lemon/max_matching.h
author Alpar Juttner <alpar@cs.elte.hu>
Fri, 21 Nov 2008 14:11:29 +0000
changeset 389 660db48f324f
parent 327 91d63b8b1a4c
child 425 cace3206223b
permissions -rw-r--r--
Port preflow push max flow alg. from svn -r3516 (#176)
Namely,
- port the files
- apply the migrate script
- apply the unify script
- break the long lines in lemon/preflow.h
- convert the .dim test file to .lgf
- fix compilation problems
deba@326
     1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@326
     2
 *
deba@326
     3
 * This file is a part of LEMON, a generic C++ optimization library.
deba@326
     4
 *
deba@326
     5
 * Copyright (C) 2003-2008
deba@326
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@326
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@326
     8
 *
deba@326
     9
 * Permission to use, modify and distribute this software is granted
deba@326
    10
 * provided that this copyright notice appears in all copies. For
deba@326
    11
 * precise terms see the accompanying LICENSE file.
deba@326
    12
 *
deba@326
    13
 * This software is provided "AS IS" with no warranty of any kind,
deba@326
    14
 * express or implied, and with no claim as to its suitability for any
deba@326
    15
 * purpose.
deba@326
    16
 *
deba@326
    17
 */
deba@326
    18
deba@326
    19
#ifndef LEMON_MAX_MATCHING_H
deba@326
    20
#define LEMON_MAX_MATCHING_H
deba@326
    21
deba@326
    22
#include <vector>
deba@326
    23
#include <queue>
deba@326
    24
#include <set>
deba@326
    25
#include <limits>
deba@326
    26
deba@326
    27
#include <lemon/core.h>
deba@326
    28
#include <lemon/unionfind.h>
deba@326
    29
#include <lemon/bin_heap.h>
deba@326
    30
#include <lemon/maps.h>
deba@326
    31
deba@326
    32
///\ingroup matching
deba@326
    33
///\file
deba@327
    34
///\brief Maximum matching algorithms in general graphs.
deba@326
    35
deba@326
    36
namespace lemon {
deba@326
    37
deba@327
    38
  /// \ingroup matching
deba@326
    39
  ///
deba@327
    40
  /// \brief Edmonds' alternating forest maximum matching algorithm.
deba@326
    41
  ///
alpar@330
    42
  /// This class implements Edmonds' alternating forest matching
alpar@330
    43
  /// algorithm. The algorithm can be started from an arbitrary initial
alpar@330
    44
  /// matching (the default is the empty one)
deba@326
    45
  ///
alpar@330
    46
  /// The dual solution of the problem is a map of the nodes to
deba@327
    47
  /// MaxMatching::Status, having values \c EVEN/D, \c ODD/A and \c
deba@327
    48
  /// MATCHED/C showing the Gallai-Edmonds decomposition of the
deba@327
    49
  /// graph. The nodes in \c EVEN/D induce a graph with
deba@327
    50
  /// factor-critical components, the nodes in \c ODD/A form the
deba@327
    51
  /// barrier, and the nodes in \c MATCHED/C induce a graph having a
alpar@330
    52
  /// perfect matching. The number of the factor-critical components
deba@327
    53
  /// minus the number of barrier nodes is a lower bound on the
alpar@330
    54
  /// unmatched nodes, and the matching is optimal if and only if this bound is
deba@327
    55
  /// tight. This decomposition can be attained by calling \c
deba@327
    56
  /// decomposition() after running the algorithm.
deba@326
    57
  ///
deba@327
    58
  /// \param _Graph The graph type the algorithm runs on.
deba@327
    59
  template <typename _Graph>
deba@326
    60
  class MaxMatching {
deba@327
    61
  public:
deba@327
    62
deba@327
    63
    typedef _Graph Graph;
deba@327
    64
    typedef typename Graph::template NodeMap<typename Graph::Arc>
deba@327
    65
    MatchingMap;
deba@327
    66
deba@327
    67
    ///\brief Indicates the Gallai-Edmonds decomposition of the graph.
deba@327
    68
    ///
alpar@330
    69
    ///Indicates the Gallai-Edmonds decomposition of the graph. The
deba@327
    70
    ///nodes with Status \c EVEN/D induce a graph with factor-critical
deba@327
    71
    ///components, the nodes in \c ODD/A form the canonical barrier,
deba@327
    72
    ///and the nodes in \c MATCHED/C induce a graph having a perfect
deba@327
    73
    ///matching.
deba@327
    74
    enum Status {
deba@327
    75
      EVEN = 1, D = 1, MATCHED = 0, C = 0, ODD = -1, A = -1, UNMATCHED = -2
deba@327
    76
    };
deba@327
    77
deba@327
    78
    typedef typename Graph::template NodeMap<Status> StatusMap;
deba@327
    79
deba@327
    80
  private:
deba@326
    81
deba@326
    82
    TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326
    83
deba@327
    84
    typedef UnionFindEnum<IntNodeMap> BlossomSet;
deba@327
    85
    typedef ExtendFindEnum<IntNodeMap> TreeSet;
deba@327
    86
    typedef RangeMap<Node> NodeIntMap;
deba@327
    87
    typedef MatchingMap EarMap;
deba@327
    88
    typedef std::vector<Node> NodeQueue;
deba@327
    89
deba@327
    90
    const Graph& _graph;
deba@327
    91
    MatchingMap* _matching;
deba@327
    92
    StatusMap* _status;
deba@327
    93
deba@327
    94
    EarMap* _ear;
deba@327
    95
deba@327
    96
    IntNodeMap* _blossom_set_index;
deba@327
    97
    BlossomSet* _blossom_set;
deba@327
    98
    NodeIntMap* _blossom_rep;
deba@327
    99
deba@327
   100
    IntNodeMap* _tree_set_index;
deba@327
   101
    TreeSet* _tree_set;
deba@327
   102
deba@327
   103
    NodeQueue _node_queue;
deba@327
   104
    int _process, _postpone, _last;
deba@327
   105
deba@327
   106
    int _node_num;
deba@327
   107
deba@327
   108
  private:
deba@327
   109
deba@327
   110
    void createStructures() {
deba@327
   111
      _node_num = countNodes(_graph);
deba@327
   112
      if (!_matching) {
deba@327
   113
        _matching = new MatchingMap(_graph);
deba@327
   114
      }
deba@327
   115
      if (!_status) {
deba@327
   116
        _status = new StatusMap(_graph);
deba@327
   117
      }
deba@327
   118
      if (!_ear) {
deba@327
   119
        _ear = new EarMap(_graph);
deba@327
   120
      }
deba@327
   121
      if (!_blossom_set) {
deba@327
   122
        _blossom_set_index = new IntNodeMap(_graph);
deba@327
   123
        _blossom_set = new BlossomSet(*_blossom_set_index);
deba@327
   124
      }
deba@327
   125
      if (!_blossom_rep) {
deba@327
   126
        _blossom_rep = new NodeIntMap(_node_num);
deba@327
   127
      }
deba@327
   128
      if (!_tree_set) {
deba@327
   129
        _tree_set_index = new IntNodeMap(_graph);
deba@327
   130
        _tree_set = new TreeSet(*_tree_set_index);
deba@327
   131
      }
deba@327
   132
      _node_queue.resize(_node_num);
deba@327
   133
    }
deba@327
   134
deba@327
   135
    void destroyStructures() {
deba@327
   136
      if (_matching) {
deba@327
   137
        delete _matching;
deba@327
   138
      }
deba@327
   139
      if (_status) {
deba@327
   140
        delete _status;
deba@327
   141
      }
deba@327
   142
      if (_ear) {
deba@327
   143
        delete _ear;
deba@327
   144
      }
deba@327
   145
      if (_blossom_set) {
deba@327
   146
        delete _blossom_set;
deba@327
   147
        delete _blossom_set_index;
deba@327
   148
      }
deba@327
   149
      if (_blossom_rep) {
deba@327
   150
        delete _blossom_rep;
deba@327
   151
      }
deba@327
   152
      if (_tree_set) {
deba@327
   153
        delete _tree_set_index;
deba@327
   154
        delete _tree_set;
deba@327
   155
      }
deba@327
   156
    }
deba@327
   157
deba@327
   158
    void processDense(const Node& n) {
deba@327
   159
      _process = _postpone = _last = 0;
deba@327
   160
      _node_queue[_last++] = n;
deba@327
   161
deba@327
   162
      while (_process != _last) {
deba@327
   163
        Node u = _node_queue[_process++];
deba@327
   164
        for (OutArcIt a(_graph, u); a != INVALID; ++a) {
deba@327
   165
          Node v = _graph.target(a);
deba@327
   166
          if ((*_status)[v] == MATCHED) {
deba@327
   167
            extendOnArc(a);
deba@327
   168
          } else if ((*_status)[v] == UNMATCHED) {
deba@327
   169
            augmentOnArc(a);
deba@327
   170
            return;
deba@327
   171
          }
deba@327
   172
        }
deba@327
   173
      }
deba@327
   174
deba@327
   175
      while (_postpone != _last) {
deba@327
   176
        Node u = _node_queue[_postpone++];
deba@327
   177
deba@327
   178
        for (OutArcIt a(_graph, u); a != INVALID ; ++a) {
deba@327
   179
          Node v = _graph.target(a);
deba@327
   180
deba@327
   181
          if ((*_status)[v] == EVEN) {
deba@327
   182
            if (_blossom_set->find(u) != _blossom_set->find(v)) {
deba@327
   183
              shrinkOnEdge(a);
deba@327
   184
            }
deba@327
   185
          }
deba@327
   186
deba@327
   187
          while (_process != _last) {
deba@327
   188
            Node w = _node_queue[_process++];
deba@327
   189
            for (OutArcIt b(_graph, w); b != INVALID; ++b) {
deba@327
   190
              Node x = _graph.target(b);
deba@327
   191
              if ((*_status)[x] == MATCHED) {
deba@327
   192
                extendOnArc(b);
deba@327
   193
              } else if ((*_status)[x] == UNMATCHED) {
deba@327
   194
                augmentOnArc(b);
deba@327
   195
                return;
deba@327
   196
              }
deba@327
   197
            }
deba@327
   198
          }
deba@327
   199
        }
deba@327
   200
      }
deba@327
   201
    }
deba@327
   202
deba@327
   203
    void processSparse(const Node& n) {
deba@327
   204
      _process = _last = 0;
deba@327
   205
      _node_queue[_last++] = n;
deba@327
   206
      while (_process != _last) {
deba@327
   207
        Node u = _node_queue[_process++];
deba@327
   208
        for (OutArcIt a(_graph, u); a != INVALID; ++a) {
deba@327
   209
          Node v = _graph.target(a);
deba@327
   210
deba@327
   211
          if ((*_status)[v] == EVEN) {
deba@327
   212
            if (_blossom_set->find(u) != _blossom_set->find(v)) {
deba@327
   213
              shrinkOnEdge(a);
deba@327
   214
            }
deba@327
   215
          } else if ((*_status)[v] == MATCHED) {
deba@327
   216
            extendOnArc(a);
deba@327
   217
          } else if ((*_status)[v] == UNMATCHED) {
deba@327
   218
            augmentOnArc(a);
deba@327
   219
            return;
deba@327
   220
          }
deba@327
   221
        }
deba@327
   222
      }
deba@327
   223
    }
deba@327
   224
deba@327
   225
    void shrinkOnEdge(const Edge& e) {
deba@327
   226
      Node nca = INVALID;
deba@327
   227
deba@327
   228
      {
deba@327
   229
        std::set<Node> left_set, right_set;
deba@327
   230
deba@327
   231
        Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))];
deba@327
   232
        left_set.insert(left);
deba@327
   233
deba@327
   234
        Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))];
deba@327
   235
        right_set.insert(right);
deba@327
   236
deba@327
   237
        while (true) {
deba@327
   238
          if ((*_matching)[left] == INVALID) break;
deba@327
   239
          left = _graph.target((*_matching)[left]);
deba@327
   240
          left = (*_blossom_rep)[_blossom_set->
deba@327
   241
                                 find(_graph.target((*_ear)[left]))];
deba@327
   242
          if (right_set.find(left) != right_set.end()) {
deba@327
   243
            nca = left;
deba@327
   244
            break;
deba@327
   245
          }
deba@327
   246
          left_set.insert(left);
deba@327
   247
deba@327
   248
          if ((*_matching)[right] == INVALID) break;
deba@327
   249
          right = _graph.target((*_matching)[right]);
deba@327
   250
          right = (*_blossom_rep)[_blossom_set->
deba@327
   251
                                  find(_graph.target((*_ear)[right]))];
deba@327
   252
          if (left_set.find(right) != left_set.end()) {
deba@327
   253
            nca = right;
deba@327
   254
            break;
deba@327
   255
          }
deba@327
   256
          right_set.insert(right);
deba@327
   257
        }
deba@327
   258
deba@327
   259
        if (nca == INVALID) {
deba@327
   260
          if ((*_matching)[left] == INVALID) {
deba@327
   261
            nca = right;
deba@327
   262
            while (left_set.find(nca) == left_set.end()) {
deba@327
   263
              nca = _graph.target((*_matching)[nca]);
deba@327
   264
              nca =(*_blossom_rep)[_blossom_set->
deba@327
   265
                                   find(_graph.target((*_ear)[nca]))];
deba@327
   266
            }
deba@327
   267
          } else {
deba@327
   268
            nca = left;
deba@327
   269
            while (right_set.find(nca) == right_set.end()) {
deba@327
   270
              nca = _graph.target((*_matching)[nca]);
deba@327
   271
              nca = (*_blossom_rep)[_blossom_set->
deba@327
   272
                                   find(_graph.target((*_ear)[nca]))];
deba@327
   273
            }
deba@327
   274
          }
deba@327
   275
        }
deba@327
   276
      }
deba@327
   277
deba@327
   278
      {
deba@327
   279
deba@327
   280
        Node node = _graph.u(e);
deba@327
   281
        Arc arc = _graph.direct(e, true);
deba@327
   282
        Node base = (*_blossom_rep)[_blossom_set->find(node)];
deba@327
   283
deba@327
   284
        while (base != nca) {
deba@327
   285
          _ear->set(node, arc);
deba@327
   286
deba@327
   287
          Node n = node;
deba@327
   288
          while (n != base) {
deba@327
   289
            n = _graph.target((*_matching)[n]);
deba@327
   290
            Arc a = (*_ear)[n];
deba@327
   291
            n = _graph.target(a);
deba@327
   292
            _ear->set(n, _graph.oppositeArc(a));
deba@327
   293
          }
deba@327
   294
          node = _graph.target((*_matching)[base]);
deba@327
   295
          _tree_set->erase(base);
deba@327
   296
          _tree_set->erase(node);
deba@327
   297
          _blossom_set->insert(node, _blossom_set->find(base));
deba@327
   298
          _status->set(node, EVEN);
deba@327
   299
          _node_queue[_last++] = node;
deba@327
   300
          arc = _graph.oppositeArc((*_ear)[node]);
deba@327
   301
          node = _graph.target((*_ear)[node]);
deba@327
   302
          base = (*_blossom_rep)[_blossom_set->find(node)];
deba@327
   303
          _blossom_set->join(_graph.target(arc), base);
deba@327
   304
        }
deba@327
   305
      }
deba@327
   306
deba@327
   307
      _blossom_rep->set(_blossom_set->find(nca), nca);
deba@327
   308
deba@327
   309
      {
deba@327
   310
deba@327
   311
        Node node = _graph.v(e);
deba@327
   312
        Arc arc = _graph.direct(e, false);
deba@327
   313
        Node base = (*_blossom_rep)[_blossom_set->find(node)];
deba@327
   314
deba@327
   315
        while (base != nca) {
deba@327
   316
          _ear->set(node, arc);
deba@327
   317
deba@327
   318
          Node n = node;
deba@327
   319
          while (n != base) {
deba@327
   320
            n = _graph.target((*_matching)[n]);
deba@327
   321
            Arc a = (*_ear)[n];
deba@327
   322
            n = _graph.target(a);
deba@327
   323
            _ear->set(n, _graph.oppositeArc(a));
deba@327
   324
          }
deba@327
   325
          node = _graph.target((*_matching)[base]);
deba@327
   326
          _tree_set->erase(base);
deba@327
   327
          _tree_set->erase(node);
deba@327
   328
          _blossom_set->insert(node, _blossom_set->find(base));
deba@327
   329
          _status->set(node, EVEN);
deba@327
   330
          _node_queue[_last++] = node;
deba@327
   331
          arc = _graph.oppositeArc((*_ear)[node]);
deba@327
   332
          node = _graph.target((*_ear)[node]);
deba@327
   333
          base = (*_blossom_rep)[_blossom_set->find(node)];
deba@327
   334
          _blossom_set->join(_graph.target(arc), base);
deba@327
   335
        }
deba@327
   336
      }
deba@327
   337
deba@327
   338
      _blossom_rep->set(_blossom_set->find(nca), nca);
deba@327
   339
    }
deba@327
   340
deba@327
   341
deba@327
   342
deba@327
   343
    void extendOnArc(const Arc& a) {
deba@327
   344
      Node base = _graph.source(a);
deba@327
   345
      Node odd = _graph.target(a);
deba@327
   346
deba@327
   347
      _ear->set(odd, _graph.oppositeArc(a));
deba@327
   348
      Node even = _graph.target((*_matching)[odd]);
deba@327
   349
      _blossom_rep->set(_blossom_set->insert(even), even);
deba@327
   350
      _status->set(odd, ODD);
deba@327
   351
      _status->set(even, EVEN);
deba@327
   352
      int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]);
deba@327
   353
      _tree_set->insert(odd, tree);
deba@327
   354
      _tree_set->insert(even, tree);
deba@327
   355
      _node_queue[_last++] = even;
deba@327
   356
deba@327
   357
    }
deba@327
   358
deba@327
   359
    void augmentOnArc(const Arc& a) {
deba@327
   360
      Node even = _graph.source(a);
deba@327
   361
      Node odd = _graph.target(a);
deba@327
   362
deba@327
   363
      int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]);
deba@327
   364
deba@327
   365
      _matching->set(odd, _graph.oppositeArc(a));
deba@327
   366
      _status->set(odd, MATCHED);
deba@327
   367
deba@327
   368
      Arc arc = (*_matching)[even];
deba@327
   369
      _matching->set(even, a);
deba@327
   370
deba@327
   371
      while (arc != INVALID) {
deba@327
   372
        odd = _graph.target(arc);
deba@327
   373
        arc = (*_ear)[odd];
deba@327
   374
        even = _graph.target(arc);
deba@327
   375
        _matching->set(odd, arc);
deba@327
   376
        arc = (*_matching)[even];
deba@327
   377
        _matching->set(even, _graph.oppositeArc((*_matching)[odd]));
deba@327
   378
      }
deba@327
   379
deba@327
   380
      for (typename TreeSet::ItemIt it(*_tree_set, tree);
deba@327
   381
           it != INVALID; ++it) {
deba@327
   382
        if ((*_status)[it] == ODD) {
deba@327
   383
          _status->set(it, MATCHED);
deba@327
   384
        } else {
deba@327
   385
          int blossom = _blossom_set->find(it);
deba@327
   386
          for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom);
deba@327
   387
               jt != INVALID; ++jt) {
deba@327
   388
            _status->set(jt, MATCHED);
deba@327
   389
          }
deba@327
   390
          _blossom_set->eraseClass(blossom);
deba@327
   391
        }
deba@327
   392
      }
deba@327
   393
      _tree_set->eraseClass(tree);
deba@327
   394
deba@327
   395
    }
deba@326
   396
deba@326
   397
  public:
deba@326
   398
deba@327
   399
    /// \brief Constructor
deba@326
   400
    ///
deba@327
   401
    /// Constructor.
