lemon/network_simplex.h
author Peter Kovacs <kpeter@inf.elte.hu>
Wed, 25 Mar 2009 15:58:44 +0100
changeset 652 5232721b3f14
parent 651 8c3112a66878
child 653 c7d160f73d52
permissions -rw-r--r--
Rework the interface of NetworkSimplex (#234)

The parameters of the problem can be set with separate functions
instead of different constructors.
kpeter@648
     1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@648
     2
 *
kpeter@648
     3
 * This file is a part of LEMON, a generic C++ optimization library.
kpeter@648
     4
 *
kpeter@648
     5
 * Copyright (C) 2003-2009
kpeter@648
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@648
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@648
     8
 *
kpeter@648
     9
 * Permission to use, modify and distribute this software is granted
kpeter@648
    10
 * provided that this copyright notice appears in all copies. For
kpeter@648
    11
 * precise terms see the accompanying LICENSE file.
kpeter@648
    12
 *
kpeter@648
    13
 * This software is provided "AS IS" with no warranty of any kind,
kpeter@648
    14
 * express or implied, and with no claim as to its suitability for any
kpeter@648
    15
 * purpose.
kpeter@648
    16
 *
kpeter@648
    17
 */
kpeter@648
    18
kpeter@648
    19
#ifndef LEMON_NETWORK_SIMPLEX_H
kpeter@648
    20
#define LEMON_NETWORK_SIMPLEX_H
kpeter@648
    21
kpeter@648
    22
/// \ingroup min_cost_flow
kpeter@648
    23
///
kpeter@648
    24
/// \file
kpeter@652
    25
/// \brief Network Simplex algorithm for finding a minimum cost flow.
kpeter@648
    26
kpeter@648
    27
#include <vector>
kpeter@648
    28
#include <limits>
kpeter@648
    29
#include <algorithm>
kpeter@648
    30
kpeter@650
    31
#include <lemon/core.h>
kpeter@648
    32
#include <lemon/math.h>
kpeter@648
    33
kpeter@648
    34
namespace lemon {
kpeter@648
    35
kpeter@648
    36
  /// \addtogroup min_cost_flow
kpeter@648
    37
  /// @{
kpeter@648
    38
kpeter@652
    39
  /// \brief Implementation of the primal Network Simplex algorithm
kpeter@648
    40
  /// for finding a \ref min_cost_flow "minimum cost flow".
kpeter@648
    41
  ///
kpeter@652
    42
  /// \ref NetworkSimplex implements the primal Network Simplex algorithm
kpeter@648
    43
  /// for finding a \ref min_cost_flow "minimum cost flow".
kpeter@648
    44
  ///
kpeter@652
    45
  /// \tparam GR The digraph type the algorithm runs on.
kpeter@652
    46
  /// \tparam V The value type used in the algorithm.
kpeter@652
    47
  /// By default it is \c int.
kpeter@648
    48
  ///
kpeter@652
    49
  /// \warning \c V must be a signed integer type.
kpeter@648
    50
  ///
kpeter@652
    51
  /// \note %NetworkSimplex provides five different pivot rule
kpeter@652
    52
  /// implementations. For more information see \ref PivotRule.
kpeter@652
    53
  template <typename GR, typename V = int>
kpeter@648
    54
  class NetworkSimplex
kpeter@648
    55
  {
kpeter@652
    56
  public:
kpeter@648
    57
kpeter@652
    58
    /// The value type of the algorithm
kpeter@652
    59
    typedef V Value;
kpeter@652
    60
    /// The type of the flow map
kpeter@652
    61
    typedef typename GR::template ArcMap<Value> FlowMap;
kpeter@652
    62
    /// The type of the potential map
kpeter@652
    63
    typedef typename GR::template NodeMap<Value> PotentialMap;
kpeter@652
    64
kpeter@652
    65
  public:
kpeter@652
    66
kpeter@652
    67
    /// \brief Enum type for selecting the pivot rule.
kpeter@652
    68
    ///
kpeter@652
    69
    /// Enum type for selecting the pivot rule for the \ref run()
kpeter@652
    70
    /// function.
