                old_linearization is topologically valid.
1795   * @return                        A tuple of:
1796   *                                - The resulting linearization. It is guaranteed to be at least as
1797   *                                  good (in the feerate diagram sense) as old_linearization.
1798   *                                - A boolean indicating whether the result is guaranteed to be
1799   *                                  optimal with minimal chunks.
1800   *                                - How many optimization steps were actually performed.
1801   */
1802  template<typename SetType>
1803  std::tuple<std::vector<DepGraphIndex>, bool, uint64_t> Linearize(
1804      const DepGraph<SetType>& depgraph,
1805      uint64_t max_cost,
1806      uint64_t rng_seed,
1807      const StrongComparator<DepGraphIndex> auto& fallback_order,
1808      std::span<const DepGraphIndex> old_linearization = {},
1809      bool is_topological = true) noexcept
1810  {
1811      /** Initialize a spanning forest data structure for this cluster. */
1812      SpanningForestState forest(depgraph, rng_seed);
1813      if (!old_linearization.empty()) {
1814          forest.LoadLinearization(old_linearization);
1815          if (!is_topological) forest.MakeTopological();
1816      } else {
1817          forest.MakeTopological();
1818      }
1819      // Make improvement steps to it until we hit the max_iterations limit, or an optimal result
1820      // is found.
1821      if (forest.GetCost() < max_cost) {
1822          forest.StartOptimizing();
1823          do {
1824              if (!forest.OptimizeStep()) break;
1825          } while (forest.GetCost() < max_cost);
1826      }
1827      // Make chunk minimization steps until we hit the max_iterations limit, or all chunks are
1828      // minimal.
1829      bool optimal = false;
1830      if (forest.GetCost() < max_cost) {
1831          forest.StartMinimizing();
1832          do {
1833              if (!forest.MinimizeStep()) {
1834                  optimal = true;
1835                  break;
1836              }
1837          } while (forest.GetCost() < max_cost);
1838      }
1839      return {forest.GetLinearization(fallback_order), optimal, forest.GetCost()};
1840  }
1841  
1842  /** Improve a given linearization.
1843   *
1844   * @param[in]     depgraph       Dependency graph of the cluster being linearized.
1845   * @param[in,out] linearization  On input, an existing linearization for depgraph. On output, a
1846   *                               potentially better linearization for the same graph.
1847   *
1848   * Postlinearization guarantees:
1849   * - The resulting chunks are connected.
1850   * - If the input has a tree shape (either all transactions have at most one child, or all
1851   *   transactions have at most one parent), the result is optimal.
1852   * - Given a linearization L1 and a leaf transaction T in it. Let L2 be L1 with T moved to the end,
1853   *   optionally with its fee increased. Let L3 be the postlinearization of L2. L3 will be at least
1854   *   as good as L1. This means that replacing transactions with same-size higher-fee transactions
1855   *   will not worsen linearizations through a "drop conflicts, append new transactions,
1856   *   postlinearize" process.
1857   */
1858  template<typename SetType>
1859  void PostLinearize(const DepGraph<SetType>& depgraph, std::span<DepGraphIndex> linearization)
1860  {
1861      // This algorithm performs a number of passes (currently 2); the even ones operate from back to
1862      // front, the odd ones from front to back. Each results in an equal-or-better linearization
1863      // than the one started from.
1864      // - One pass in either direction guarantees that the resulting chunks are connected.
1865      // - Each direction corresponds to one shape of tree being linearized optimally (forward passes
1866      //   guarantee this for graphs where each transaction has at most one child; backward passes
1867      //   guarantee this for graphs where each transaction has at most one parent).
1868      // - Starting with a backward pass guarantees the moved-tree property.
1869      //
1870      // During an odd (forward) pass, the high-level operation is:
1871      // - Start with an empty list of groups L=[].
1872      // - For every transaction i in the old linearization, from front to back:
1873      //   - Append a new group C=[i], containing just i, to the back of L.
1874      //   - While L has at least one group before C, and the group immediately before C has feerate
1875      //     lower than C:
1876      //     - If C depends on P:
1877      //       - Merge P into C, making C the concatenation of P+C, continuing with the combined C.
1878      //     - Otherwise:
1879      //       - Swap P with C, continuing with the now-moved C.
1880      // - The output linearization is the concatenation of the groups in L.