deba@327
   402
    MaxMatching(const Graph& graph)
deba@327
   403
      : _graph(graph), _matching(0), _status(0), _ear(0),
deba@327
   404
        _blossom_set_index(0), _blossom_set(0), _blossom_rep(0),
deba@327
   405
        _tree_set_index(0), _tree_set(0) {}
deba@327
   406
deba@327
   407
    ~MaxMatching() {
deba@327
   408
      destroyStructures();
deba@327
   409
    }
deba@327
   410
deba@327
   411
    /// \name Execution control
alpar@330
   412
    /// The simplest way to execute the algorithm is to use the
deba@327
   413
    /// \c run() member function.
deba@327
   414
    /// \n
deba@327
   415
alpar@330
   416
    /// If you need better control on the execution, you must call
deba@327
   417
    /// \ref init(), \ref greedyInit() or \ref matchingInit()
alpar@330
   418
    /// functions first, then you can start the algorithm with the \ref
deba@327
   419
    /// startParse() or startDense() functions.
deba@327
   420
deba@327
   421
    ///@{
deba@327
   422
deba@327
   423
    /// \brief Sets the actual matching to the empty matching.
deba@326
   424
    ///
deba@327
   425
    /// Sets the actual matching to the empty matching.
deba@326
   426
    ///
deba@326
   427
    void init() {
deba@327
   428
      createStructures();
deba@327
   429
      for(NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   430
        _matching->set(n, INVALID);
deba@327
   431
        _status->set(n, UNMATCHED);
deba@326
   432
      }
deba@326
   433
    }
deba@326
   434
alpar@330
   435
    ///\brief Finds an initial matching in a greedy way
deba@326
   436
    ///
alpar@330
   437
    ///It finds an initial matching in a greedy way.
deba@326
   438
    void greedyInit() {
deba@327
   439
      createStructures();
deba@327
   440
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   441
        _matching->set(n, INVALID);
deba@327
   442
        _status->set(n, UNMATCHED);
deba@326
   443
      }
deba@327
   444
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   445
        if ((*_matching)[n] == INVALID) {
deba@327
   446
          for (OutArcIt a(_graph, n); a != INVALID ; ++a) {
deba@327
   447
            Node v = _graph.target(a);
deba@327
   448
            if ((*_matching)[v] == INVALID && v != n) {
deba@327
   449
              _matching->set(n, a);
deba@327
   450
              _status->set(n, MATCHED);
deba@327
   451
              _matching->set(v, _graph.oppositeArc(a));
deba@327
   452
              _status->set(v, MATCHED);
deba@326
   453
              break;
deba@326
   454
            }
deba@326
   455
          }
deba@326
   456
        }
deba@326
   457
      }
deba@326
   458
    }
deba@326
   459
deba@327
   460
alpar@330
   461
    /// \brief Initialize the matching from a map containing.
deba@326
   462
    ///
deba@327
   463
    /// Initialize the matching from a \c bool valued \c Edge map. This
deba@327
   464
    /// map must have the property that there are no two incident edges
deba@327
   465
    /// with true value, ie. it contains a matching.
deba@327
   466
    /// \return %True if the map contains a matching.
deba@327
   467
    template <typename MatchingMap>
deba@327
   468
    bool matchingInit(const MatchingMap& matching) {
deba@327
   469
      createStructures();
deba@327
   470
deba@327
   471
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   472
        _matching->set(n, INVALID);
deba@327
   473
        _status->set(n, UNMATCHED);
deba@326
   474
      }
deba@327
   475
      for(EdgeIt e(_graph); e!=INVALID; ++e) {
deba@327
   476
        if (matching[e]) {
deba@327
   477
deba@327
   478
          Node u = _graph.u(e);
deba@327
   479
          if ((*_matching)[u] != INVALID) return false;
deba@327
   480
          _matching->set(u, _graph.direct(e, true));
deba@327
   481
          _status->set(u, MATCHED);
deba@327
   482
deba@327
   483
          Node v = _graph.v(e);
deba@327
   484
          if ((*_matching)[v] != INVALID) return false;
deba@327
   485
          _matching->set(v, _graph.direct(e, false));
deba@327
   486
          _status->set(v, MATCHED);
deba@327
   487
        }
deba@327
   488
      }
deba@327
   489
      return true;
deba@326
   490
    }
deba@326
   491
deba@327
   492
    /// \brief Starts Edmonds' algorithm
deba@326
   493
    ///
deba@327
   494
    /// If runs the original Edmonds' algorithm.
deba@327
   495
    void startSparse() {
deba@327
   496
      for(NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   497
        if ((*_status)[n] == UNMATCHED) {
deba@327
   498
          (*_blossom_rep)[_blossom_set->insert(n)] = n;
deba@327
   499
          _tree_set->insert(n);
deba@327
   500
          _status->set(n, EVEN);
deba@327
   501
          processSparse(n);
deba@326
   502
        }
deba@326
   503
      }
deba@326
   504
    }
deba@326
   505
deba@327
   506
    /// \brief Starts Edmonds' algorithm.
deba@326
   507
    ///
deba@327
   508
    /// It runs Edmonds' algorithm with a heuristic of postponing
alpar@330
   509
    /// shrinks, therefore resulting in a faster algorithm for dense graphs.
deba@327
   510
    void startDense() {
deba@327
   511
      for(NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   512
        if ((*_status)[n] == UNMATCHED) {
deba@327
   513
          (*_blossom_rep)[_blossom_set->insert(n)] = n;
deba@327
   514
          _tree_set->insert(n);
deba@327
   515
          _status->set(n, EVEN);
deba@327
   516
          processDense(n);
deba@327
   517
        }
deba@327
   518
      }
deba@327
   519
    }
deba@327
   520
deba@327
   521
deba@327
   522
    /// \brief Runs Edmonds' algorithm
deba@327
   523
    ///
deba@327
   524
    /// Runs Edmonds' algorithm for sparse graphs (<tt>m<2*n</tt>)
deba@327
   525
    /// or Edmonds' algorithm with a heuristic of
deba@327
   526
    /// postponing shrinks for dense graphs.
deba@326
   527
    void run() {
deba@327
   528
      if (countEdges(_graph) < 2 * countNodes(_graph)) {
deba@326
   529
        greedyInit();
deba@326
   530
        startSparse();
deba@326
   531
      } else {
deba@326
   532
        init();
deba@326
   533
        startDense();
deba@326
   534
      }
deba@326
   535
    }
deba@326
   536
deba@327
   537
    /// @}
deba@327
   538
deba@327
   539
    /// \name Primal solution
alpar@330
   540
    /// Functions to get the primal solution, ie. the matching.
deba@327
   541
deba@327
   542
    /// @{
deba@326
   543
alpar@330
   544
    ///\brief Returns the size of the current matching.
deba@326
   545
    ///
alpar@330
   546
    ///Returns the size of the current matching. After \ref
deba@327
   547
    ///run() it returns the size of the maximum matching in the graph.
deba@327
   548
    int matchingSize() const {
deba@327
   549
      int size = 0;
deba@327
   550
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   551
        if ((*_matching)[n] != INVALID) {
deba@327
   552
          ++size;
deba@326
   553
        }
deba@326
   554
      }
deba@327
   555
      return size / 2;
deba@326
   556
    }
deba@326
   557
deba@327
   558
    /// \brief Returns true when the edge is in the matching.
deba@327
   559
    ///
deba@327
   560
    /// Returns true when the edge is in the matching.
deba@327
   561
    bool matching(const Edge& edge) const {
deba@327
   562
      return edge == (*_matching)[_graph.u(edge)];
deba@327
   563
    }
deba@327
   564
deba@327
   565
    /// \brief Returns the matching edge incident to the given node.
deba@327
   566
    ///
deba@327
   567
    /// Returns the matching edge of a \c node in the actual matching or
deba@327
   568
    /// INVALID if the \c node is not covered by the actual matching.
deba@327
   569
    Arc matching(const Node& n) const {
deba@327
   570
      return (*_matching)[n];
deba@327
   571
    }
deba@326
   572
deba@326
   573
    ///\brief Returns the mate of a node in the actual matching.
deba@326
   574
    ///
deba@327
   575
    ///Returns the mate of a \c node in the actual matching or
deba@327
   576
    ///INVALID if the \c node is not covered by the actual matching.
deba@327
   577
    Node mate(const Node& n) const {
deba@327
   578
      return (*_matching)[n] != INVALID ?
deba@327
   579
        _graph.target((*_matching)[n]) : INVALID;
deba@326
   580
    }
deba@326
   581
deba@327
   582
    /// @}
deba@327
   583
deba@327
   584
    /// \name Dual solution
alpar@330
   585
    /// Functions to get the dual solution, ie. the decomposition.
deba@327
   586
deba@327
   587
    /// @{
deba@326
   588
deba@326
   589
    /// \brief Returns the class of the node in the Edmonds-Gallai
deba@326
   590
    /// decomposition.
deba@326
   591
    ///
deba@326
   592
    /// Returns the class of the node in the Edmonds-Gallai
deba@326
   593
    /// decomposition.
deba@327
   594
    Status decomposition(const Node& n) const {
deba@327
   595
      return (*_status)[n];
deba@326
   596
    }
deba@326
   597
deba@326
   598
    /// \brief Returns true when the node is in the barrier.
deba@326
   599
    ///
deba@326
   600
    /// Returns true when the node is in the barrier.
deba@327
   601
    bool barrier(const Node& n) const {
deba@327
   602
      return (*_status)[n] == ODD;
deba@326
   603
    }
deba@326
   604
deba@327
   605
    /// @}
deba@326
   606
deba@326
   607
  };
deba@326
   608
deba@326
   609
  /// \ingroup matching
deba@326
   610
  ///
deba@326
   611
  /// \brief Weighted matching in general graphs
deba@326
   612
  ///
deba@326
   613
  /// This class provides an efficient implementation of Edmond's
deba@326
   614
  /// maximum weighted matching algorithm. The implementation is based
deba@326
   615
  /// on extensive use of priority queues and provides
deba@326
   616
  /// \f$O(nm\log(n))\f$ time complexity.
deba@326
   617
  ///
deba@326
   618
  /// The maximum weighted matching problem is to find undirected
deba@327
   619
  /// edges in the graph with maximum overall weight and no two of
deba@327
   620
  /// them shares their ends. The problem can be formulated with the
deba@327
   621
  /// following linear program.
deba@326
   622
  /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
deba@327
   623
  /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
deba@327
   624
      \quad \forall B\in\mathcal{O}\f] */
deba@326
   625
  /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@326
   626
  /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@327
   627
  /// where \f$\delta(X)\f$ is the set of edges incident to a node in
deba@327
   628
  /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
deba@327
   629
  /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
deba@327
   630
  /// subsets of the nodes.
deba@326
   631
  ///
deba@326
   632
  /// The algorithm calculates an optimal matching and a proof of the
deba@326
   633
  /// optimality. The solution of the dual problem can be used to check
deba@327
   634
  /// the result of the algorithm. The dual linear problem is the
deba@327
   635
  /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}
deba@327
   636
      z_B \ge w_{uv} \quad \forall uv\in E\f] */
deba@326
   637
  /// \f[y_u \ge 0 \quad \forall u \in V\f]
deba@326
   638
  /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@327
   639
  /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
deba@327
   640
      \frac{\vert B \vert - 1}{2}z_B\f] */
deba@326
   641
  ///
deba@326
   642
  /// The algorithm can be executed with \c run() or the \c init() and
deba@326
   643
  /// then the \c start() member functions. After it the matching can
deba@326
   644
  /// be asked with \c matching() or mate() functions. The dual
deba@326
   645
  /// solution can be get with \c nodeValue(), \c blossomNum() and \c
deba@326
   646
  /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
alpar@330
   647
  /// "BlossomIt" nested class, which is able to iterate on the nodes
deba@326
   648
  /// of a blossom. If the value type is integral then the dual
deba@326
   649
  /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
deba@326
   650
  template <typename _Graph,
deba@326
   651
            typename _WeightMap = typename _Graph::template EdgeMap<int> >
deba@326
   652
  class MaxWeightedMatching {
deba@326
   653
  public:
deba@326
   654
deba@326
   655
    typedef _Graph Graph;
deba@326
   656
    typedef _WeightMap WeightMap;
deba@326
   657
    typedef typename WeightMap::Value Value;
deba@326
   658
deba@326
   659
    /// \brief Scaling factor for dual solution
deba@326
   660
    ///
deba@326
   661
    /// Scaling factor for dual solution, it is equal to 4 or 1
deba@326
   662
    /// according to the value type.