kpeter@652
    71
    ///
kpeter@652
    72
    /// \ref NetworkSimplex provides five different pivot rule
kpeter@652
    73
    /// implementations that significantly affect the running time
kpeter@652
    74
    /// of the algorithm.
kpeter@652
    75
    /// By default \ref BLOCK_SEARCH "Block Search" is used, which
kpeter@652
    76
    /// proved to be the most efficient and the most robust on various
kpeter@652
    77
    /// test inputs according to our benchmark tests.
kpeter@652
    78
    /// However another pivot rule can be selected using the \ref run()
kpeter@652
    79
    /// function with the proper parameter.
kpeter@652
    80
    enum PivotRule {
kpeter@652
    81
kpeter@652
    82
      /// The First Eligible pivot rule.
kpeter@652
    83
      /// The next eligible arc is selected in a wraparound fashion
kpeter@652
    84
      /// in every iteration.
kpeter@652
    85
      FIRST_ELIGIBLE,
kpeter@652
    86
kpeter@652
    87
      /// The Best Eligible pivot rule.
kpeter@652
    88
      /// The best eligible arc is selected in every iteration.
kpeter@652
    89
      BEST_ELIGIBLE,
kpeter@652
    90
kpeter@652
    91
      /// The Block Search pivot rule.
kpeter@652
    92
      /// A specified number of arcs are examined in every iteration
kpeter@652
    93
      /// in a wraparound fashion and the best eligible arc is selected
kpeter@652
    94
      /// from this block.
kpeter@652
    95
      BLOCK_SEARCH,
kpeter@652
    96
kpeter@652
    97
      /// The Candidate List pivot rule.
kpeter@652
    98
      /// In a major iteration a candidate list is built from eligible arcs
kpeter@652
    99
      /// in a wraparound fashion and in the following minor iterations
kpeter@652
   100
      /// the best eligible arc is selected from this list.
kpeter@652
   101
      CANDIDATE_LIST,
kpeter@652
   102
kpeter@652
   103
      /// The Altering Candidate List pivot rule.
kpeter@652
   104
      /// It is a modified version of the Candidate List method.
kpeter@652
   105
      /// It keeps only the several best eligible arcs from the former
kpeter@652
   106
      /// candidate list and extends this list in every iteration.
kpeter@652
   107
      ALTERING_LIST
kpeter@652
   108
    };
kpeter@652
   109
kpeter@652
   110
  private:
kpeter@652
   111
kpeter@652
   112
    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
kpeter@652
   113
kpeter@652
   114
    typedef typename GR::template ArcMap<Value> ValueArcMap;
kpeter@652
   115
    typedef typename GR::template NodeMap<Value> ValueNodeMap;
kpeter@648
   116
kpeter@648
   117
    typedef std::vector<Arc> ArcVector;
kpeter@648
   118
    typedef std::vector<Node> NodeVector;
kpeter@648
   119
    typedef std::vector<int> IntVector;
kpeter@648
   120
    typedef std::vector<bool> BoolVector;
kpeter@652
   121
    typedef std::vector<Value> ValueVector;
kpeter@648
   122
kpeter@648
   123
    // State constants for arcs
kpeter@648
   124
    enum ArcStateEnum {
kpeter@648
   125
      STATE_UPPER = -1,
kpeter@648
   126
      STATE_TREE  =  0,
kpeter@648
   127
      STATE_LOWER =  1
kpeter@648
   128
    };
kpeter@648
   129
kpeter@648
   130
  private:
kpeter@648
   131
kpeter@652
   132
    // Data related to the underlying digraph
kpeter@652
   133
    const GR &_graph;
kpeter@652
   134
    int _node_num;
kpeter@652
   135
    int _arc_num;
kpeter@652
   136
kpeter@652
   137
    // Parameters of the problem
kpeter@652
   138
    ValueArcMap *_plower;
kpeter@652
   139
    ValueArcMap *_pupper;
kpeter@652
   140
    ValueArcMap *_pcost;
kpeter@652
   141
    ValueNodeMap *_psupply;
kpeter@652
   142
    bool _pstsup;
kpeter@652
   143
    Node _psource, _ptarget;
kpeter@652
   144
    Value _pstflow;