1881      //
1882      // During even (backward) passes, i iterates from the back to the front of the existing
1883      // linearization, and new groups are prepended instead of appended to the list L. To enable
1884      // more code reuse, both passes append groups, but during even passes the meanings of
1885      // parent/child, and of high/low feerate are reversed, and the final concatenation is reversed
1886      // on output.
1887      //
1888      // In the implementation below, the groups are represented by singly-linked lists (pointing
1889      // from the back to the front), which are themselves organized in a singly-linked circular
1890      // list (each group pointing to its predecessor, with a special sentinel group at the front
1891      // that points back to the last group).
1892      //
1893      // Information about transaction t is stored in entries[t + 1], while the sentinel is in
1894      // entries[0].
1895  
1896      /** Index of the sentinel in the entries array below. */
1897      static constexpr DepGraphIndex SENTINEL{0};
1898      /** Indicator that a group has no previous transaction. */
1899      static constexpr DepGraphIndex NO_PREV_TX{0};
1900  
1901  
1902      /** Data structure per transaction entry. */
1903      struct TxEntry
1904      {
1905          /** The index of the previous transaction in this group; NO_PREV_TX if this is the first
1906           *  entry of a group. */
1907          DepGraphIndex prev_tx;
1908  
1909          // The fields below are only used for transactions that are the last one in a group
1910          // (referred to as tail transactions below).
1911  
1912          /** Index of the first transaction in this group, possibly itself. */
1913          DepGraphIndex first_tx;
1914          /** Index of the last transaction in the previous group. The first group (the sentinel)
1915           *  points back to the last group here, making it a singly-linked circular list. */
1916          DepGraphIndex prev_group;
1917          /** All transactions in the group. Empty for the sentinel. */
1918          SetType group;
1919          /** All dependencies of the group (descendants in even passes; ancestors in odd ones). */
1920          SetType deps;
1921          /** The combined fee/size of transactions in the group. Fee is negated in even passes. */
1922          FeeFrac feerate;
1923      };
1924  
1925      // As an example, consider the state corresponding to the linearization [1,0,3,2], with
1926      // groups [1,0,3] and [2], in an odd pass. The linked lists would be:
1927      //
1928      //                                        +-----+
1929      //                                 0<-P-- | 0 S | ---\     Legend:
1930      //                                        +-----+    |
1931      //                                           ^       |     - digit in box: entries index
1932      //             /--------------F---------+    G       |       (note: one more than tx value)
1933      //             v                         \   |       |     - S: sentinel group
1934      //          +-----+        +-----+        +-----+    |          (empty feerate)
1935      //   0<-P-- | 2   | <--P-- | 1   | <--P-- | 4 T |    |     - T: tail transaction, contains
1936      //          +-----+        +-----+        +-----+    |          fields beyond prev_tv.
1937      //                                           ^       |     - P: prev_tx reference
1938      //                                           G       G     - F: first_tx reference
1939      //                                           |       |     - G: prev_group reference
1940      //                                        +-----+    |
1941      //                                 0<-P-- | 3 T | <--/
1942      //                                        +-----+
1943      //                                         ^   |
1944      //                                         \-F-/
1945      //
1946      // During an even pass, the diagram above would correspond to linearization [2,3,0,1], with
1947      // groups [2] and [3,0,1].
1948  
1949      std::vector<TxEntry> entries(depgraph.PositionRange() + 1);
1950  
1951      // Perform two passes over the linearization.
1952      for (int pass = 0; pass < 2; ++pass) {
1953          int rev = !(pass & 1);
1954          // Construct a sentinel group, identifying the start of the list.
1955          entries[SENTINEL].prev_group = SENTINEL;
1956          Assume(entries[SENTINEL].feerate.IsEmpty());
1957  
1958          // Iterate over all elements in the existing linearization.
1959          for (DepGraphIndex i = 0; i < linearization.size(); ++i) {
1960              // Even passes are from back to front; odd passes from front to back.
1961              DepGraphIndex idx = linearization[rev ? linearization.size() - 1 - i : i];
1962              // Construct a new group containing just idx. In even passes, the meaning of
1963              // parent/child and high/low feerate are swapped.