deba@326
   663
    static const int dualScale =
deba@326
   664
      std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@326
   665
deba@326
   666
    typedef typename Graph::template NodeMap<typename Graph::Arc>
deba@326
   667
    MatchingMap;
deba@326
   668
deba@326
   669
  private:
deba@326
   670
deba@326
   671
    TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326
   672
deba@326
   673
    typedef typename Graph::template NodeMap<Value> NodePotential;
deba@326
   674
    typedef std::vector<Node> BlossomNodeList;
deba@326
   675
deba@326
   676
    struct BlossomVariable {
deba@326
   677
      int begin, end;
deba@326
   678
      Value value;
deba@326
   679
deba@326
   680
      BlossomVariable(int _begin, int _end, Value _value)
deba@326
   681
        : begin(_begin), end(_end), value(_value) {}
deba@326
   682
deba@326
   683
    };
deba@326
   684
deba@326
   685
    typedef std::vector<BlossomVariable> BlossomPotential;
deba@326
   686
deba@326
   687
    const Graph& _graph;
deba@326
   688
    const WeightMap& _weight;
deba@326
   689
deba@326
   690
    MatchingMap* _matching;
deba@326
   691
deba@326
   692
    NodePotential* _node_potential;
deba@326
   693
deba@326
   694
    BlossomPotential _blossom_potential;
deba@326
   695
    BlossomNodeList _blossom_node_list;
deba@326
   696
deba@326
   697
    int _node_num;
deba@326
   698
    int _blossom_num;
deba@326
   699
deba@326
   700
    typedef RangeMap<int> IntIntMap;
deba@326
   701
deba@326
   702
    enum Status {
deba@326
   703
      EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2
deba@326
   704
    };
deba@326
   705
deba@327
   706
    typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
deba@326
   707
    struct BlossomData {
deba@326
   708
      int tree;
deba@326
   709
      Status status;
deba@326
   710
      Arc pred, next;
deba@326
   711
      Value pot, offset;
deba@326
   712
      Node base;
deba@326
   713
    };
deba@326
   714
deba@327
   715
    IntNodeMap *_blossom_index;
deba@326
   716
    BlossomSet *_blossom_set;
deba@326
   717
    RangeMap<BlossomData>* _blossom_data;
deba@326
   718
deba@327
   719
    IntNodeMap *_node_index;
deba@327
   720
    IntArcMap *_node_heap_index;
deba@326
   721
deba@326
   722
    struct NodeData {
deba@326
   723
deba@327
   724
      NodeData(IntArcMap& node_heap_index)
deba@326
   725
        : heap(node_heap_index) {}
deba@326
   726
deba@326
   727
      int blossom;
deba@326
   728
      Value pot;
deba@327
   729
      BinHeap<Value, IntArcMap> heap;
deba@326
   730
      std::map<int, Arc> heap_index;
deba@326
   731
deba@326
   732
      int tree;
deba@326
   733
    };
deba@326
   734
deba@326
   735
    RangeMap<NodeData>* _node_data;
deba@326
   736
deba@326
   737
    typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@326
   738
deba@326
   739
    IntIntMap *_tree_set_index;
deba@326
   740
    TreeSet *_tree_set;
deba@326
   741
deba@327
   742
    IntNodeMap *_delta1_index;
deba@327
   743
    BinHeap<Value, IntNodeMap> *_delta1;
deba@326
   744
deba@326
   745
    IntIntMap *_delta2_index;
deba@326
   746
    BinHeap<Value, IntIntMap> *_delta2;
deba@326
   747
deba@327
   748
    IntEdgeMap *_delta3_index;
deba@327
   749
    BinHeap<Value, IntEdgeMap> *_delta3;
deba@326
   750
deba@326
   751
    IntIntMap *_delta4_index;
deba@326
   752
    BinHeap<Value, IntIntMap> *_delta4;
deba@326
   753
deba@326
   754
    Value _delta_sum;
deba@326
   755
deba@326
   756
    void createStructures() {
deba@326
   757
      _node_num = countNodes(_graph);
deba@326
   758
      _blossom_num = _node_num * 3 / 2;
deba@326
   759
deba@326
   760
      if (!_matching) {
deba@326
   761
        _matching = new MatchingMap(_graph);
deba@326
   762
      }
deba@326
   763
      if (!_node_potential) {
deba@326
   764
        _node_potential = new NodePotential(_graph);
deba@326
   765
      }
deba@326
   766
      if (!_blossom_set) {
deba@327
   767
        _blossom_index = new IntNodeMap(_graph);
deba@326
   768
        _blossom_set = new BlossomSet(*_blossom_index);
deba@326
   769
        _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@326
   770
      }
deba@326
   771
deba@326
   772
      if (!_node_index) {
deba@327
   773
        _node_index = new IntNodeMap(_graph);
deba@327
   774
        _node_heap_index = new IntArcMap(_graph);
deba@326
   775
        _node_data = new RangeMap<NodeData>(_node_num,
deba@326
   776
                                              NodeData(*_node_heap_index));
deba@326
   777
      }
deba@326
   778
deba@326
   779
      if (!_tree_set) {
deba@326
   780
        _tree_set_index = new IntIntMap(_blossom_num);
deba@326
   781
        _tree_set = new TreeSet(*_tree_set_index);
deba@326
   782
      }
deba@326
   783
      if (!_delta1) {
deba@327
   784
        _delta1_index = new IntNodeMap(_graph);
deba@327
   785
        _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index);
deba@326
   786
      }
deba@326
   787
      if (!_delta2) {
deba@326
   788
        _delta2_index = new IntIntMap(_blossom_num);
deba@326
   789
        _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@326
   790
      }
deba@326
   791
      if (!_delta3) {
deba@327
   792
        _delta3_index = new IntEdgeMap(_graph);
deba@327
   793
        _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
deba@326
   794
      }
deba@326
   795
      if (!_delta4) {
deba@326
   796
        _delta4_index = new IntIntMap(_blossom_num);
deba@326
   797
        _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@326
   798
      }
deba@326
   799
    }
deba@326
   800
deba@326
   801
    void destroyStructures() {
deba@326
   802
      _node_num = countNodes(_graph);
deba@326
   803
      _blossom_num = _node_num * 3 / 2;
deba@326
   804
deba@326
   805
      if (_matching) {
deba@326
   806
        delete _matching;
deba@326
   807
      }
deba@326
   808
      if (_node_potential) {
deba@326
   809
        delete _node_potential;
deba@326
   810
      }
deba@326
   811
      if (_blossom_set) {
deba@326
   812
        delete _blossom_index;
deba@326
   813
        delete _blossom_set;
deba@326
   814
        delete _blossom_data;
deba@326
   815
      }
deba@326
   816
deba@326
   817
      if (_node_index) {
deba@326
   818
        delete _node_index;
deba@326
   819
        delete _node_heap_index;
deba@326
   820
        delete _node_data;
deba@326
   821
      }
deba@326
   822
deba@326
   823
      if (_tree_set) {
deba@326
   824
        delete _tree_set_index;
deba@326
   825
        delete _tree_set;
deba@326
   826
      }
deba@326
   827
      if (_delta1) {
deba@326
   828
        delete _delta1_index;
deba@326
   829
        delete _delta1;
deba@326
   830
      }
deba@326
   831
      if (_delta2) {
deba@326
   832
        delete _delta2_index;
deba@326
   833
        delete _delta2;
deba@326
   834
      }
deba@326
   835
      if (_delta3) {
deba@326
   836
        delete _delta3_index;
deba@326
   837
        delete _delta3;
deba@326
   838
      }
deba@326
   839
      if (_delta4) {
deba@326
   840
        delete _delta4_index;
deba@326
   841
        delete _delta4;
deba@326
   842
      }
deba@326
   843
    }
deba@326
   844
deba@326
   845
    void matchedToEven(int blossom, int tree) {
deba@326
   846
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
   847
        _delta2->erase(blossom);
deba@326
   848
      }
deba@326
   849
deba@326
   850
      if (!_blossom_set->trivial(blossom)) {
deba@326
   851
        (*_blossom_data)[blossom].pot -=
deba@326
   852
          2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@326
   853
      }
deba@326
   854
deba@326
   855
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
   856
           n != INVALID; ++n) {
deba@326
   857
deba@326
   858
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
   859
        int ni = (*_node_index)[n];
deba@326
   860
deba@326
   861
        (*_node_data)[ni].heap.clear();
deba@326
   862
        (*_node_data)[ni].heap_index.clear();
deba@326
   863
deba@326
   864
        (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@326
   865
deba@326
   866
        _delta1->push(n, (*_node_data)[ni].pot);
deba@326
   867
deba@326
   868
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
   869
          Node v = _graph.source(e);
deba@326
   870
          int vb = _blossom_set->find(v);
deba@326
   871
          int vi = (*_node_index)[v];
deba@326
   872
deba@326
   873
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
   874
            dualScale * _weight[e];
deba@326
   875
deba@326
   876
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
   877
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326
   878
              _delta3->push(e, rw / 2);
deba@326
   879
            }
deba@326
   880
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326
   881
            if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@326
   882
              _delta3->push(e, rw);
deba@326
   883
            }
deba@326
   884
          } else {
deba@326
   885
            typename std::map<int, Arc>::iterator it =
deba@326
   886
              (*_node_data)[vi].heap_index.find(tree);
deba@326
   887
deba@326
   888
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
   889
              if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326
   890
                (*_node_data)[vi].heap.replace(it->second, e);
deba@326
   891
                (*_node_data)[vi].heap.decrease(e, rw);
deba@326
   892
                it->second = e;
deba@326
   893
              }
deba@326
   894
            } else {
deba@326
   895
              (*_node_data)[vi].heap.push(e, rw);
deba@326
   896
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326
   897
            }
deba@326
   898
deba@326
   899
            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326
   900
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326
   901
deba@326
   902
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
   903
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326
   904
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326
   905
                               (*_blossom_data)[vb].offset);
deba@326
   906
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326
   907
                           (*_blossom_data)[vb].offset){
deba@326
   908
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326
   909
                                   (*_blossom_data)[vb].offset);
deba@326
   910
                }
deba@326
   911
              }
deba@326
   912
            }
deba@326
   913
          }
deba@326
   914
        }
deba@326
   915
      }
deba@326
   916
      (*_blossom_data)[blossom].offset = 0;
deba@326
   917
    }
deba@326
   918
deba@326
   919
    void matchedToOdd(int blossom) {
deba@326
   920
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
   921
        _delta2->erase(blossom);
deba@326
   922
      }
deba@326
   923
      (*_blossom_data)[blossom].offset += _delta_sum;
deba@326
   924
      if (!_blossom_set->trivial(blossom)) {
deba@326
   925
        _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
deba@326
   926
                     (*_blossom_data)[blossom].offset);
deba@326
   927
      }
deba@326
   928
    }
deba@326
   929
deba@326
   930
    void evenToMatched(int blossom, int tree) {
deba@326
   931
      if (!_blossom_set->trivial(blossom)) {
deba@326
   932
        (*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@326
   933
      }
deba@326
   934
deba@326
   935
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
   936
           n != INVALID; ++n) {
deba@326
   937
        int ni = (*_node_index)[n];
deba@326
   938
        (*_node_data)[ni].pot -= _delta_sum;
deba@326
   939
deba@326
   940
        _delta1->erase(n);
deba@326
   941
deba@326
   942
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
   943
          Node v = _graph.source(e);
deba@326
   944
          int vb = _blossom_set->find(v);
deba@326
   945
          int vi = (*_node_index)[v];
deba@326
   946
deba@326
   947
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
   948
            dualScale * _weight[e];
deba@326
   949
deba@326
   950
          if (vb == blossom) {
deba@326
   951
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
   952
              _delta3->erase(e);
deba@326
   953
            }
deba@326
   954
          } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326
   955
deba@326
   956
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
   957
              _delta3->erase(e);
deba@326
   958
            }
deba@326
   959
deba@326
   960
            int vt = _tree_set->find(vb);
deba@326
   961
deba@326
   962
            if (vt != tree) {
deba@326
   963
deba@326
   964
              Arc r = _graph.oppositeArc(e);
deba@326
   965
deba@326
   966
              typename std::map<int, Arc>::iterator it =
deba@326
   967
                (*_node_data)[ni].heap_index.find(vt);
deba@326
   968
deba@326
   969
              if (it != (*_node_data)[ni].heap_index.end()) {
deba@326
   970
                if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326
   971
                  (*_node_data)[ni].heap.replace(it->second, r);
deba@326
   972
                  (*_node_data)[ni].heap.decrease(r, rw);
deba@326
   973
                  it->second = r;
deba@326
   974
                }
deba@326
   975
              } else {
deba@326
   976
                (*_node_data)[ni].heap.push(r, rw);
deba@326
   977
                (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326
   978
              }
deba@326
   979
deba@326
   980
              if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326
   981
                _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326
   982
deba@326
   983
                if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326
   984
                  _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
   985
                               (*_blossom_data)[blossom].offset);
deba@326
   986
                } else if ((*_delta2)[blossom] >
deba@326
   987
                           _blossom_set->classPrio(blossom) -
deba@326
   988
                           (*_blossom_data)[blossom].offset){
deba@326
   989
                  _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326
   990
                                   (*_blossom_data)[blossom].offset);
deba@326
   991
                }
deba@326
   992
              }
deba@326
   993
            }
deba@326
   994
deba@326
   995
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326
   996
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
   997
              _delta3->erase(e);
deba@326
   998
            }
deba@326
   999
          } else {
deba@326
  1000
deba@326
  1001
            typename std::map<int, Arc>::iterator it =
deba@326
  1002
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  1003
deba@326
  1004
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  1005
              (*_node_data)[vi].heap.erase(it->second);
deba@326
  1006
              (*_node_data)[vi].heap_index.erase(it);
deba@326
  1007
              if ((*_node_data)[vi].heap.empty()) {
deba@326
  1008
                _blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@326
  1009
              } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@326
  1010
                _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@326
  1011
              }
deba@326
  1012
deba@326
  1013
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  1014
                if (_blossom_set->classPrio(vb) ==
deba@326
  1015
                    std::numeric_limits<Value>::max()) {
deba@326
  1016
                  _delta2->erase(vb);
deba@326
  1017
                } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@326
  1018
                           (*_blossom_data)[vb].offset) {
deba@326
  1019
                  _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@326
  1020
                                   (*_blossom_data)[vb].offset);
deba@326
  1021
                }
deba@326
  1022
              }
deba@326
  1023
            }
deba@326
  1024
          }
deba@326
  1025
        }
deba@326
  1026
      }
deba@326
  1027
    }
deba@326
  1028
deba@326
  1029
    void oddToMatched(int blossom) {
deba@326
  1030
      (*_blossom_data)[blossom].offset -= _delta_sum;
deba@326
  1031
deba@326
  1032
      if (_blossom_set->classPrio(blossom) !=
deba@326
  1033
          std::numeric_limits<Value>::max()) {
deba@326
  1034
        _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
  1035
                       (*_blossom_data)[blossom].offset);
deba@326
  1036
      }
deba@326
  1037
deba@326
  1038
      if (!_blossom_set->trivial(blossom)) {
deba@326
  1039
        _delta4->erase(blossom);
deba@326
  1040
      }
deba@326
  1041
    }
deba@326
  1042
deba@326
  1043
    void oddToEven(int blossom, int tree) {
deba@326
  1044
      if (!_blossom_set->trivial(blossom)) {
deba@326
  1045
        _delta4->erase(blossom);
deba@326
  1046
        (*_blossom_data)[blossom].pot -=
deba@326
  1047
          2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@326
  1048
      }
deba@326
  1049
deba@326
  1050
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  1051
           n != INVALID; ++n) {
deba@326
  1052
        int ni = (*_node_index)[n];
deba@326
  1053
deba@326
  1054
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
  1055
deba@326
  1056
        (*_node_data)[ni].heap.clear();
deba@326
  1057
        (*_node_data)[ni].heap_index.clear();
deba@326
  1058
        (*_node_data)[ni].pot +=
deba@326
  1059
          2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@326
  1060
deba@326
  1061
        _delta1->push(n, (*_node_data)[ni].pot);
deba@326
  1062
deba@326
  1063
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  1064
          Node v = _graph.source(e);
deba@326
  1065
          int vb = _blossom_set->find(v);
deba@326
  1066
          int vi = (*_node_index)[v];
deba@326
  1067
deba@326
  1068
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  1069
            dualScale * _weight[e];
deba@326
  1070
deba@326
  1071
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  1072
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326
  1073
              _delta3->push(e, rw / 2);
deba@326
  1074
            }
deba@326
  1075
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326
  1076
            if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@326
  1077
              _delta3->push(e, rw);
deba@326
  1078
            }
deba@326
  1079
          } else {
deba@326
  1080
deba@326
  1081
            typename std::map<int, Arc>::iterator it =
deba@326
  1082
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  1083
deba@326
  1084
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  1085
              if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326
  1086
                (*_node_data)[vi].heap.replace(it->second, e);
deba@326
  1087
                (*_node_data)[vi].heap.decrease(e, rw);
deba@326
  1088
                it->second = e;
deba@326
  1089
              }
deba@326
  1090
            } else {
deba@326
  1091
              (*_node_data)[vi].heap.push(e, rw);
deba@326
  1092
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326
  1093
            }
deba@326
  1094
deba@326
  1095
            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326
  1096
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326
  1097
deba@326
  1098
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  1099
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326
  1100
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326
  1101
                               (*_blossom_data)[vb].offset);
deba@326
  1102
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326
  1103
                           (*_blossom_data)[vb].offset) {
deba@326
  1104
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326
  1105
                                   (*_blossom_data)[vb].offset);
deba@326
  1106
                }
deba@326
  1107
              }
deba@326
  1108
            }
deba@326
  1109
          }
deba@326
  1110
        }
deba@326
  1111
      }
deba@326
  1112
      (*_blossom_data)[blossom].offset = 0;
deba@326
  1113
    }
deba@326
  1114
deba@326
  1115
deba@326
  1116
    void matchedToUnmatched(int blossom) {
deba@326
  1117
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  1118
        _delta2->erase(blossom);
deba@326
  1119
      }
deba@326
  1120
deba@326
  1121
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  1122
           n != INVALID; ++n) {
deba@326
  1123
        int ni = (*_node_index)[n];
deba@326
  1124
deba@326
  1125
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
  1126
deba@326
  1127
        (*_node_data)[ni].heap.clear();
deba@326
  1128
        (*_node_data)[ni].heap_index.clear();
deba@326
  1129
deba@326
  1130
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  1131
          Node v = _graph.target(e);
deba@326
  1132
          int vb = _blossom_set->find(v);
deba@326
  1133
          int vi = (*_node_index)[v];
deba@326
  1134
deba@326
  1135
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  1136
            dualScale * _weight[e];
deba@326
  1137
deba@326
  1138
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  1139
            if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@326
  1140
              _delta3->push(e, rw);
deba@326
  1141
            }
deba@326
  1142
          }
deba@326
  1143
        }
deba@326
  1144
      }
deba@326
  1145
    }
deba@326
  1146
deba@326
  1147
    void unmatchedToMatched(int blossom) {
deba@326
  1148
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  1149
           n != INVALID; ++n) {
deba@326