kpeter@648
   145
kpeter@648
   146
    // Result maps
kpeter@650
   147
    FlowMap *_flow_map;
kpeter@650
   148
    PotentialMap *_potential_map;
kpeter@648
   149
    bool _local_flow;
kpeter@648
   150
    bool _local_potential;
kpeter@648
   151
kpeter@652
   152
    // Data structures for storing the digraph
kpeter@650
   153
    IntNodeMap _node_id;
kpeter@650
   154
    ArcVector _arc_ref;
kpeter@650
   155
    IntVector _source;
kpeter@650
   156
    IntVector _target;
kpeter@650
   157
kpeter@652
   158
    // Node and arc data
kpeter@652
   159
    ValueVector _cap;
kpeter@652
   160
    ValueVector _cost;
kpeter@652
   161
    ValueVector _supply;
kpeter@652
   162
    ValueVector _flow;
kpeter@652
   163
    ValueVector _pi;
kpeter@648
   164
kpeter@650
   165
    // Data for storing the spanning tree structure
kpeter@648
   166
    IntVector _parent;
kpeter@648
   167
    IntVector _pred;
kpeter@648
   168
    IntVector _thread;
kpeter@651
   169
    IntVector _rev_thread;
kpeter@651
   170
    IntVector _succ_num;
kpeter@651
   171
    IntVector _last_succ;
kpeter@651
   172
    IntVector _dirty_revs;
kpeter@648
   173
    BoolVector _forward;
kpeter@648
   174
    IntVector _state;
kpeter@648
   175
    int _root;
kpeter@648
   176
kpeter@648
   177
    // Temporary data used in the current pivot iteration
kpeter@650
   178
    int in_arc, join, u_in, v_in, u_out, v_out;
kpeter@650
   179
    int first, second, right, last;
kpeter@648
   180
    int stem, par_stem, new_stem;
kpeter@652
   181
    Value delta;
kpeter@648
   182
kpeter@648
   183
  private:
kpeter@648
   184
kpeter@652
   185
    // Implementation of the First Eligible pivot rule
kpeter@648
   186
    class FirstEligiblePivotRule
kpeter@648
   187
    {
kpeter@648
   188
    private:
kpeter@648
   189
kpeter@648
   190
      // References to the NetworkSimplex class
kpeter@648
   191
      const IntVector  &_source;
kpeter@648
   192
      const IntVector  &_target;
kpeter@652
   193
      const ValueVector &_cost;
kpeter@648
   194
      const IntVector  &_state;
kpeter@652
   195
      const ValueVector &_pi;
kpeter@648
   196
      int &_in_arc;
kpeter@648
   197
      int _arc_num;
kpeter@648
   198
kpeter@648
   199
      // Pivot rule data
kpeter@648
   200
      int _next_arc;
kpeter@648
   201
kpeter@648
   202
    public:
kpeter@648
   203
kpeter@652
   204
      // Constructor
kpeter@648
   205
      FirstEligiblePivotRule(NetworkSimplex &ns) :
kpeter@650
   206
        _source(ns._source), _target(ns._target),
kpeter@648
   207
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@650
   208
        _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0)
kpeter@648
   209
      {}
kpeter@648
   210
kpeter@652
   211
      // Find next entering arc
kpeter@648
   212
      bool findEnteringArc() {
kpeter@652
   213
        Value c;
kpeter@648
   214
        for (int e = _next_arc; e < _arc_num; ++e) {
kpeter@648
   215
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   216
          if (c < 0) {
kpeter@648
   217
            _in_arc = e;
kpeter@648
   218
            _next_arc = e + 1;
kpeter@648
   219
            return true;
kpeter@648
   220
          }
kpeter@648
   221
        }
kpeter@648
   222
        for (int e = 0; e < _next_arc; ++e) {
kpeter@648
   223
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   224
          if (c < 0) {
kpeter@648
   225
            _in_arc = e;
kpeter@648
   226
            _next_arc = e + 1;
kpeter@648
   227
            return true;
kpeter@648
   228
          }
kpeter@648
   229
        }
kpeter@648
   230
        return false;
kpeter@648
   231
      }
kpeter@648
   232
kpeter@648
   233
    }; //class FirstEligiblePivotRule