1964              DepGraphIndex cur_group = idx + 1;
1965              entries[cur_group].group = SetType::Singleton(idx);
1966              entries[cur_group].deps = rev ? depgraph.Descendants(idx): depgraph.Ancestors(idx);
1967              entries[cur_group].feerate = depgraph.FeeRate(idx);
1968              if (rev) entries[cur_group].feerate.fee = -entries[cur_group].feerate.fee;
1969              entries[cur_group].prev_tx = NO_PREV_TX; // No previous transaction in group.
1970              entries[cur_group].first_tx = cur_group; // Transaction itself is first of group.
1971              // Insert the new group at the back of the groups linked list.
1972              entries[cur_group].prev_group = entries[SENTINEL].prev_group;
1973              entries[SENTINEL].prev_group = cur_group;
1974  
1975              // Start merge/swap cycle.
1976              DepGraphIndex next_group = SENTINEL; // We inserted at the end, so next group is sentinel.
1977              DepGraphIndex prev_group = entries[cur_group].prev_group;
1978              // Continue as long as the current group has higher feerate than the previous one.
1979              while (entries[cur_group].feerate >> entries[prev_group].feerate) {
1980                  // prev_group/cur_group/next_group refer to (the last transactions of) 3
1981                  // consecutive entries in groups list.
1982                  Assume(cur_group == entries[next_group].prev_group);
1983                  Assume(prev_group == entries[cur_group].prev_group);
1984                  // The sentinel has empty feerate, which is neither higher or lower than other
1985                  // feerates. Thus, the while loop we are in here guarantees that cur_group and
1986                  // prev_group are not the sentinel.
1987                  Assume(cur_group != SENTINEL);
1988                  Assume(prev_group != SENTINEL);
1989                  if (entries[cur_group].deps.Overlaps(entries[prev_group].group)) {
1990                      // There is a dependency between cur_group and prev_group; merge prev_group
1991                      // into cur_group. The group/deps/feerate fields of prev_group remain unchanged
1992                      // but become unused.
1993                      entries[cur_group].group |= entries[prev_group].group;
1994                      entries[cur_group].deps |= entries[prev_group].deps;
1995                      entries[cur_group].feerate += entries[prev_group].feerate;
1996                      // Make the first of the current group point to the tail of the previous group.
1997                      entries[entries[cur_group].first_tx].prev_tx = prev_group;
1998                      // The first of the previous group becomes the first of the newly-merged group.
1999                      entries[cur_group].first_tx = entries[prev_group].first_tx;
2000                      // The previous group becomes whatever group was before the former one.
2001                      prev_group = entries[prev_group].prev_group;
2002                      entries[cur_group].prev_group = prev_group;
2003                  } else {
2004                      // There is no dependency between cur_group and prev_group; swap them.
2005                      DepGraphIndex preprev_group = entries[prev_group].prev_group;
2006                      // If PP, P, C, N were the old preprev, prev, cur, next groups, then the new
2007                      // layout becomes [PP, C, P, N]. Update prev_groups to reflect that order.
2008                      entries[next_group].prev_group = prev_group;
2009                      entries[prev_group].prev_group = cur_group;
2010                      entries[cur_group].prev_group = preprev_group;
2011                      // The current group remains the same, but the groups before/after it have
2012                      // changed.
2013                      next_group = prev_group;
2014                      prev_group = preprev_group;
2015                  }
2016              }
2017          }
2018  
2019          // Convert the entries back to linearization (overwriting the existing one).
2020          DepGraphIndex cur_group = entries[0].prev_group;
2021          DepGraphIndex done = 0;
2022          while (cur_group != SENTINEL) {
2023              DepGraphIndex cur_tx = cur_group;
2024              // Traverse the transactions of cur_group (from back to front), and write them in the
2025              // same order during odd passes, and reversed (front to back) in even passes.
2026              if (rev) {
2027                  do {
2028                      *(linearization.begin() + (done++)) = cur_tx - 1;
2029                      cur_tx = entries[cur_tx].prev_tx;
2030                  } while (cur_tx != NO_PREV_TX);
2031              } else {
2032                  do {
2033                      *(linearization.end() - (++done)) = cur_tx - 1;
2034                      cur_tx = entries[cur_tx].prev_tx;
2035                  } while (cur_tx != NO_PREV_TX);
2036              }
2037              cur_group = entries[cur_group].prev_group;
2038          }
2039          Assume(done == linearization.size());
2040      }
2041  }
2042  
2043  } // namespace cluster_linearize
2044  
2045  #endif // BITCOIN_CLUSTER_LINEARIZE_H