  1150
        int ni = (*_node_index)[n];
deba@326
  1151
deba@326
  1152
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  1153
          Node v = _graph.source(e);
deba@326
  1154
          int vb = _blossom_set->find(v);
deba@326
  1155
          int vi = (*_node_index)[v];
deba@326
  1156
deba@326
  1157
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  1158
            dualScale * _weight[e];
deba@326
  1159
deba@326
  1160
          if (vb == blossom) {
deba@326
  1161
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  1162
              _delta3->erase(e);
deba@326
  1163
            }
deba@326
  1164
          } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  1165
deba@326
  1166
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  1167
              _delta3->erase(e);
deba@326
  1168
            }
deba@326
  1169
deba@326
  1170
            int vt = _tree_set->find(vb);
deba@326
  1171
deba@326
  1172
            Arc r = _graph.oppositeArc(e);
deba@326
  1173
deba@326
  1174
            typename std::map<int, Arc>::iterator it =
deba@326
  1175
              (*_node_data)[ni].heap_index.find(vt);
deba@326
  1176
deba@326
  1177
            if (it != (*_node_data)[ni].heap_index.end()) {
deba@326
  1178
              if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326
  1179
                (*_node_data)[ni].heap.replace(it->second, r);
deba@326
  1180
                (*_node_data)[ni].heap.decrease(r, rw);
deba@326
  1181
                it->second = r;
deba@326
  1182
              }
deba@326
  1183
            } else {
deba@326
  1184
              (*_node_data)[ni].heap.push(r, rw);
deba@326
  1185
              (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326
  1186
            }
deba@326
  1187
deba@326
  1188
            if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326
  1189
              _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326
  1190
deba@326
  1191
              if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326
  1192
                _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
  1193
                             (*_blossom_data)[blossom].offset);
deba@326
  1194
              } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)-
deba@326
  1195
                         (*_blossom_data)[blossom].offset){
deba@326
  1196
                _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326
  1197
                                 (*_blossom_data)[blossom].offset);
deba@326
  1198
              }
deba@326
  1199
            }
deba@326
  1200
deba@326
  1201
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326
  1202
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  1203
              _delta3->erase(e);
deba@326
  1204
            }
deba@326
  1205
          }
deba@326
  1206
        }
deba@326
  1207
      }
deba@326
  1208
    }
deba@326
  1209
deba@326
  1210
    void alternatePath(int even, int tree) {
deba@326
  1211
      int odd;
deba@326
  1212
deba@326
  1213
      evenToMatched(even, tree);
deba@326
  1214
      (*_blossom_data)[even].status = MATCHED;
deba@326
  1215
deba@326
  1216
      while ((*_blossom_data)[even].pred != INVALID) {
deba@326
  1217
        odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
deba@326
  1218
        (*_blossom_data)[odd].status = MATCHED;
deba@326
  1219
        oddToMatched(odd);
deba@326
  1220
        (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@326
  1221
deba@326
  1222
        even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
deba@326
  1223
        (*_blossom_data)[even].status = MATCHED;
deba@326
  1224
        evenToMatched(even, tree);
deba@326
  1225
        (*_blossom_data)[even].next =
deba@326
  1226
          _graph.oppositeArc((*_blossom_data)[odd].pred);
deba@326
  1227
      }
deba@326
  1228
deba@326
  1229
    }
deba@326
  1230
deba@326
  1231
    void destroyTree(int tree) {
deba@326
  1232
      for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@326
  1233
        if ((*_blossom_data)[b].status == EVEN) {
deba@326
  1234
          (*_blossom_data)[b].status = MATCHED;
deba@326
  1235
          evenToMatched(b, tree);
deba@326
  1236
        } else if ((*_blossom_data)[b].status == ODD) {
deba@326
  1237
          (*_blossom_data)[b].status = MATCHED;
deba@326
  1238
          oddToMatched(b);
deba@326
  1239
        }
deba@326
  1240
      }
deba@326
  1241
      _tree_set->eraseClass(tree);
deba@326
  1242
    }
deba@326
  1243
deba@326
  1244
deba@326
  1245
    void unmatchNode(const Node& node) {
deba@326
  1246
      int blossom = _blossom_set->find(node);
deba@326
  1247
      int tree = _tree_set->find(blossom);
deba@326
  1248
deba@326
  1249
      alternatePath(blossom, tree);
deba@326
  1250
      destroyTree(tree);
deba@326
  1251
deba@326
  1252
      (*_blossom_data)[blossom].status = UNMATCHED;
deba@326
  1253
      (*_blossom_data)[blossom].base = node;
deba@326
  1254
      matchedToUnmatched(blossom);
deba@326
  1255
    }
deba@326
  1256
deba@326
  1257
deba@327
  1258
    void augmentOnEdge(const Edge& edge) {
deba@327
  1259
deba@327
  1260
      int left = _blossom_set->find(_graph.u(edge));
deba@327
  1261
      int right = _blossom_set->find(_graph.v(edge));
deba@326
  1262
deba@326
  1263
      if ((*_blossom_data)[left].status == EVEN) {
deba@326
  1264
        int left_tree = _tree_set->find(left);
deba@326
  1265
        alternatePath(left, left_tree);
deba@326
  1266
        destroyTree(left_tree);
deba@326
  1267
      } else {
deba@326
  1268
        (*_blossom_data)[left].status = MATCHED;
deba@326
  1269
        unmatchedToMatched(left);
deba@326
  1270
      }
deba@326
  1271
deba@326
  1272
      if ((*_blossom_data)[right].status == EVEN) {
deba@326
  1273
        int right_tree = _tree_set->find(right);
deba@326
  1274
        alternatePath(right, right_tree);
deba@326
  1275
        destroyTree(right_tree);
deba@326
  1276
      } else {
deba@326
  1277
        (*_blossom_data)[right].status = MATCHED;
deba@326
  1278
        unmatchedToMatched(right);
deba@326
  1279
      }
deba@326
  1280
deba@327
  1281
      (*_blossom_data)[left].next = _graph.direct(edge, true);
deba@327
  1282
      (*_blossom_data)[right].next = _graph.direct(edge, false);
deba@326
  1283
    }
deba@326
  1284
deba@326
  1285
    void extendOnArc(const Arc& arc) {
deba@326
  1286
      int base = _blossom_set->find(_graph.target(arc));
deba@326
  1287
      int tree = _tree_set->find(base);
deba@326
  1288
deba@326
  1289
      int odd = _blossom_set->find(_graph.source(arc));
deba@326
  1290
      _tree_set->insert(odd, tree);
deba@326
  1291
      (*_blossom_data)[odd].status = ODD;
deba@326
  1292
      matchedToOdd(odd);
deba@326
  1293
      (*_blossom_data)[odd].pred = arc;
deba@326
  1294
deba@326
  1295
      int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
deba@326
  1296
      (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@326
  1297
      _tree_set->insert(even, tree);
deba@326
  1298
      (*_blossom_data)[even].status = EVEN;
deba@326
  1299
      matchedToEven(even, tree);
deba@326
  1300
    }
deba@326
  1301
deba@327
  1302
    void shrinkOnEdge(const Edge& edge, int tree) {
deba@326
  1303
      int nca = -1;
deba@326
  1304
      std::vector<int> left_path, right_path;
deba@326
  1305
deba@326
  1306
      {
deba@326
  1307
        std::set<int> left_set, right_set;
deba@326
  1308
        int left = _blossom_set->find(_graph.u(edge));
deba@326
  1309
        left_path.push_back(left);
deba@326
  1310
        left_set.insert(left);
deba@326
  1311
deba@326
  1312
        int right = _blossom_set->find(_graph.v(edge));
deba@326
  1313
        right_path.push_back(right);
deba@326
  1314
        right_set.insert(right);
deba@326
  1315
deba@326
  1316
        while (true) {
deba@326
  1317
deba@326
  1318
          if ((*_blossom_data)[left].pred == INVALID) break;
deba@326
  1319
deba@326
  1320
          left =
deba@326
  1321
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326
  1322
          left_path.push_back(left);
deba@326
  1323
          left =
deba@326
  1324
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326
  1325
          left_path.push_back(left);
deba@326
  1326
deba@326
  1327
          left_set.insert(left);
deba@326
  1328
deba@326
  1329
          if (right_set.find(left) != right_set.end()) {
deba@326
  1330
            nca = left;
deba@326
  1331
            break;
deba@326
  1332
          }
deba@326
  1333
deba@326
  1334
          if ((*_blossom_data)[right].pred == INVALID) break;
deba@326
  1335
deba@326
  1336
          right =
deba@326
  1337
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326
  1338
          right_path.push_back(right);
deba@326
  1339
          right =
deba@326
  1340
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326
  1341
          right_path.push_back(right);
deba@326
  1342
deba@326
  1343
          right_set.insert(right);
deba@326
  1344
deba@326
  1345
          if (left_set.find(right) != left_set.end()) {
deba@326
  1346
            nca = right;
deba@326
  1347
            break;
deba@326
  1348
          }
deba@326
  1349
deba@326
  1350
        }
deba@326
  1351
deba@326
  1352
        if (nca == -1) {
deba@326
  1353
          if ((*_blossom_data)[left].pred == INVALID) {
deba@326
  1354
            nca = right;
deba@326
  1355
            while (left_set.find(nca) == left_set.end()) {
deba@326
  1356
              nca =
deba@326
  1357
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  1358
              right_path.push_back(nca);
deba@326
  1359
              nca =
deba@326
  1360
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  1361
              right_path.push_back(nca);
deba@326
  1362
            }
deba@326
  1363
          } else {
deba@326
  1364
            nca = left;
deba@326
  1365
            while (right_set.find(nca) == right_set.end()) {
deba@326
  1366
              nca =
deba@326
  1367
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  1368
              left_path.push_back(nca);
deba@326
  1369
              nca =
deba@326
  1370
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  1371
              left_path.push_back(nca);
deba@326
  1372
            }
deba@326
  1373
          }
deba@326
  1374
        }
deba@326
  1375
      }
deba@326
  1376
deba@326
  1377
      std::vector<int> subblossoms;
deba@326
  1378
      Arc prev;
deba@326
  1379
deba@326
  1380
      prev = _graph.direct(edge, true);
deba@326
  1381
      for (int i = 0; left_path[i] != nca; i += 2) {
deba@326
  1382
        subblossoms.push_back(left_path[i]);
deba@326
  1383
        (*_blossom_data)[left_path[i]].next = prev;
deba@326
  1384
        _tree_set->erase(left_path[i]);
deba@326
  1385
deba@326
  1386
        subblossoms.push_back(left_path[i + 1]);
deba@326
  1387
        (*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@326
  1388
        oddToEven(left_path[i + 1], tree);
deba@326
  1389
        _tree_set->erase(left_path[i + 1]);
deba@326
  1390
        prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
deba@326
  1391
      }
deba@326
  1392
deba@326
  1393
      int k = 0;
deba@326
  1394
      while (right_path[k] != nca) ++k;
deba@326
  1395
deba@326
  1396
      subblossoms.push_back(nca);
deba@326
  1397
      (*_blossom_data)[nca].next = prev;
deba@326
  1398
deba@326
  1399
      for (int i = k - 2; i >= 0; i -= 2) {
deba@326
  1400
        subblossoms.push_back(right_path[i + 1]);
deba@326
  1401
        (*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@326
  1402
        oddToEven(right_path[i + 1], tree);
deba@326
  1403
        _tree_set->erase(right_path[i + 1]);
deba@326
  1404
deba@326
  1405
        (*_blossom_data)[right_path[i + 1]].next =
deba@326
  1406
          (*_blossom_data)[right_path[i + 1]].pred;
deba@326
  1407
deba@326
  1408
        subblossoms.push_back(right_path[i]);
deba@326
  1409
        _tree_set->erase(right_path[i]);
deba@326
  1410
      }
deba@326
  1411
deba@326
  1412
      int surface =
deba@326
  1413
        _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@326
  1414
deba@326
  1415
      for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  1416
        if (!_blossom_set->trivial(subblossoms[i])) {
deba@326
  1417
          (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@326
  1418
        }
deba@326
  1419
        (*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@326
  1420
      }
deba@326
  1421
deba@326
  1422
      (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@326
  1423
      (*_blossom_data)[surface].offset = 0;
deba@326
  1424
      (*_blossom_data)[surface].status = EVEN;
deba@326
  1425
      (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@326
  1426
      (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@326
  1427
deba@326
  1428
      _tree_set->insert(surface, tree);
deba@326
  1429
      _tree_set->erase(nca);
deba@326
  1430
    }
deba@326
  1431
deba@326
  1432
    void splitBlossom(int blossom) {
deba@326
  1433
      Arc next = (*_blossom_data)[blossom].next;
deba@326
  1434
      Arc pred = (*_blossom_data)[blossom].pred;
deba@326
  1435
deba@326
  1436
      int tree = _tree_set->find(blossom);
deba@326
  1437
deba@326
  1438
      (*_blossom_data)[blossom].status = MATCHED;
deba@326
  1439
      oddToMatched(blossom);
deba@326
  1440
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  1441
        _delta2->erase(blossom);
deba@326
  1442
      }
deba@326
  1443
deba@326
  1444
      std::vector<int> subblossoms;
deba@326
  1445
      _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326
  1446
deba@326
  1447
      Value offset = (*_blossom_data)[blossom].offset;
deba@326
  1448
      int b = _blossom_set->find(_graph.source(pred));
deba@326
  1449
      int d = _blossom_set->find(_graph.source(next));
deba@326
  1450
deba@326
  1451
      int ib = -1, id = -1;
deba@326
  1452
      for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  1453
        if (subblossoms[i] == b) ib = i;
deba@326
  1454
        if (subblossoms[i] == d) id = i;
deba@326
  1455
deba@326
  1456
        (*_blossom_data)[subblossoms[i]].offset = offset;
deba@326
  1457
        if (!_blossom_set->trivial(subblossoms[i])) {
deba@326
  1458
          (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@326
  1459
        }
deba@326
  1460
        if (_blossom_set->classPrio(subblossoms[i]) !=
deba@326
  1461
            std::numeric_limits<Value>::max()) {
deba@326
  1462
          _delta2->push(subblossoms[i],
deba@326
  1463
                        _blossom_set->classPrio(subblossoms[i]) -
deba@326
  1464
                        (*_blossom_data)[subblossoms[i]].offset);
deba@326
  1465
        }
deba@326
  1466
      }
deba@326
  1467
deba@326
  1468
      if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@326
  1469
        for (int i = (id + 1) % subblossoms.size();
deba@326
  1470
             i != ib; i = (i + 2) % subblossoms.size()) {
deba@326
  1471
          int sb = subblossoms[i];
deba@326
  1472
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  1473
          (*_blossom_data)[sb].next =
deba@326
  1474
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  1475
        }
deba@326
  1476
deba@326
  1477
        for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@326
  1478
          int sb = subblossoms[i];
deba@326
  1479
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  1480
          int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326
  1481
deba@326
  1482
          (*_blossom_data)[sb].status = ODD;
deba@326
  1483
          matchedToOdd(sb);
deba@326
  1484
          _tree_set->insert(sb, tree);
deba@326
  1485
          (*_blossom_data)[sb].pred = pred;
deba@326
  1486
          (*_blossom_data)[sb].next =
deba@326
  1487
                           _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  1488
deba@326
  1489
          pred = (*_blossom_data)[ub].next;
deba@326
  1490
deba@326
  1491
          (*_blossom_data)[tb].status = EVEN;
deba@326
  1492
          matchedToEven(tb, tree);
deba@326
  1493
          _tree_set->insert(tb, tree);
deba@326
  1494
          (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@326
  1495
        }
deba@326
  1496
deba@326
  1497
        (*_blossom_data)[subblossoms[id]].status = ODD;
deba@326
  1498
        matchedToOdd(subblossoms[id]);
deba@326
  1499
        _tree_set->insert(subblossoms[id], tree);
deba@326
  1500
        (*_blossom_data)[subblossoms[id]].next = next;
deba@326
  1501
        (*_blossom_data)[subblossoms[id]].pred = pred;
deba@326
  1502
deba@326
  1503
      } else {
deba@326
  1504
deba@326
  1505
        for (int i = (ib + 1) % subblossoms.size();
deba@326
  1506
             i != id; i = (i + 2) % subblossoms.size()) {
deba@326
  1507
          int sb = subblossoms[i];
deba@326
  1508
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  1509
          (*_blossom_data)[sb].next =
deba@326
  1510
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  1511
        }
deba@326
  1512
deba@326
  1513
        for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@326
  1514
          int sb = subblossoms[i];
deba@326
  1515
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  1516
          int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326
  1517
deba@326
  1518
          (*_blossom_data)[sb].status = ODD;
deba@326
  1519
          matchedToOdd(sb);
deba@326
  1520
          _tree_set->insert(sb, tree);
deba@326
  1521
          (*_blossom_data)[sb].next = next;
deba@326
  1522
          (*_blossom_data)[sb].pred =
deba@326
  1523
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  1524
deba@326
  1525
          (*_blossom_data)[tb].status = EVEN;
deba@326
  1526
          matchedToEven(tb, tree);
deba@326
  1527
          _tree_set->insert(tb, tree);
deba@326
  1528
          (*_blossom_data)[tb].pred =
deba@326
  1529
            (*_blossom_data)[tb].next =
deba@326
  1530
            _graph.oppositeArc((*_blossom_data)[ub].next);
deba@326
  1531
          next = (*_blossom_data)[ub].next;
deba@326
  1532
        }
deba@326
  1533
deba@326
  1534
        (*_blossom_data)[subblossoms[ib]].status = ODD;
deba@326
  1535
        matchedToOdd(subblossoms[ib]);
deba@326
  1536
        _tree_set->insert(subblossoms[ib], tree);
deba@326
  1537
        (*_blossom_data)[subblossoms[ib]].next = next;
deba@326
  1538
        (*_blossom_data)[subblossoms[ib]].pred = pred;
deba@326
  1539
      }
deba@326
  1540
      _tree_set->erase(blossom);
deba@326
  1541
    }
deba@326
  1542
deba@326
  1543
    void extractBlossom(int blossom, const Node& base, const Arc& matching) {
deba@326
  1544
      if (_blossom_set->trivial(blossom)) {
deba@326
  1545
        int bi = (*_node_index)[base];
deba@326
  1546
        Value pot = (*_node_data)[bi].pot;
deba@326
  1547
deba@326
  1548
        _matching->set(base, matching);
deba@326
  1549
        _blossom_node_list.push_back(base);
deba@326
  1550
        _node_potential->set(base, pot);
deba@326
  1551
      } else {
deba@326
  1552
deba@326
  1553
        Value pot = (*_blossom_data)[blossom].pot;
deba@326
  1554
        int bn = _blossom_node_list.size();
deba@326
  1555
deba@326
  1556
        std::vector<int> subblossoms;
deba@326
  1557
        _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326
  1558
        int b = _blossom_set->find(base);
deba@326
  1559
        int ib = -1;
deba@326
  1560
        for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  1561
          if (subblossoms[i] == b) { ib = i; break; }
deba@326
  1562
        }
deba@326
  1563
deba@326
  1564
        for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@326
  1565
          int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@326
  1566
          int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@326
  1567
deba@326
  1568
          Arc m = (*_blossom_data)[tb].next;
deba@326
  1569
          extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
deba@326
  1570
          extractBlossom(tb, _graph.source(m), m);
deba@326
  1571
        }
deba@326
  1572
        extractBlossom(subblossoms[ib], base, matching);
deba@326
  1573
deba@326
  1574
        int en = _blossom_node_list.size();
deba@326
  1575
deba@326
  1576
        _blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@326
  1577
      }
deba@326
  1578
    }
deba@326
  1579
deba@326
  1580
    void extractMatching() {
deba@326
  1581
      std::vector<int> blossoms;
deba@326
  1582
      for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@326
  1583
        blossoms.push_back(c);
deba@326
  1584
      }
deba@326
  1585
deba@326
  1586
      for (int i = 0; i < int(blossoms.size()); ++i) {
deba@326
  1587
        if ((*_blossom_data)[blossoms[i]].status == MATCHED) {
deba@326
  1588
deba@326
  1589
          Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@326
  1590
          (*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@326
  1591
          for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
deba@326
  1592
               n != INVALID; ++n) {
deba@326
  1593
            (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@326
  1594
          }
deba@326
  1595
deba@326
  1596
          Arc matching = (*_blossom_data)[blossoms[i]].next;
deba@326
  1597
          Node base = _graph.source(matching);
deba@326
  1598
          extractBlossom(blossoms[i], base, matching);
deba@326
  1599
        } else {
deba@326
  1600
          Node base = (*_blossom_data)[blossoms[i]].base;
deba@326
  1601
          extractBlossom(blossoms[i], base, INVALID);
deba@326
  1602
        }
deba@326
  1603
      }
deba@326
  1604
    }
deba@326
  1605
deba@326
  1606
  public:
deba@326
  1607
deba@326
  1608
    /// \brief Constructor
deba@326
  1609
    ///
deba@326
  1610
    /// Constructor.