kpeter@648
   234
kpeter@648
   235
kpeter@652
   236
    // Implementation of the Best Eligible pivot rule
kpeter@648
   237
    class BestEligiblePivotRule
kpeter@648
   238
    {
kpeter@648
   239
    private:
kpeter@648
   240
kpeter@648
   241
      // References to the NetworkSimplex class
kpeter@648
   242
      const IntVector  &_source;
kpeter@648
   243
      const IntVector  &_target;
kpeter@652
   244
      const ValueVector &_cost;
kpeter@648
   245
      const IntVector  &_state;
kpeter@652
   246
      const ValueVector &_pi;
kpeter@648
   247
      int &_in_arc;
kpeter@648
   248
      int _arc_num;
kpeter@648
   249
kpeter@648
   250
    public:
kpeter@648
   251
kpeter@652
   252
      // Constructor
kpeter@648
   253
      BestEligiblePivotRule(NetworkSimplex &ns) :
kpeter@650
   254
        _source(ns._source), _target(ns._target),
kpeter@648
   255
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@650
   256
        _in_arc(ns.in_arc), _arc_num(ns._arc_num)
kpeter@648
   257
      {}
kpeter@648
   258
kpeter@652
   259
      // Find next entering arc
kpeter@648
   260
      bool findEnteringArc() {
kpeter@652
   261
        Value c, min = 0;
kpeter@648
   262
        for (int e = 0; e < _arc_num; ++e) {
kpeter@648
   263
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   264
          if (c < min) {
kpeter@648
   265
            min = c;
kpeter@648
   266
            _in_arc = e;
kpeter@648
   267
          }
kpeter@648
   268
        }
kpeter@648
   269
        return min < 0;
kpeter@648
   270
      }
kpeter@648
   271
kpeter@648
   272
    }; //class BestEligiblePivotRule
kpeter@648
   273
kpeter@648
   274
kpeter@652
   275
    // Implementation of the Block Search pivot rule
kpeter@648
   276
    class BlockSearchPivotRule
kpeter@648
   277
    {
kpeter@648
   278
    private:
kpeter@648
   279
kpeter@648
   280
      // References to the NetworkSimplex class
kpeter@648
   281
      const IntVector  &_source;
kpeter@648
   282
      const IntVector  &_target;
kpeter@652
   283
      const ValueVector &_cost;
kpeter@648
   284
      const IntVector  &_state;
kpeter@652
   285
      const ValueVector &_pi;
kpeter@648
   286
      int &_in_arc;
kpeter@648
   287
      int _arc_num;
kpeter@648
   288
kpeter@648
   289
      // Pivot rule data
kpeter@648
   290
      int _block_size;
kpeter@648
   291
      int _next_arc;
kpeter@648
   292
kpeter@648
   293
    public:
kpeter@648
   294
kpeter@652
   295
      // Constructor
kpeter@648
   296
      BlockSearchPivotRule(NetworkSimplex &ns) :
kpeter@650
   297
        _source(ns._source), _target(ns._target),
kpeter@648
   298
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@650
   299
        _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0)
kpeter@648
   300
      {
kpeter@648
   301
        // The main parameters of the pivot rule
kpeter@648
   302
        const double BLOCK_SIZE_FACTOR = 2.0;
kpeter@648
   303
        const int MIN_BLOCK_SIZE = 10;
kpeter@648
   304
kpeter@648
   305
        _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
kpeter@648
   306
                                MIN_BLOCK_SIZE );
kpeter@648
   307
      }
kpeter@648
   308
kpeter@652
   309
      // Find next entering arc
kpeter@648
   310
      bool findEnteringArc() {
kpeter@652
   311
        Value c, min = 0;
kpeter@648
   312
        int cnt = _block_size;
kpeter@648
   313
        int e, min_arc = _next_arc;
kpeter@648
   314
        for (e = _next_arc; e < _arc_num; ++e) {
kpeter@648
   315
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   316
          if (c < min) {
kpeter@648
   317
            min = c;
kpeter@648
   318
            min_arc = e;
kpeter@648
   319
          }
kpeter@648