deba@326
  1611
    MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
deba@326
  1612
      : _graph(graph), _weight(weight), _matching(0),
deba@326
  1613
        _node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@326
  1614
        _node_num(0), _blossom_num(0),
deba@326
  1615
deba@326
  1616
        _blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@326
  1617
        _node_index(0), _node_heap_index(0), _node_data(0),
deba@326
  1618
        _tree_set_index(0), _tree_set(0),
deba@326
  1619
deba@326
  1620
        _delta1_index(0), _delta1(0),
deba@326
  1621
        _delta2_index(0), _delta2(0),
deba@326
  1622
        _delta3_index(0), _delta3(0),
deba@326
  1623
        _delta4_index(0), _delta4(0),
deba@326
  1624
deba@326
  1625
        _delta_sum() {}
deba@326
  1626
deba@326
  1627
    ~MaxWeightedMatching() {
deba@326
  1628
      destroyStructures();
deba@326
  1629
    }
deba@326
  1630
deba@326
  1631
    /// \name Execution control
alpar@330
  1632
    /// The simplest way to execute the algorithm is to use the
deba@326
  1633
    /// \c run() member function.
deba@326
  1634
deba@326
  1635
    ///@{
deba@326
  1636
deba@326
  1637
    /// \brief Initialize the algorithm
deba@326
  1638
    ///
deba@326
  1639
    /// Initialize the algorithm
deba@326
  1640
    void init() {
deba@326
  1641
      createStructures();
deba@326
  1642
deba@326
  1643
      for (ArcIt e(_graph); e != INVALID; ++e) {
deba@327
  1644
        _node_heap_index->set(e, BinHeap<Value, IntArcMap>::PRE_HEAP);
deba@326
  1645
      }
deba@326
  1646
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  1647
        _delta1_index->set(n, _delta1->PRE_HEAP);
deba@326
  1648
      }
deba@326
  1649
      for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326
  1650
        _delta3_index->set(e, _delta3->PRE_HEAP);
deba@326
  1651
      }
deba@326
  1652
      for (int i = 0; i < _blossom_num; ++i) {
deba@326
  1653
        _delta2_index->set(i, _delta2->PRE_HEAP);
deba@326
  1654
        _delta4_index->set(i, _delta4->PRE_HEAP);
deba@326
  1655
      }
deba@326
  1656
deba@326
  1657
      int index = 0;
deba@326
  1658
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  1659
        Value max = 0;
deba@326
  1660
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  1661
          if (_graph.target(e) == n) continue;
deba@326
  1662
          if ((dualScale * _weight[e]) / 2 > max) {
deba@326
  1663
            max = (dualScale * _weight[e]) / 2;
deba@326
  1664
          }
deba@326
  1665
        }
deba@326
  1666
        _node_index->set(n, index);
deba@326
  1667
        (*_node_data)[index].pot = max;
deba@326
  1668
        _delta1->push(n, max);
deba@326
  1669
        int blossom =
deba@326
  1670
          _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@326
  1671
deba@326
  1672
        _tree_set->insert(blossom);
deba@326
  1673
deba@326
  1674
        (*_blossom_data)[blossom].status = EVEN;
deba@326
  1675
        (*_blossom_data)[blossom].pred = INVALID;
deba@326
  1676
        (*_blossom_data)[blossom].next = INVALID;
deba@326
  1677
        (*_blossom_data)[blossom].pot = 0;
deba@326
  1678
        (*_blossom_data)[blossom].offset = 0;
deba@326
  1679
        ++index;
deba@326
  1680
      }
deba@326
  1681
      for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326
  1682
        int si = (*_node_index)[_graph.u(e)];
deba@326
  1683
        int ti = (*_node_index)[_graph.v(e)];
deba@326
  1684
        if (_graph.u(e) != _graph.v(e)) {
deba@326
  1685
          _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@326
  1686
                            dualScale * _weight[e]) / 2);
deba@326
  1687
        }
deba@326
  1688
      }
deba@326
  1689
    }
deba@326
  1690
deba@326
  1691
    /// \brief Starts the algorithm
deba@326
  1692
    ///
deba@326
  1693
    /// Starts the algorithm
deba@326
  1694
    void start() {
deba@326
  1695
      enum OpType {
deba@326
  1696
        D1, D2, D3, D4
deba@326
  1697
      };
deba@326
  1698
deba@326
  1699
      int unmatched = _node_num;
deba@326
  1700
      while (unmatched > 0) {
deba@326
  1701
        Value d1 = !_delta1->empty() ?
deba@326
  1702
          _delta1->prio() : std::numeric_limits<Value>::max();
deba@326
  1703
deba@326
  1704
        Value d2 = !_delta2->empty() ?
deba@326
  1705
          _delta2->prio() : std::numeric_limits<Value>::max();
deba@326
  1706
deba@326
  1707
        Value d3 = !_delta3->empty() ?
deba@326
  1708
          _delta3->prio() : std::numeric_limits<Value>::max();
deba@326
  1709
deba@326
  1710
        Value d4 = !_delta4->empty() ?
deba@326
  1711
          _delta4->prio() : std::numeric_limits<Value>::max();
deba@326
  1712
deba@326
  1713
        _delta_sum = d1; OpType ot = D1;
deba@326
  1714
        if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
deba@326
  1715
        if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
deba@326
  1716
        if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@326
  1717
deba@326
  1718
deba@326
  1719
        switch (ot) {
deba@326
  1720
        case D1:
deba@326
  1721
          {
deba@326
  1722
            Node n = _delta1->top();
deba@326
  1723
            unmatchNode(n);
deba@326
  1724
            --unmatched;
deba@326
  1725
          }
deba@326
  1726
          break;
deba@326
  1727
        case D2:
deba@326
  1728
          {
deba@326
  1729
            int blossom = _delta2->top();
deba@326
  1730
            Node n = _blossom_set->classTop(blossom);
deba@326
  1731
            Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
deba@326
  1732
            extendOnArc(e);
deba@326
  1733
          }
deba@326
  1734
          break;
deba@326
  1735
        case D3:
deba@326
  1736
          {
deba@326
  1737
            Edge e = _delta3->top();
deba@326
  1738
deba@326
  1739
            int left_blossom = _blossom_set->find(_graph.u(e));
deba@326
  1740
            int right_blossom = _blossom_set->find(_graph.v(e));
deba@326
  1741
deba@326
  1742
            if (left_blossom == right_blossom) {
deba@326
  1743
              _delta3->pop();
deba@326
  1744
            } else {
deba@326
  1745
              int left_tree;
deba@326
  1746
              if ((*_blossom_data)[left_blossom].status == EVEN) {
deba@326
  1747
                left_tree = _tree_set->find(left_blossom);
deba@326
  1748
              } else {
deba@326
  1749
                left_tree = -1;
deba@326
  1750
                ++unmatched;
deba@326
  1751
              }
deba@326
  1752
              int right_tree;
deba@326
  1753
              if ((*_blossom_data)[right_blossom].status == EVEN) {
deba@326
  1754
                right_tree = _tree_set->find(right_blossom);
deba@326
  1755
              } else {
deba@326
  1756
                right_tree = -1;
deba@326
  1757
                ++unmatched;
deba@326
  1758
              }
deba@326
  1759
deba@326
  1760
              if (left_tree == right_tree) {
deba@327
  1761
                shrinkOnEdge(e, left_tree);
deba@326
  1762
              } else {
deba@327
  1763
                augmentOnEdge(e);
deba@326
  1764
                unmatched -= 2;
deba@326
  1765
              }
deba@326
  1766
            }
deba@326
  1767
          } break;
deba@326
  1768
        case D4:
deba@326
  1769
          splitBlossom(_delta4->top());
deba@326
  1770
          break;
deba@326
  1771
        }
deba@326
  1772
      }
deba@326
  1773
      extractMatching();
deba@326
  1774
    }
deba@326
  1775
deba@326
  1776
    /// \brief Runs %MaxWeightedMatching algorithm.
deba@326
  1777
    ///
deba@326
  1778
    /// This method runs the %MaxWeightedMatching algorithm.
deba@326
  1779
    ///
deba@326
  1780
    /// \note mwm.run() is just a shortcut of the following code.
deba@326
  1781
    /// \code
deba@326
  1782
    ///   mwm.init();
deba@326
  1783
    ///   mwm.start();
deba@326
  1784
    /// \endcode
deba@326
  1785
    void run() {
deba@326
  1786
      init();
deba@326
  1787
      start();
deba@326
  1788
    }
deba@326
  1789
deba@326
  1790
    /// @}
deba@326
  1791
deba@326
  1792
    /// \name Primal solution
alpar@330
  1793
    /// Functions to get the primal solution, ie. the matching.
deba@326
  1794
deba@326
  1795
    /// @{
deba@326
  1796
alpar@330
  1797
    /// \brief Returns the weight of the matching.
deba@326
  1798
    ///
alpar@330
  1799
    /// Returns the weight of the matching.
deba@326
  1800
    Value matchingValue() const {
deba@326
  1801
      Value sum = 0;
deba@326
  1802
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  1803
        if ((*_matching)[n] != INVALID) {
deba@326
  1804
          sum += _weight[(*_matching)[n]];
deba@326
  1805
        }
deba@326
  1806
      }
deba@326
  1807
      return sum /= 2;
deba@326
  1808
    }
deba@326
  1809
deba@327
  1810
    /// \brief Returns the cardinality of the matching.
deba@326
  1811
    ///
deba@327
  1812
    /// Returns the cardinality of the matching.
deba@327
  1813
    int matchingSize() const {
deba@327
  1814
      int num = 0;
deba@327
  1815
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327
  1816
        if ((*_matching)[n] != INVALID) {
deba@327
  1817
          ++num;
deba@327
  1818
        }
deba@327
  1819
      }
deba@327
  1820
      return num /= 2;
deba@327
  1821
    }
deba@327
  1822
deba@327
  1823
    /// \brief Returns true when the edge is in the matching.
deba@327
  1824
    ///
deba@327
  1825
    /// Returns true when the edge is in the matching.
deba@327
  1826
    bool matching(const Edge& edge) const {
deba@327
  1827
      return edge == (*_matching)[_graph.u(edge)];
deba@326
  1828
    }
deba@326
  1829
deba@326
  1830
    /// \brief Returns the incident matching arc.
deba@326
  1831
    ///
deba@326
  1832
    /// Returns the incident matching arc from given node. If the
deba@326
  1833
    /// node is not matched then it gives back \c INVALID.
deba@326
  1834
    Arc matching(const Node& node) const {
deba@326
  1835
      return (*_matching)[node];
deba@326
  1836
    }
deba@326
  1837
deba@326
  1838
    /// \brief Returns the mate of the node.
deba@326
  1839
    ///
deba@326
  1840
    /// Returns the adjancent node in a mathcing arc. If the node is
deba@326
  1841
    /// not matched then it gives back \c INVALID.
deba@326
  1842
    Node mate(const Node& node) const {
deba@326
  1843
      return (*_matching)[node] != INVALID ?
deba@326
  1844
        _graph.target((*_matching)[node]) : INVALID;
deba@326
  1845
    }
deba@326
  1846
deba@326
  1847
    /// @}
deba@326
  1848
deba@326
  1849
    /// \name Dual solution
alpar@330
  1850
    /// Functions to get the dual solution.
deba@326
  1851
deba@326
  1852
    /// @{
deba@326
  1853
deba@326
  1854
    /// \brief Returns the value of the dual solution.
deba@326
  1855
    ///
deba@326
  1856
    /// Returns the value of the dual solution. It should be equal to
deba@326
  1857
    /// the primal value scaled by \ref dualScale "dual scale".
deba@326
  1858
    Value dualValue() const {
deba@326
  1859
      Value sum = 0;
deba@326
  1860
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  1861
        sum += nodeValue(n);
deba@326
  1862
      }
deba@326
  1863
      for (int i = 0; i < blossomNum(); ++i) {
deba@326
  1864
        sum += blossomValue(i) * (blossomSize(i) / 2);
deba@326
  1865
      }
deba@326
  1866
      return sum;
deba@326
  1867
    }
deba@326
  1868
deba@326
  1869
    /// \brief Returns the value of the node.
deba@326
  1870
    ///
deba@326
  1871
    /// Returns the the value of the node.
deba@326
  1872
    Value nodeValue(const Node& n) const {
deba@326
  1873
      return (*_node_potential)[n];
deba@326
  1874
    }
deba@326
  1875
deba@326
  1876
    /// \brief Returns the number of the blossoms in the basis.
deba@326
  1877
    ///
deba@326
  1878
    /// Returns the number of the blossoms in the basis.
deba@326
  1879
    /// \see BlossomIt
deba@326
  1880
    int blossomNum() const {
deba@326
  1881
      return _blossom_potential.size();
deba@326
  1882
    }
deba@326
  1883
deba@326
  1884
deba@326
  1885
    /// \brief Returns the number of the nodes in the blossom.
deba@326
  1886
    ///
deba@326
  1887
    /// Returns the number of the nodes in the blossom.
deba@326
  1888
    int blossomSize(int k) const {
deba@326
  1889
      return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@326
  1890
    }
deba@326
  1891
deba@326
  1892
    /// \brief Returns the value of the blossom.
deba@326
  1893
    ///
deba@326
  1894
    /// Returns the the value of the blossom.
deba@326
  1895
    /// \see BlossomIt
deba@326
  1896
    Value blossomValue(int k) const {
deba@326
  1897
      return _blossom_potential[k].value;
deba@326
  1898
    }
deba@326
  1899
alpar@330
  1900
    /// \brief Iterator for obtaining the nodes of the blossom.
deba@326
  1901
    ///
alpar@330
  1902
    /// Iterator for obtaining the nodes of the blossom. This class
alpar@330
  1903
    /// provides a common lemon style iterator for listing a
deba@326
  1904
    /// subset of the nodes.
deba@326
  1905
    class BlossomIt {
deba@326
  1906
    public:
deba@326
  1907
deba@326
  1908
      /// \brief Constructor.
deba@326
  1909
      ///
alpar@330
  1910
      /// Constructor to get the nodes of the variable.
deba@326
  1911
      BlossomIt(const MaxWeightedMatching& algorithm, int variable)
deba@326
  1912
        : _algorithm(&algorithm)
deba@326
  1913
      {
deba@326
  1914
        _index = _algorithm->_blossom_potential[variable].begin;
deba@326
  1915
        _last = _algorithm->_blossom_potential[variable].end;
deba@326
  1916
      }
deba@326
  1917
deba@326
  1918
      /// \brief Conversion to node.
deba@326
  1919
      ///
deba@326
  1920
      /// Conversion to node.
deba@326
  1921
      operator Node() const {
deba@327
  1922
        return _algorithm->_blossom_node_list[_index];
deba@326
  1923
      }
deba@326
  1924
deba@326
  1925
      /// \brief Increment operator.
deba@326
  1926
      ///
deba@326
  1927
      /// Increment operator.
deba@326
  1928
      BlossomIt& operator++() {
deba@326
  1929
        ++_index;
deba@326
  1930
        return *this;
deba@326
  1931
      }
deba@326
  1932
deba@327
  1933
      /// \brief Validity checking
deba@327
  1934
      ///
deba@327
  1935
      /// Checks whether the iterator is invalid.
deba@327
  1936
      bool operator==(Invalid) const { return _index == _last; }
deba@327
  1937
deba@327
  1938
      /// \brief Validity checking
deba@327
  1939
      ///
deba@327
  1940
      /// Checks whether the iterator is valid.
deba@327
  1941
      bool operator!=(Invalid) const { return _index != _last; }
deba@326
  1942
deba@326
  1943
    private:
deba@326
  1944
      const MaxWeightedMatching* _algorithm;
deba@326
  1945
      int _last;
deba@326
  1946
      int _index;
deba@326
  1947
    };
deba@326
  1948
deba@326
  1949
    /// @}
deba@326
  1950
deba@326
  1951
  };
deba@326
  1952
deba@326
  1953
  /// \ingroup matching
deba@326
  1954
  ///
deba@326
  1955
  /// \brief Weighted perfect matching in general graphs
deba@326
  1956
  ///
deba@326
  1957
  /// This class provides an efficient implementation of Edmond's
deba@327
  1958
  /// maximum weighted perfect matching algorithm. The implementation
deba@326
  1959
  /// is based on extensive use of priority queues and provides
deba@326
  1960
  /// \f$O(nm\log(n))\f$ time complexity.
deba@326
  1961
  ///
deba@326
  1962
  /// The maximum weighted matching problem is to find undirected
deba@327
  1963
  /// edges in the graph with maximum overall weight and no two of
deba@327
  1964
  /// them shares their ends and covers all nodes. The problem can be
deba@327
  1965
  /// formulated with the following linear program.
deba@326
  1966
  /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
deba@327
  1967
  /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
deba@327
  1968
      \quad \forall B\in\mathcal{O}\f] */
deba@326
  1969
  /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@326
  1970
  /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@327
  1971
  /// where \f$\delta(X)\f$ is the set of edges incident to a node in
deba@327
  1972
  /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
deba@327
  1973
  /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
deba@327
  1974
  /// subsets of the nodes.
deba@326
  1975
  ///
deba@326
  1976
  /// The algorithm calculates an optimal matching and a proof of the
deba@326
  1977
  /// optimality. The solution of the dual problem can be used to check
deba@327
  1978
  /// the result of the algorithm. The dual linear problem is the
deba@327
  1979
  /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge
deba@327
  1980
      w_{uv} \quad \forall uv\in E\f] */
deba@326
  1981
  /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@327
  1982
  /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
deba@327
  1983
      \frac{\vert B \vert - 1}{2}z_B\f] */
deba@326
  1984
  ///
deba@326
  1985
  /// The algorithm can be executed with \c run() or the \c init() and
deba@326
  1986
  /// then the \c start() member functions. After it the matching can
deba@326
  1987
  /// be asked with \c matching() or mate() functions. The dual
deba@326
  1988
  /// solution can be get with \c nodeValue(), \c blossomNum() and \c
deba@326
  1989
  /// blossomValue() members and \ref MaxWeightedMatching::BlossomIt
deba@326
  1990
  /// "BlossomIt" nested class which is able to iterate on the nodes
deba@326
  1991
  /// of a blossom. If the value type is integral then the dual
deba@326
  1992
  /// solution is multiplied by \ref MaxWeightedMatching::dualScale "4".
deba@326
  1993
  template <typename _Graph,
deba@326
  1994
            typename _WeightMap = typename _Graph::template EdgeMap<int> >
deba@326
  1995
  class MaxWeightedPerfectMatching {
deba@326
  1996
  public:
deba@326
  1997
deba@326
  1998
    typedef _Graph Graph;
deba@326
  1999
    typedef _WeightMap WeightMap;
deba@326
  2000
    typedef typename WeightMap::Value Value;
deba@326
  2001
deba@326
  2002
    /// \brief Scaling factor for dual solution
deba@326
  2003
    ///
deba@326
  2004
    /// Scaling factor for dual solution, it is equal to 4 or 1
deba@326
  2005
    /// according to the value type.
deba@326
  2006
    static const int dualScale =
deba@326
  2007
      std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@326
  2008
deba@326
  2009
    typedef typename Graph::template NodeMap<typename Graph::Arc>
deba@326
  2010
    MatchingMap;
deba@326
  2011
deba@326
  2012
  private:
deba@326
  2013
deba@326
  2014
    TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326
  2015
deba@326
  2016
    typedef typename Graph::template NodeMap<Value> NodePotential;
deba@326
  2017
    typedef std::vector<Node> BlossomNodeList;
deba@326
  2018
deba@326
  2019
    struct BlossomVariable {
deba@326
  2020
      int begin, end;
deba@326
  2021
      Value value;
deba@326
  2022
deba@326
  2023
      BlossomVariable(int _begin, int _end, Value _value)
deba@326
  2024
        : begin(_begin), end(_end), value(_value) {}
deba@326
  2025
deba@326
  2026
    };
deba@326
  2027
deba@326
  2028
    typedef std::vector<BlossomVariable> BlossomPotential;
deba@326
  2029
deba@326
  2030
    const Graph& _graph;
deba@326
  2031
    const WeightMap& _weight;
deba@326
  2032
deba@326
  2033
    MatchingMap* _matching;
deba@326
  2034
deba@326
  2035
    NodePotential* _node_potential;
deba@326
  2036
deba@326
  2037
    BlossomPotential _blossom_potential;
deba@326
  2038
    BlossomNodeList _blossom_node_list;
deba@326
  2039
deba@326
  2040
    int _node_num;
deba@326
  2041
    int _blossom_num;
deba@326
  2042
deba@326
  2043
    typedef RangeMap<int> IntIntMap;
deba@326
  2044
deba@326
  2045
    enum Status {
deba@326
  2046
      EVEN = -1, MATCHED = 0, ODD = 1
deba@326
  2047
    };
deba@326
  2048
deba@327
  2049
    typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
deba@326
  2050
    struct BlossomData {
deba@326
  2051
      int tree;
deba@326
  2052
      Status status;
deba@326
  2053
      Arc pred, next;
deba@326
  2054
      Value pot, offset;
deba@326
  2055
    };
deba@326
  2056
deba@327
  2057
    IntNodeMap *_blossom_index;
deba@326
  2058
    BlossomSet *_blossom_set;
deba@326
  2059
    RangeMap<BlossomData>* _blossom_data;
deba@326
  2060
deba@327
  2061
    IntNodeMap *_node_index;
deba@327
  2062
    IntArcMap *_node_heap_index;
deba@326
  2063
deba@326
  2064
    struct NodeData {
deba@326
  2065
deba@327
  2066
      NodeData(IntArcMap& node_heap_index)
deba@326
  2067
        : heap(node_heap_index) {}
deba@326
  2068
deba@326
  2069
      int blossom;
deba@326
  2070
      Value pot;
deba@327
  2071
      BinHeap<Value, IntArcMap> heap;
deba@326
  2072
      std::map<int, Arc> heap_index;
deba@326
  2073
deba@326
  2074
      int tree;
deba@326
  2075
    };
deba@326
  2076
deba@326
  2077
    RangeMap<NodeData>* _node_data;
deba@326
  2078
deba@326
  2079
    typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@326
  2080
deba@326
  2081
    IntIntMap *_tree_set_index;
deba@326
  2082
    TreeSet *_tree_set;
deba@326
  2083
deba@326
  2084
    IntIntMap *_delta2_index;
deba@326
  2085
    BinHeap<Value, IntIntMap> *_delta2;
deba@326
  2086
deba@327
  2087
    IntEdgeMap *_delta3_index;
deba@327
  2088
    BinHeap<Value, IntEdgeMap> *_delta3;
deba@326
  2089
deba@326
  2090
    IntIntMap *_delta4_index;
deba@326
  2091
    BinHeap<Value, IntIntMap> *_delta4;
deba@326
  2092
deba@326
  2093
    Value _delta_sum;
deba@326
  2094
deba@326
  2095
    void createStructures() {
deba@326
  2096
      _node_num = countNodes(_graph);
deba@326
  2097
      _blossom_num = _node_num * 3 / 2;
deba@326
  2098
deba@326
  2099
      if (!_matching) {
deba@326
  2100
        _matching = new MatchingMap(_graph);
deba@326
  2101
      }
deba@326
  2102
      if (!_node_potential) {
deba@326
  2103
        _node_potential = new NodePotential(_graph);
deba@326
  2104
      }
deba@326
  2105
      if (!_blossom_set) {
deba@327
  2106
        _blossom_index = new IntNodeMap(_graph);
deba@326
  2107
        _blossom_set = new BlossomSet(*_blossom_index);
deba@326
  2108
        _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@326
  2109
      }
deba@326
  2110
deba@326
  2111
      if (!_node_index) {
deba@327
  2112
        _node_index = new IntNodeMap(_graph);
deba@327
  2113
        _node_heap_index = new IntArcMap(_graph);
deba@326
  2114
        _node_data = new RangeMap<NodeData>(_node_num,
deba@327
  2115
                                            NodeData(*_node_heap_index));
deba@326
  2116
      }
deba@326
  2117
deba@326
  2118
      if (!_tree_set) {
deba@326
  2119
        _tree_set_index = new IntIntMap(_blossom_num);
deba@326
  2120
        _tree_set = new TreeSet(*_tree_set_index);
deba@326
  2121
      }
deba@326
  2122
      if (!_delta2) {
deba@326
  2123
        _delta2_index = new IntIntMap(_blossom_num);
deba@326
  2124
        _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@326
  2125
      }
deba@326
  2126
      if (!_delta3) {
deba@327
  2127
        _delta3_index = new IntEdgeMap(_graph);
deba@327
  2128
        _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
deba@326
  2129
      }
deba@326
  2130
      if (!_delta4) {
deba@326
  2131
        _delta4_index = new IntIntMap(_blossom_num);
deba@326
  2132
        _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@326
  2133
      }
deba@326
  2134
    }
deba@326
  2135
deba@326
  2136
    void destroyStructures() {
deba@326
  2137
      _node_num = countNodes(_graph);
deba@326
  2138
      _blossom_num = _node_num * 3 / 2;
deba@326
  2139
deba@326
  2140
      if (_matching) {
deba@326
  2141
        delete _matching;
deba@326
  2142
      }
deba@326
  2143
      if (_node_potential) {
deba@326
  2144
        delete _node_potential;
deba@326
  2145
      }
deba@326
  2146
      if (_blossom_set) {
deba@326
  2147
        delete _blossom_index;
deba@326
  2148
        delete _blossom_set;
deba@326
  2149
        delete _blossom_data;
deba@326
  2150
      }
deba@326
  2151
deba@326
  2152
      if (_node_index) {
deba@326
  2153
        delete _node_index;
deba@326
  2154
        delete _node_heap_index;
deba@326
  2155
        delete _node_data;
deba@326
  2156
      }
deba@326
  2157
deba@326
  2158
      if (_tree_set) {
deba@326
  2159
        delete _tree_set_index;
deba@326
  2160
        delete _tree_set;
deba@326
  2161
      }
deba@326
  2162
      if (_delta2) {
deba@326
  2163
        delete _delta2_index;
deba@326
  2164
        delete _delta2;
deba@326
  2165
      }
deba@326
  2166
      if (_delta3) {
deba@326
  2167
        delete _delta3_index;
deba@326
  2168
        delete _delta3;
deba@326
  2169
      }
deba@326
  2170
      if (_delta4) {
deba@326
  2171
        delete _delta4_index;
deba@326
  2172
        delete _delta4;
deba@326
  2173
      }
deba@326
  2174
    }
deba@326
  2175
deba@326
  2176
    void matchedToEven(int blossom, int tree) {
deba@326
  2177
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  2178
        _delta2->erase(blossom);
deba@326
  2179
      }
deba@326
  2180
deba@326
  2181
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2182
        (*_blossom_data)[blossom].pot -=
deba@326
  2183
          2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@326
  2184
      }
deba@326
  2185
deba@326
  2186
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  2187
           n != INVALID; ++n) {
deba@326
  2188
deba@326
  2189
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
  2190
        int ni = (*_node_index)[n];
deba@326
  2191
deba@326
  2192
        (*_node_data)[ni].heap.clear();
deba@326
  2193
        (*_node_data)[ni].heap_index.clear();
deba@326
  2194
deba@326
  2195
        (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@326
  2196
deba@326
  2197
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  2198
          Node v = _graph.source(e);
deba@326
  2199
          int vb = _blossom_set->find(v);
deba@326
  2200
          int vi = (*_node_index)[v];
deba@326
  2201
deba@326
  2202
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  2203
            dualScale * _weight[e];
deba@326
  2204
deba@326
  2205
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  2206
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326
  2207
              _delta3->push(e, rw / 2);
deba@326
  2208
            }
deba@326
  2209
          } else {
deba@326
  2210
            typename std::map<int, Arc>::iterator it =
deba@326
  2211
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  2212
deba@326
  2213
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  2214
              if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326
  2215
                (*_node_data)[vi].heap.replace(it->second, e);
deba@326
  2216
                (*_node_data)[vi].heap.decrease(e, rw);
deba@326
  2217
                it->second = e;
deba@326
  2218
              }
deba@326
  2219
            } else {
deba@326
  2220
              (*_node_data)[vi].heap.push(e, rw);
deba@326
  2221
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326
  2222
            }
deba@326
  2223
deba@326
  2224
            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326
  2225
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326
  2226
deba@326
  2227
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  2228
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326
  2229
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326
  2230
                               (*_blossom_data)[vb].offset);
deba@326
  2231
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326
  2232
                           (*_blossom_data)[vb].offset){
deba@326
  2233
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326
  2234
                                   (*_blossom_data)[vb].offset);
deba@326
  2235
                }
deba@326
  2236
              }
deba@326
  2237
            }
deba@326
  2238
          }
deba@326
  2239
        }
deba@326
  2240
      }
deba@326
  2241
      (*_blossom_data)[blossom].offset = 0;
deba@326
  2242
    }
deba@326
  2243
deba@326
  2244
    void matchedToOdd(int blossom) {
deba@326
  2245
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  2246
        _delta2->erase(blossom);
deba@326
  2247
      }
deba@326
  2248
      (*_blossom_data)[blossom].offset += _delta_sum;
deba@326
  2249
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2250
        _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
deba@326
  2251
                     (*_blossom_data)[blossom].offset);
deba@326
  2252
      }
deba@326
  2253
    }
deba@326
  2254
deba@326
  2255
    void evenToMatched(int blossom, int tree) {
deba@326
  2256
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2257
        (*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@326
  2258
      }
deba@326
  2259
deba@326
  2260
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  2261
           n != INVALID; ++n) {
deba@326
  2262
        int ni = (*_node_index)[n];
deba@326
  2263
        (*_node_data)[ni].pot -= _delta_sum;
deba@326
  2264
deba@326
  2265
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  2266
          Node v = _graph.source(e);
deba@326
  2267
          int vb = _blossom_set->find(v);
deba@326
  2268
          int vi = (*_node_index)[v];
deba@326
  2269
deba@326
  2270
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  2271
            dualScale * _weight[e];
deba@326
  2272
deba@326
  2273
          if (vb == blossom) {
deba@326
  2274
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  2275
              _delta3->erase(e);
deba@326
  2276
            }
deba@326
  2277
          } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  2278
deba@326
  2279
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  2280
              _delta3->erase(e);
deba@326
  2281
            }
deba@326
  2282
deba@326
  2283
            int vt = _tree_set->find(vb);
deba@326
  2284
deba@326
  2285
            if (vt != tree) {
deba@326
  2286
deba@326
  2287
              Arc r = _graph.oppositeArc(e);
deba@326
  2288
deba@326
  2289
              typename std::map<int, Arc>::iterator it =
deba@326
  2290
                (*_node_data)[ni].heap_index.find(vt);
deba@326
  2291
deba@326
  2292
              if (it != (*_node_data)[ni].heap_index.end()) {
deba@326
  2293
                if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326
  2294
                  (*_node_data)[ni].heap.replace(it->second, r);
deba@326
  2295
                  (*_node_data)[ni].heap.decrease(r, rw);
deba@326
  2296
                  it->second = r;
deba@326
  2297
                }
deba@326
  2298
              } else {
deba@326
  2299
                (*_node_data)[ni].heap.push(r, rw);
deba@326
  2300
                (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326
  2301
              }
deba@326
  2302
deba@326
  2303
              if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326
  2304
                _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326
  2305
deba@326
  2306
                if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326
  2307
                  _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
  2308
                               (*_blossom_data)[blossom].offset);
deba@326
  2309
                } else if ((*_delta2)[blossom] >
deba@326
  2310
                           _blossom_set->classPrio(blossom) -
deba@326
  2311
                           (*_blossom_data)[blossom].offset){
deba@326
  2312
                  _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326
  2313
                                   (*_blossom_data)[blossom].offset);
deba@326
  2314
                }
deba@326
  2315
              }
deba@326
  2316
            }
deba@326
  2317
          } else {
deba@326
  2318
deba@326
  2319
            typename std::map<int, Arc>::iterator it =
deba@326
  2320
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  2321
deba@326
  2322
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  2323
              (*_node_data)[vi].heap.erase(it->second);
deba@326
  2324
              (*_node_data)[vi].heap_index.erase(it);
deba@326
  2325
              if ((*_node_data)[vi].heap.empty()) {
deba@326
  2326
                _blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@326
  2327
              } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@326
  2328
                _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@326
  2329
              }
deba@326
  2330
deba@326
  2331
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  2332
                if (_blossom_set->classPrio(vb) ==
deba@326
  2333
                    std::numeric_limits<Value>::max()) {
deba@326
  2334
                  _delta2->erase(vb);
deba@326
  2335
                } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@326
  2336
                           (*_blossom_data)[vb].offset) {
deba@326
  2337
                  _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@326
  2338
                                   (*_blossom_data)[vb].offset);
deba@326
  2339
                }
deba@326
  2340
              }
deba@326
  2341
            }
deba@326
  2342
          }
deba@326
  2343
        }
deba@326
  2344
      }
deba@326
  2345
    }
deba@326
  2346
deba@326
  2347
    void oddToMatched(int blossom) {
deba@326
  2348
      (*_blossom_data)[blossom].offset -= _delta_sum;
deba@326
  2349
deba@326
  2350
      if (_blossom_set->classPrio(blossom) !=
deba@326
  2351
          std::numeric_limits<Value>::max()) {
deba@326
  2352
        _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
  2353
                       (*_blossom_data)[blossom].offset);
deba@326
  2354
      }
deba@326
  2355
deba@326
  2356
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2357
        _delta4->erase(blossom);
deba@326
  2358
      }
deba@326
  2359
    }
deba@326
  2360
deba@326
  2361
    void oddToEven(int blossom, int tree) {
deba@326
  2362
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2363
        _delta4->erase(blossom);
deba@326
  2364
        (*_blossom_data)[blossom].pot -=
deba@326
  2365
          2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@326
  2366
      }
deba@326
  2367
deba@326
  2368
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  2369
           n != INVALID; ++n) {
deba@326
  2370
        int ni = (*_node_index)[n];
deba@326
  2371
deba@326
  2372
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