   320
          if (--cnt == 0) {
kpeter@648
   321
            if (min < 0) break;
kpeter@648
   322
            cnt = _block_size;
kpeter@648
   323
          }
kpeter@648
   324
        }
kpeter@648
   325
        if (min == 0 || cnt > 0) {
kpeter@648
   326
          for (e = 0; e < _next_arc; ++e) {
kpeter@648
   327
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   328
            if (c < min) {
kpeter@648
   329
              min = c;
kpeter@648
   330
              min_arc = e;
kpeter@648
   331
            }
kpeter@648
   332
            if (--cnt == 0) {
kpeter@648
   333
              if (min < 0) break;
kpeter@648
   334
              cnt = _block_size;
kpeter@648
   335
            }
kpeter@648
   336
          }
kpeter@648
   337
        }
kpeter@648
   338
        if (min >= 0) return false;
kpeter@648
   339
        _in_arc = min_arc;
kpeter@648
   340
        _next_arc = e;
kpeter@648
   341
        return true;
kpeter@648
   342
      }
kpeter@648
   343
kpeter@648
   344
    }; //class BlockSearchPivotRule
kpeter@648
   345
kpeter@648
   346
kpeter@652
   347
    // Implementation of the Candidate List pivot rule
kpeter@648
   348
    class CandidateListPivotRule
kpeter@648
   349
    {
kpeter@648
   350
    private:
kpeter@648
   351
kpeter@648
   352
      // References to the NetworkSimplex class
kpeter@648
   353
      const IntVector  &_source;
kpeter@648
   354
      const IntVector  &_target;
kpeter@652
   355
      const ValueVector &_cost;
kpeter@648
   356
      const IntVector  &_state;
kpeter@652
   357
      const ValueVector &_pi;
kpeter@648
   358
      int &_in_arc;
kpeter@648
   359
      int _arc_num;
kpeter@648
   360
kpeter@648
   361
      // Pivot rule data
kpeter@648
   362
      IntVector _candidates;
kpeter@648
   363
      int _list_length, _minor_limit;
kpeter@648
   364
      int _curr_length, _minor_count;
kpeter@648
   365
      int _next_arc;
kpeter@648
   366
kpeter@648
   367
    public:
kpeter@648
   368
kpeter@648
   369
      /// Constructor
kpeter@648
   370
      CandidateListPivotRule(NetworkSimplex &ns) :
kpeter@650
   371
        _source(ns._source), _target(ns._target),
kpeter@648
   372
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@650
   373
        _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0)
kpeter@648
   374
      {
kpeter@648
   375
        // The main parameters of the pivot rule
kpeter@648
   376
        const double LIST_LENGTH_FACTOR = 1.0;
kpeter@648
   377
        const int MIN_LIST_LENGTH = 10;
kpeter@648
   378
        const double MINOR_LIMIT_FACTOR = 0.1;
kpeter@648
   379
        const int MIN_MINOR_LIMIT = 3;
kpeter@648
   380
kpeter@648
   381
        _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)),
kpeter@648
   382
                                 MIN_LIST_LENGTH );
kpeter@648
   383
        _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
kpeter@648
   384
                                 MIN_MINOR_LIMIT );
kpeter@648
   385
        _curr_length = _minor_count = 0;
kpeter@648
   386
        _candidates.resize(_list_length);
kpeter@648
   387
      }
kpeter@648
   388
kpeter@648
   389
      /// Find next entering arc
kpeter@648
   390
      bool findEnteringArc() {
kpeter@652
   391
        Value min, c;
kpeter@648
   392
        int e, min_arc = _next_arc;
kpeter@648
   393
        if (_curr_length > 0 && _minor_count < _minor_limit) {
kpeter@648
   394
          // Minor iteration: select the best eligible arc from the
kpeter@648
   395
          // current candidate list
kpeter@648
   396
          ++_minor_count;
kpeter@648
   397
          min = 0;
kpeter@648
   398
          for (int i = 0; i < _curr_length; ++i) {
kpeter@648
   399