  2373
deba@326
  2374
        (*_node_data)[ni].heap.clear();
deba@326
  2375
        (*_node_data)[ni].heap_index.clear();
deba@326
  2376
        (*_node_data)[ni].pot +=
deba@326
  2377
          2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@326
  2378
deba@326
  2379
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  2380
          Node v = _graph.source(e);
deba@326
  2381
          int vb = _blossom_set->find(v);
deba@326
  2382
          int vi = (*_node_index)[v];
deba@326
  2383
deba@326
  2384
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  2385
            dualScale * _weight[e];
deba@326
  2386
deba@326
  2387
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  2388
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326
  2389
              _delta3->push(e, rw / 2);
deba@326
  2390
            }
deba@326
  2391
          } else {
deba@326
  2392
deba@326
  2393
            typename std::map<int, Arc>::iterator it =
deba@326
  2394
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  2395
deba@326
  2396
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  2397
              if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326
  2398
                (*_node_data)[vi].heap.replace(it->second, e);
deba@326
  2399
                (*_node_data)[vi].heap.decrease(e, rw);
deba@326
  2400
                it->second = e;
deba@326
  2401
              }
deba@326
  2402
            } else {
deba@326
  2403
              (*_node_data)[vi].heap.push(e, rw);
deba@326
  2404
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326
  2405
            }
deba@326
  2406
deba@326
  2407
            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326
  2408
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326
  2409
deba@326
  2410
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  2411
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326
  2412
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326
  2413
                               (*_blossom_data)[vb].offset);
deba@326
  2414
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326
  2415
                           (*_blossom_data)[vb].offset) {
deba@326
  2416
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326
  2417
                                   (*_blossom_data)[vb].offset);
deba@326
  2418
                }
deba@326
  2419
              }
deba@326
  2420
            }
deba@326
  2421
          }
deba@326
  2422
        }
deba@326
  2423
      }
deba@326
  2424
      (*_blossom_data)[blossom].offset = 0;
deba@326
  2425
    }
deba@326
  2426
deba@326
  2427
    void alternatePath(int even, int tree) {
deba@326
  2428
      int odd;
deba@326
  2429
deba@326
  2430
      evenToMatched(even, tree);
deba@326
  2431
      (*_blossom_data)[even].status = MATCHED;
deba@326
  2432
deba@326
  2433
      while ((*_blossom_data)[even].pred != INVALID) {
deba@326
  2434
        odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
deba@326
  2435
        (*_blossom_data)[odd].status = MATCHED;
deba@326
  2436
        oddToMatched(odd);
deba@326
  2437
        (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@326
  2438
deba@326
  2439
        even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
deba@326
  2440
        (*_blossom_data)[even].status = MATCHED;
deba@326
  2441
        evenToMatched(even, tree);
deba@326
  2442
        (*_blossom_data)[even].next =
deba@326
  2443
          _graph.oppositeArc((*_blossom_data)[odd].pred);
deba@326
  2444
      }
deba@326
  2445
deba@326
  2446
    }
deba@326
  2447
deba@326
  2448
    void destroyTree(int tree) {
deba@326
  2449
      for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@326
  2450
        if ((*_blossom_data)[b].status == EVEN) {
deba@326
  2451
          (*_blossom_data)[b].status = MATCHED;
deba@326
  2452
          evenToMatched(b, tree);
deba@326
  2453
        } else if ((*_blossom_data)[b].status == ODD) {
deba@326
  2454
          (*_blossom_data)[b].status = MATCHED;
deba@326
  2455
          oddToMatched(b);
deba@326
  2456
        }
deba@326
  2457
      }
deba@326
  2458
      _tree_set->eraseClass(tree);
deba@326
  2459
    }
deba@326
  2460
deba@327
  2461
    void augmentOnEdge(const Edge& edge) {
deba@327
  2462
deba@327
  2463
      int left = _blossom_set->find(_graph.u(edge));
deba@327
  2464
      int right = _blossom_set->find(_graph.v(edge));
deba@326
  2465
deba@326
  2466
      int left_tree = _tree_set->find(left);
deba@326
  2467
      alternatePath(left, left_tree);
deba@326
  2468
      destroyTree(left_tree);
deba@326
  2469
deba@326
  2470
      int right_tree = _tree_set->find(right);
deba@326
  2471
      alternatePath(right, right_tree);
deba@326
  2472
      destroyTree(right_tree);
deba@326
  2473
deba@327
  2474
      (*_blossom_data)[left].next = _graph.direct(edge, true);
deba@327
  2475
      (*_blossom_data)[right].next = _graph.direct(edge, false);
deba@326
  2476
    }
deba@326
  2477
deba@326
  2478
    void extendOnArc(const Arc& arc) {
deba@326
  2479
      int base = _blossom_set->find(_graph.target(arc));
deba@326
  2480
      int tree = _tree_set->find(base);
deba@326
  2481
deba@326
  2482
      int odd = _blossom_set->find(_graph.source(arc));
deba@326
  2483
      _tree_set->insert(odd, tree);
deba@326
  2484
      (*_blossom_data)[odd].status = ODD;
deba@326
  2485
      matchedToOdd(odd);
deba@326
  2486
      (*_blossom_data)[odd].pred = arc;
deba@326
  2487
deba@326
  2488
      int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
deba@326
  2489
      (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@326
  2490
      _tree_set->insert(even, tree);
deba@326
  2491
      (*_blossom_data)[even].status = EVEN;
deba@326
  2492
      matchedToEven(even, tree);
deba@326
  2493
    }
deba@326
  2494
deba@327
  2495
    void shrinkOnEdge(const Edge& edge, int tree) {
deba@326
  2496
      int nca = -1;
deba@326
  2497
      std::vector<int> left_path, right_path;
deba@326
  2498
deba@326
  2499
      {
deba@326
  2500
        std::set<int> left_set, right_set;
deba@326
  2501
        int left = _blossom_set->find(_graph.u(edge));
deba@326
  2502
        left_path.push_back(left);
deba@326
  2503
        left_set.insert(left);
deba@326
  2504
deba@326
  2505
        int right = _blossom_set->find(_graph.v(edge));
deba@326
  2506
        right_path.push_back(right);
deba@326
  2507
        right_set.insert(right);
deba@326
  2508
deba@326
  2509
        while (true) {
deba@326
  2510
deba@326
  2511
          if ((*_blossom_data)[left].pred == INVALID) break;
deba@326
  2512
deba@326
  2513
          left =
deba@326
  2514
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326
  2515
          left_path.push_back(left);
deba@326
  2516
          left =
deba@326
  2517
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326
  2518
          left_path.push_back(left);
deba@326
  2519
deba@326
  2520
          left_set.insert(left);
deba@326
  2521
deba@326
  2522
          if (right_set.find(left) != right_set.end()) {
deba@326
  2523
            nca = left;
deba@326
  2524
            break;
deba@326
  2525
          }
deba@326
  2526
deba@326
  2527
          if ((*_blossom_data)[right].pred == INVALID) break;
deba@326
  2528
deba@326
  2529
          right =
deba@326
  2530
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326
  2531
          right_path.push_back(right);
deba@326
  2532
          right =
deba@326
  2533
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326
  2534
          right_path.push_back(right);
deba@326
  2535
deba@326
  2536
          right_set.insert(right);
deba@326
  2537
deba@326
  2538
          if (left_set.find(right) != left_set.end()) {
deba@326
  2539
            nca = right;
deba@326
  2540
            break;
deba@326
  2541
          }
deba@326
  2542
deba@326
  2543
        }
deba@326
  2544
deba@326
  2545
        if (nca == -1) {
deba@326
  2546
          if ((*_blossom_data)[left].pred == INVALID) {
deba@326
  2547
            nca = right;
deba@326
  2548
            while (left_set.find(nca) == left_set.end()) {
deba@326
  2549
              nca =
deba@326
  2550
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  2551
              right_path.push_back(nca);
deba@326
  2552
              nca =
deba@326
  2553
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  2554
              right_path.push_back(nca);
deba@326
  2555
            }
deba@326
  2556
          } else {
deba@326
  2557
            nca = left;
deba@326
  2558
            while (right_set.find(nca) == right_set.end()) {
deba@326
  2559
              nca =
deba@326
  2560
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  2561
              left_path.push_back(nca);
deba@326
  2562
              nca =
deba@326
  2563
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  2564
              left_path.push_back(nca);
deba@326
  2565
            }
deba@326
  2566
          }
deba@326
  2567
        }
deba@326
  2568
      }
deba@326
  2569
deba@326
  2570
      std::vector<int> subblossoms;
deba@326
  2571
      Arc prev;
deba@326
  2572
deba@326
  2573
      prev = _graph.direct(edge, true);
deba@326
  2574
      for (int i = 0; left_path[i] != nca; i += 2) {
deba@326
  2575
        subblossoms.push_back(left_path[i]);
deba@326
  2576
        (*_blossom_data)[left_path[i]].next = prev;
deba@326
  2577
        _tree_set->erase(left_path[i]);
deba@326
  2578
deba@326
  2579
        subblossoms.push_back(left_path[i + 1]);
deba@326
  2580
        (*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@326
  2581
        oddToEven(left_path[i + 1], tree);
deba@326
  2582
        _tree_set->erase(left_path[i + 1]);
deba@326
  2583
        prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
deba@326
  2584
      }
deba@326
  2585
deba@326
  2586
      int k = 0;
deba@326
  2587
      while (right_path[k] != nca) ++k;
deba@326
  2588
deba@326
  2589
      subblossoms.push_back(nca);
deba@326
  2590
      (*_blossom_data)[nca].next = prev;
deba@326
  2591
deba@326
  2592
      for (int i = k - 2; i >= 0; i -= 2) {
deba@326
  2593
        subblossoms.push_back(right_path[i + 1]);
deba@326
  2594
        (*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@326
  2595
        oddToEven(right_path[i + 1], tree);
deba@326
  2596
        _tree_set->erase(right_path[i + 1]);
deba@326
  2597
deba@326
  2598
        (*_blossom_data)[right_path[i + 1]].next =
deba@326
  2599
          (*_blossom_data)[right_path[i + 1]].pred;
deba@326
  2600
deba@326
  2601
        subblossoms.push_back(right_path[i]);
deba@326
  2602
        _tree_set->erase(right_path[i]);
deba@326
  2603
      }
deba@326
  2604
deba@326
  2605
      int surface =
deba@326
  2606
        _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@326
  2607
deba@326
  2608
      for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  2609
        if (!_blossom_set->trivial(subblossoms[i])) {
deba@326
  2610
          (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@326
  2611
        }
deba@326
  2612
        (*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@326
  2613
      }
deba@326
  2614
deba@326
  2615
      (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@326
  2616
      (*_blossom_data)[surface].offset = 0;
deba@326
  2617
      (*_blossom_data)[surface].status = EVEN;
deba@326
  2618
      (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@326
  2619
      (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@326
  2620
deba@326
  2621
      _tree_set->insert(surface, tree);
deba@326
  2622
      _tree_set->erase(nca);
deba@326
  2623
    }
deba@326
  2624
deba@326
  2625
    void splitBlossom(int blossom) {
deba@326
  2626
      Arc next = (*_blossom_data)[blossom].next;
deba@326
  2627
      Arc pred = (*_blossom_data)[blossom].pred;
deba@326
  2628
deba@326
  2629
      int tree = _tree_set->find(blossom);
deba@326
  2630
deba@326
  2631
      (*_blossom_data)[blossom].status = MATCHED;
deba@326
  2632
      oddToMatched(blossom);
deba@326
  2633
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  2634
        _delta2->erase(blossom);
deba@326
  2635
      }
deba@326
  2636
deba@326
  2637
      std::vector<int> subblossoms;
deba@326
  2638
      _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326
  2639
deba@326
  2640
      Value offset = (*_blossom_data)[blossom].offset;
deba@326
  2641
      int b = _blossom_set->find(_graph.source(pred));
deba@326
  2642
      int d = _blossom_set->find(_graph.source(next));
deba@326
  2643
deba@326
  2644
      int ib = -1, id = -1;
deba@326
  2645
      for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  2646
        if (subblossoms[i] == b) ib = i;
deba@326
  2647
        if (subblossoms[i] == d) id = i;
deba@326
  2648
deba@326
  2649
        (*_blossom_data)[subblossoms[i]].offset = offset;
deba@326
  2650
        if (!_blossom_set->trivial(subblossoms[i])) {
deba@326
  2651
          (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@326
  2652
        }
deba@326
  2653
        if (_blossom_set->classPrio(subblossoms[i]) !=
deba@326
  2654
            std::numeric_limits<Value>::max()) {
deba@326
  2655
          _delta2->push(subblossoms[i],
deba@326
  2656
                        _blossom_set->classPrio(subblossoms[i]) -
deba@326
  2657
                        (*_blossom_data)[subblossoms[i]].offset);
deba@326
  2658
        }
deba@326
  2659
      }
deba@326
  2660
deba@326
  2661
      if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@326
  2662
        for (int i = (id + 1) % subblossoms.size();
deba@326
  2663
             i != ib; i = (i + 2) % subblossoms.size()) {
deba@326
  2664
          int sb = subblossoms[i];
deba@326
  2665
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  2666
          (*_blossom_data)[sb].next =
deba@326
  2667
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  2668
        }
deba@326
  2669
deba@326
  2670
        for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@326
  2671
          int sb = subblossoms[i];
deba@326
  2672
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  2673
          int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326
  2674
deba@326
  2675
          (*_blossom_data)[sb].status = ODD;
deba@326
  2676
          matchedToOdd(sb);
deba@326
  2677
          _tree_set->insert(sb, tree);
deba@326
  2678
          (*_blossom_data)[sb].pred = pred;
deba@326
  2679
          (*_blossom_data)[sb].next =
deba@326
  2680
                           _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  2681
deba@326
  2682
          pred = (*_blossom_data)[ub].next;
deba@326
  2683
deba@326
  2684
          (*_blossom_data)[tb].status = EVEN;
deba@326
  2685
          matchedToEven(tb, tree);
deba@326
  2686
          _tree_set->insert(tb, tree);
deba@326
  2687
          (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@326
  2688
        }
deba@326
  2689
deba@326
  2690
        (*_blossom_data)[subblossoms[id]].status = ODD;
deba@326
  2691
        matchedToOdd(subblossoms[id]);
deba@326
  2692
        _tree_set->insert(subblossoms[id], tree);
deba@326
  2693
        (*_blossom_data)[subblossoms[id]].next = next;
deba@326
  2694
        (*_blossom_data)[subblossoms[id]].pred = pred;
deba@326
  2695
deba@326
  2696
      } else {
deba@326
  2697
deba@326
  2698
        for (int i = (ib + 1) % subblossoms.size();
deba@326
  2699
             i != id; i = (i + 2) % subblossoms.size()) {
deba@326
  2700
          int sb = subblossoms[i];
deba@326
  2701
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  2702
          (*_blossom_data)[sb].next =
deba@326
  2703
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  2704
        }
deba@326
  2705
deba@326
  2706
        for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@326
  2707
          int sb = subblossoms[i];
deba@326
  2708
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  2709
          int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326
  2710
deba@326
  2711
          (*_blossom_data)[sb].status = ODD;
deba@326
  2712
          matchedToOdd(sb);
deba@326
  2713
          _tree_set->insert(sb, tree);
deba@326
  2714
          (*_blossom_data)[sb].next = next;
deba@326
  2715
          (*_blossom_data)[sb].pred =
deba@326
  2716
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  2717
deba@326
  2718
          (*_blossom_data)[tb].status = EVEN;
deba@326
  2719
          matchedToEven(tb, tree);
deba@326
  2720
          _tree_set->insert(tb, tree);
deba@326
  2721
          (*_blossom_data)[tb].pred =
deba@326
  2722
            (*_blossom_data)[tb].next =
deba@326
  2723
            _graph.oppositeArc((*_blossom_data)[ub].next);
deba@326
  2724
          next = (*_blossom_data)[ub].next;
deba@326
  2725
        }
deba@326
  2726
deba@326
  2727
        (*_blossom_data)[subblossoms[ib]].status = ODD;
deba@326
  2728
        matchedToOdd(subblossoms[ib]);
deba@326
  2729
        _tree_set->insert(subblossoms[ib], tree);
deba@326
  2730
        (*_blossom_data)[subblossoms[ib]].next = next;
deba@326
  2731
        (*_blossom_data)[subblossoms[ib]].pred = pred;
deba@326
  2732
      }
deba@326
  2733
      _tree_set->erase(blossom);
deba@326
  2734
    }
deba@326
  2735
deba@326
  2736
    void extractBlossom(int blossom, const Node& base, const Arc& matching) {
deba@326
  2737
      if (_blossom_set->trivial(blossom)) {
deba@326
  2738
        int bi = (*_node_index)[base];
deba@326
  2739
        Value pot = (*_node_data)[bi].pot;
deba@326
  2740
deba@326
  2741
        _matching->set(base, matching);
deba@326
  2742
        _blossom_node_list.push_back(base);
deba@326
  2743
        _node_potential->set(base, pot);
deba@326
  2744
      } else {
deba@326
  2745
deba@326
  2746
        Value pot = (*_blossom_data)[blossom].pot;
deba@326
  2747
        int bn = _blossom_node_list.size();
deba@326
  2748
deba@326
  2749
        std::vector<int> subblossoms;
deba@326
  2750
        _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326
  2751
        int b = _blossom_set->find(base);
deba@326
  2752
        int ib = -1;
deba@326
  2753
        for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  2754
          if (subblossoms[i] == b) { ib = i; break; }
deba@326
  2755
        }
deba@326
  2756
deba@326
  2757
        for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@326
  2758
          int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@326
  2759
          int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@326
  2760
deba@326
  2761
          Arc m = (*_blossom_data)[tb].next;
deba@326
  2762
          extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
deba@326
  2763
          extractBlossom(tb, _graph.source(m), m);
deba@326
  2764
        }
deba@326
  2765
        extractBlossom(subblossoms[ib], base, matching);
deba@326
  2766
deba@326
  2767
        int en = _blossom_node_list.size();
deba@326
  2768
deba@326
  2769
        _blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@326
  2770
      }
deba@326
  2771
    }
deba@326
  2772
deba@326
  2773
    void extractMatching() {
deba@326
  2774
      std::vector<int> blossoms;
deba@326
  2775
      for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@326
  2776
        blossoms.push_back(c);
deba@326
  2777
      }
deba@326
  2778
deba@326
  2779
      for (int i = 0; i < int(blossoms.size()); ++i) {
deba@326
  2780
deba@326
  2781
        Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@326
  2782
        (*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@326
  2783
        for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
deba@326
  2784
             n != INVALID; ++n) {
deba@326
  2785
          (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@326
  2786
        }
deba@326
  2787
deba@326
  2788
        Arc matching = (*_blossom_data)[blossoms[i]].next;
deba@326
  2789
        Node base = _graph.source(matching);
deba@326
  2790
        extractBlossom(blossoms[i], base, matching);
deba@326
  2791
      }
deba@326
  2792
    }
deba@326
  2793
deba@326
  2794
  public:
deba@326
  2795
deba@326
  2796
    /// \brief Constructor
deba@326
  2797
    ///
deba@326
  2798
    /// Constructor.
deba@326
  2799
    MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
deba@326
  2800
      : _graph(graph), _weight(weight), _matching(0),
deba@326
  2801
        _node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@326
  2802
        _node_num(0), _blossom_num(0),
deba@326
  2803
deba@326
  2804
        _blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@326
  2805
        _node_index(0), _node_heap_index(0), _node_data(0),
deba@326
  2806
        _tree_set_index(0), _tree_set(0),
deba@326
  2807
deba@326
  2808
        _delta2_index(0), _delta2(0),
deba@326
  2809
        _delta3_index(0), _delta3(0),
deba@326
  2810
        _delta4_index(0), _delta4(0),
deba@326
  2811
deba@326
  2812
        _delta_sum() {}
deba@326
  2813
deba@326
  2814
    ~MaxWeightedPerfectMatching() {
deba@326
  2815
      destroyStructures();
deba@326
  2816
    }
deba@326
  2817
deba@326
  2818
    /// \name Execution control
alpar@330
  2819
    /// The simplest way to execute the algorithm is to use the
deba@326
  2820
    /// \c run() member function.
deba@326
  2821
deba@326
  2822
    ///@{
deba@326
  2823
deba@326
  2824
    /// \brief Initialize the algorithm
deba@326
  2825
    ///
deba@326
  2826
    /// Initialize the algorithm
deba@326
  2827
    void init() {
deba@326
  2828
      createStructures();
deba@326
  2829
deba@326
  2830
      for (ArcIt e(_graph); e != INVALID; ++e) {
deba@327
  2831
        _node_heap_index->set(e, BinHeap<Value, IntArcMap>::PRE_HEAP);
deba@326
  2832
      }
deba@326
  2833
      for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326
  2834
        _delta3_index->set(e, _delta3->PRE_HEAP);
deba@326
  2835
      }
deba@326
  2836
      for (int i = 0; i < _blossom_num; ++i) {
deba@326
  2837
        _delta2_index->set(i, _delta2->PRE_HEAP);
deba@326
  2838
        _delta4_index->set(i, _delta4->PRE_HEAP);
deba@326
  2839
      }
deba@326
  2840
deba@326
  2841
      int index = 0;
deba@326
  2842
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  2843
        Value max = - std::numeric_limits<Value>::max();
deba@326
  2844
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  2845
          if (_graph.target(e) == n) continue;
deba@326
  2846
          if ((dualScale * _weight[e]) / 2 > max) {
deba@326
  2847
            max = (dualScale * _weight[e]) / 2;
deba@326
  2848
          }
deba@326
  2849
        }
deba@326
  2850
        _node_index->set(n, index);
deba@326
  2851
        (*_node_data)[index].pot = max;
deba@326
  2852
        int blossom =
deba@326
  2853
          _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@326
  2854
deba@326
  2855
        _tree_set->insert(blossom);
deba@326
  2856
deba@326
  2857
        (*_blossom_data)[blossom].status = EVEN;
deba@326
  2858
        (*_blossom_data)[blossom].pred = INVALID;
deba@326
  2859
        (*_blossom_data)[blossom].next = INVALID;
deba@326
  2860
        (*_blossom_data)[blossom].pot = 0;
deba@326
  2861
        (*_blossom_data)[blossom].offset = 0;
deba@326
  2862
        ++index;
deba@326
  2863
      }
deba@326
  2864
      for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326
  2865
        int si = (*_node_index)[_graph.u(e)];
deba@326
  2866
        int ti = (*_node_index)[_graph.v(e)];
deba@326
  2867
        if (_graph.u(e) != _graph.v(e)) {
deba@326
  2868
          _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@326
  2869
                            dualScale * _weight[e]) / 2);
deba@326
  2870
        }
deba@326
  2871
      }
deba@326
  2872
    }
deba@326
  2873
deba@326
  2874
    /// \brief Starts the algorithm
deba@326
  2875
    ///
deba@326
  2876
    /// Starts the algorithm
deba@326
  2877
    bool start() {
deba@326
  2878
      enum OpType {
deba@326
  2879
        D2, D3, D4
deba@326
  2880
      };
deba@326
  2881
deba@326
  2882
      int unmatched = _node_num;
deba@326
  2883
      while (unmatched > 0) {
deba@326
  2884
        Value d2 = !_delta2->empty() ?
deba@326
  2885
          _delta2->prio() : std::numeric_limits<Value>::max();
deba@326
  2886
deba@326
  2887
        Value d3 = !_delta3->empty() ?
deba@326
  2888
          _delta3->prio() : std::numeric_limits<Value>::max();
deba@326
  2889
deba@326
  2890
        Value d4 = !_delta4->empty() ?
deba@326
  2891
          _delta4->prio() : std::numeric_limits<Value>::max();
deba@326
  2892
deba@326
  2893
        _delta_sum = d2; OpType ot = D2;
deba@326
  2894
        if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
deba@326
  2895
        if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@326
  2896
deba@326
  2897
        if (_delta_sum == std::numeric_limits<Value>::max()) {
deba@326
  2898
          return false;
deba@326
  2899
        }
deba@326
  2900
deba@326
  2901
        switch (ot) {
deba@326
  2902
        case D2:
deba@326
  2903
          {
deba@326
  2904
            int blossom = _delta2->top();
deba@326
  2905
            Node n = _blossom_set->classTop(blossom);
deba@326
  2906
            Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
deba@326
  2907
            extendOnArc(e);
deba@326
  2908
          }
deba@326
  2909
          break;
deba@326
  2910
        case D3:
deba@326
  2911
          {
deba@326
  2912
            Edge e = _delta3->top();
deba@326
  2913
deba@326
  2914
            int left_blossom = _blossom_set->find(_graph.u(e));
deba@326
  2915
            int right_blossom = _blossom_set->find(_graph.v(e));
deba@326
  2916
deba@326
  2917
            if (left_blossom == right_blossom) {
deba@326
  2918
              _delta3->pop();
deba@326
  2919
            } else {
deba@326
  2920
              int left_tree = _tree_set->find(left_blossom);
deba@326
  2921
              int right_tree = _tree_set->find(right_blossom);
deba@326
  2922
deba@326
  2923
              if (left_tree == right_tree) {
deba@327
  2924
                shrinkOnEdge(e, left_tree);
deba@326
  2925
              } else {
deba@327
  2926
                augmentOnEdge(e);
deba@326
  2927
                unmatched -= 2;
deba@326
  2928
              }
deba@326
  2929
            }
deba@326
  2930
          } break;
deba@326
  2931
        case D4:
deba@326
  2932
          splitBlossom(_delta4->top());
deba@326
  2933
          break;
deba@326
  2934
        }
deba@326
  2935
      }
deba@326
  2936
      extractMatching();
deba@326
  2937
      return true;
deba@326
  2938
    }
deba@326
  2939
deba@326
  2940
    /// \brief Runs %MaxWeightedPerfectMatching algorithm.
deba@326
  2941
    ///
deba@326
  2942
    /// This method runs the %MaxWeightedPerfectMatching algorithm.
deba@326
  2943
    ///
deba@326
  2944
    /// \note mwm.run() is just a shortcut of the following code.
deba@326
  2945
    /// \code
deba@326
  2946
    ///   mwm.init();
deba@326
  2947
    ///   mwm.start();
deba@326
  2948
    /// \endcode
deba@326
  2949
    bool run() {
deba@326
  2950
      init();
deba@326
  2951
      return start();
deba@326
  2952
    }
deba@326
  2953
deba@326
  2954
    /// @}
deba@326
  2955
deba@326
  2956
    /// \name Primal solution
alpar@330
  2957
    /// Functions to get the primal solution, ie. the matching.
deba@326
  2958
deba@326
  2959
    /// @{
deba@326
  2960
deba@326
  2961
    /// \brief Returns the matching value.
deba@326
  2962
    ///
deba@326
  2963
    /// Returns the matching value.
deba@326
  2964
    Value matchingValue() const {
deba@326
  2965
      Value sum = 0;
deba@326
  2966
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  2967
        if ((*_matching)[n] != INVALID) {
deba@326
  2968
          sum += _weight[(*_matching)[n]];
deba@326
  2969
        }
deba@326
  2970
      }
deba@326
  2971
      return sum /= 2;
deba@326
  2972
    }
deba@326
  2973
deba@327
  2974
    /// \brief Returns true when the edge is in the matching.
deba@326
  2975
    ///
deba@327
  2976
    /// Returns true when the edge is in the matching.
deba@327
  2977
    bool matching(const Edge& edge) const {
deba@327
  2978
      return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge;
deba@326
  2979
    }
deba@326
  2980
deba@327
  2981
    /// \brief Returns the incident matching edge.
deba@326
  2982
    ///
deba@327
  2983
    /// Returns the incident matching arc from given edge.
deba@326
  2984
    Arc matching(const Node& node) const {
deba@326
  2985
      return (*_matching)[node];
deba@326
  2986
    }
deba@326
  2987
deba@326
  2988
    /// \brief Returns the mate of the node.
deba@326
  2989
    ///
deba@326
  2990
    /// Returns the adjancent node in a mathcing arc.
deba@326
  2991
    Node mate(const Node& node) const {
deba@326
  2992
      return _graph.target((*_matching)[node]);
deba@326
  2993
    }
deba@326
  2994
deba@326
  2995
    /// @}
deba@326
  2996
deba@326
  2997
    /// \name Dual solution
alpar@330
  2998
    /// Functions to get the dual solution.
deba@326
  2999
deba@326
  3000
    /// @{
deba@326
  3001
deba@326
  3002
    /// \brief Returns the value of the dual solution.
deba@326
  3003
    ///
deba@326
  3004
    /// Returns the value of the dual solution. It should be equal to
deba@326
  3005
    /// the primal value scaled by \ref dualScale "dual scale".
deba@326
  3006
    Value dualValue() const {
deba@326
  3007
      Value sum = 0;
deba@326
  3008
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  3009
        sum += nodeValue(n);
deba@326
  3010
      }
deba@326
  3011
      for (int i = 0; i < blossomNum(); ++i) {
deba@326
  3012
        sum += blossomValue(i) * (blossomSize(i) / 2);
deba@326
  3013
      }
deba@326
  3014
      return sum;
deba@326
  3015
    }
deba@326
  3016
deba@326
  3017
    /// \brief Returns the value of the node.
deba@326
  3018
    ///
deba@326
  3019
    /// Returns the the value of the node.
deba@326
  3020
    Value nodeValue(const Node& n) const {
deba@326
  3021
      return (*_node_potential)[n];
deba@326
  3022
    }
deba@326
  3023
deba@326
  3024
    /// \brief Returns the number of the blossoms in the basis.
deba@326
  3025
    ///
deba@326
  3026
    /// Returns the number of the blossoms in the basis.
deba@326
  3027
    /// \see BlossomIt
deba@326
  3028
    int blossomNum() const {
deba@326
  3029
      return _blossom_potential.size();
deba@326
  3030
    }
deba@326
  3031
deba@326
  3032
deba@326
  3033
    /// \brief Returns the number of the nodes in the blossom.
deba@326
  3034
    ///
deba@326
  3035
    /// Returns the number of the nodes in the blossom.
deba@326
  3036
    int blossomSize(int k) const {
deba@326
  3037
      return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@326
  3038
    }
deba@326
  3039
deba@326
  3040
    /// \brief Returns the value of the blossom.
deba@326
  3041
    ///
deba@326
  3042
    /// Returns the the value of the blossom.
deba@326
  3043
    /// \see BlossomIt
deba@326
  3044
    Value blossomValue(int k) const {
deba@326
  3045
      return _blossom_potential[k].value;
deba@326
  3046
    }
deba@326
  3047
alpar@330
  3048
    /// \brief Iterator for obtaining the nodes of the blossom.
deba@326
  3049
    ///
alpar@330
  3050
    /// Iterator for obtaining the nodes of the blossom. This class
alpar@330
  3051
    /// provides a common lemon style iterator for listing a
deba@326
  3052
    /// subset of the nodes.
deba@326
  3053
    class BlossomIt {
deba@326
  3054
    public:
deba@326
  3055
deba@326
  3056
      /// \brief Constructor.
deba@326
  3057
      ///
alpar@330
  3058
      /// Constructor to get the nodes of the variable.
deba@326
  3059
      BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
deba@326
  3060
        : _algorithm(&algorithm)
deba@326
  3061
      {
deba@326
  3062
        _index = _algorithm->_blossom_potential[variable].begin;
deba@326
  3063
        _last = _algorithm->_blossom_potential[variable].end;
deba@326
  3064
      }
deba@326
  3065
deba@326
  3066
      /// \brief Conversion to node.
deba@326
  3067
      ///
deba@326
  3068
      /// Conversion to node.
deba@326
  3069
      operator Node() const {
deba@327
  3070
        return _algorithm->_blossom_node_list[_index];
deba@326
  3071
      }
deba@326
  3072
deba@326
  3073
      /// \brief Increment operator.
deba@326
  3074
      ///
deba@326
  3075
      /// Increment operator.
deba@326
  3076
      BlossomIt& operator++() {
deba@326
  3077
        ++_index;
deba@326
  3078
        return *this;
deba@326
  3079
      }
deba@326
  3080
deba@327
  3081
      /// \brief Validity checking
deba@327
  3082
      ///
deba@327
  3083
      /// Checks whether the iterator is invalid.
deba@327
  3084
      bool operator==(Invalid) const { return _index == _last; }
deba@327
  3085
deba@327
  3086
      /// \brief Validity checking
deba@327
  3087
      ///
deba@327
  3088
      /// Checks whether the iterator is valid.
deba@327
  3089
      bool operator!=(Invalid) const { return _index != _last; }
deba@326
  3090
deba@326
  3091
    private:
deba@326
  3092
      const MaxWeightedPerfectMatching* _algorithm;
deba@326
  3093
      int _last;
deba@326
  3094
      int _index;
deba@326
  3095
    };
deba@326
  3096
deba@326
  3097
    /// @}
deba@326
  3098
deba@326
  3099
  };
deba@326
  3100
deba@326
  3101
deba@326
  3102
} //END OF NAMESPACE LEMON
deba@326
  3103
deba@326
  3104
#endif //LEMON_MAX_MATCHING_H