            e = _candidates[i];
kpeter@648
   400
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   401
            if (c < min) {
kpeter@648
   402
              min = c;
kpeter@648
   403
              min_arc = e;
kpeter@648
   404
            }
kpeter@648
   405
            if (c >= 0) {
kpeter@648
   406
              _candidates[i--] = _candidates[--_curr_length];
kpeter@648
   407
            }
kpeter@648
   408
          }
kpeter@648
   409
          if (min < 0) {
kpeter@648
   410
            _in_arc = min_arc;
kpeter@648
   411
            return true;
kpeter@648
   412
          }
kpeter@648
   413
        }
kpeter@648
   414
kpeter@648
   415
        // Major iteration: build a new candidate list
kpeter@648
   416
        min = 0;
kpeter@648
   417
        _curr_length = 0;
kpeter@648
   418
        for (e = _next_arc; e < _arc_num; ++e) {
kpeter@648
   419
          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   420
          if (c < 0) {
kpeter@648
   421
            _candidates[_curr_length++] = e;
kpeter@648
   422
            if (c < min) {
kpeter@648
   423
              min = c;
kpeter@648
   424
              min_arc = e;
kpeter@648
   425
            }
kpeter@648
   426
            if (_curr_length == _list_length) break;
kpeter@648
   427
          }
kpeter@648
   428
        }
kpeter@648
   429
        if (_curr_length < _list_length) {
kpeter@648
   430
          for (e = 0; e < _next_arc; ++e) {
kpeter@648
   431
            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   432
            if (c < 0) {
kpeter@648
   433
              _candidates[_curr_length++] = e;
kpeter@648
   434
              if (c < min) {
kpeter@648
   435
                min = c;
kpeter@648
   436
                min_arc = e;
kpeter@648
   437
              }
kpeter@648
   438
              if (_curr_length == _list_length) break;
kpeter@648
   439
            }
kpeter@648
   440
          }
kpeter@648
   441
        }
kpeter@648
   442
        if (_curr_length == 0) return false;
kpeter@648
   443
        _minor_count = 1;
kpeter@648
   444
        _in_arc = min_arc;
kpeter@648
   445
        _next_arc = e;
kpeter@648
   446
        return true;
kpeter@648
   447
      }
kpeter@648
   448
kpeter@648
   449
    }; //class CandidateListPivotRule
kpeter@648
   450
kpeter@648
   451
kpeter@652
   452
    // Implementation of the Altering Candidate List pivot rule
kpeter@648
   453
    class AlteringListPivotRule
kpeter@648
   454
    {
kpeter@648
   455
    private:
kpeter@648
   456
kpeter@648
   457
      // References to the NetworkSimplex class
kpeter@648
   458
      const IntVector  &_source;
kpeter@648
   459
      const IntVector  &_target;
kpeter@652
   460
      const ValueVector &_cost;
kpeter@648
   461
      const IntVector  &_state;
kpeter@652
   462
      const ValueVector &_pi;
kpeter@648
   463
      int &_in_arc;
kpeter@648
   464
      int _arc_num;
kpeter@648
   465
kpeter@648
   466
      // Pivot rule data
kpeter@648
   467
      int _block_size, _head_length, _curr_length;
kpeter@648
   468
      int _next_arc;
kpeter@648
   469
      IntVector _candidates;
kpeter@652
   470
      ValueVector _cand_cost;
kpeter@648
   471
kpeter@648
   472
      // Functor class to compare arcs during sort of the candidate list
kpeter@648
   473
      class SortFunc
kpeter@648
   474
      {
kpeter@648
   475
      private:
kpeter@652
   476
        const ValueVector &_map;
kpeter@648
   477
      public:
kpeter@652
   478
        SortFunc(const ValueVector &map) : _map(map) {}
kpeter@648
   479
        bool operator()(int left, int right) {
kpeter@648
   480
          return _map[left] > _map[right];
kpeter@648
   481
        }
kpeter@648
   482
      };
kpeter@648
   483
kpeter@648
   484
      SortFunc _sort_func;
kpeter@648
   485
kpeter@648
   486
    public:
kpeter@648
   487
kpeter@652
   488
      // Constructor
kpeter@648
   489
      AlteringListPivotRule(NetworkSimplex &ns) :
kpeter@650
   490
        _source(ns._source), _target(ns._target),
kpeter@648
   491
        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@650
   492
        _in_arc(ns.in_arc), _arc_num(ns._arc_num),
kpeter@648
   493
        _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost)
kpeter@648
   494
      {
kpeter@648
   495
        // The main parameters of the pivot rule
kpeter@648
   496
        const double BLOCK_SIZE_FACTOR = 1.5;
kpeter@648
   497
        const int MIN_BLOCK_SIZE = 10;
kpeter@648
   498
        const double HEAD_LENGTH_FACTOR = 0.1;
kpeter@648
   499
        const int MIN_HEAD_LENGTH = 3;
kpeter@648
   500
kpeter@648
   501
        _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
kpeter@648
   502
                                MIN_BLOCK_SIZE );
kpeter@648
   503
        _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
kpeter@648
   504
                                 MIN_HEAD_LENGTH );
kpeter@648
   505
        _candidates.resize(_head_length + _block_size);
kpeter@648
   506
        _curr_length = 0;
kpeter@648
   507
      }
kpeter@648
   508
kpeter@652
   509
      // Find next entering arc
kpeter@648
   510
      bool findEnteringArc() {
kpeter@648
   511
        // Check the current candidate list
kpeter@648
   512
        int e;
kpeter@648
   513
        for (int i = 0; i < _curr_length; ++i) {
kpeter@648
   514
          e = _candidates[i];
kpeter@648
   515
          _cand_cost[e] = _state[e] *
kpeter@648
   516
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   517
          if (_cand_cost[e] >= 0) {
kpeter@648
   518
            _candidates[i--] = _candidates[--_curr_length];
kpeter@648
   519
          }
kpeter@648
   520
        }
kpeter@648
   521
kpeter@648
   522
        // Extend the list
kpeter@648
   523
        int cnt = _block_size;
kpeter@650
   524
        int last_arc = 0;
kpeter@648
   525
        int limit = _head_length;
kpeter@648
   526
kpeter@648
   527
        for (int e = _next_arc; e < _arc_num; ++e) {
kpeter@648
   528
          _cand_cost[e] = _state[e] *
kpeter@648
   529
            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   530
          if (_cand_cost[e] < 0) {
kpeter@648
   531
            _candidates[_curr_length++] = e;
kpeter@650
   532
            last_arc = e;
kpeter@648
   533
          }
kpeter@648
   534
          if (--cnt == 0) {
kpeter@648
   535
            if (_curr_length > limit) break;
kpeter@648
   536
            limit = 0;
kpeter@648
   537
            cnt = _block_size;
kpeter@648
   538
          }
kpeter@648
   539
        }
kpeter@648
   540
        if (_curr_length <= limit) {
kpeter@648
   541
          for (int e = 0; e < _next_arc; ++e) {
kpeter@648
   542
            _cand_cost[e] = _state[e] *
kpeter@648
   543
              (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@648
   544
            if (_cand_cost[e] < 0) {
kpeter@648
   545
              _candidates[_curr_length++] = e;
kpeter@650
   546
              last_arc = e;
kpeter@648
   547
            }
kpeter@648
   548
            if (--cnt == 0) {
kpeter@648
   549
              if (_curr_length > limit) break;
kpeter@648
   550
              limit = 0;
kpeter@648
   551
              cnt = _block_size;
kpeter@648
   552
            }
kpeter@648
   553
          }
kpeter@648
   554
        }
kpeter@648
   555
        if (_curr_length == 0) return false;
kpeter@650
   556
        _next_arc = last_arc + 1;
kpeter@648
   557
kpeter@648
   558
        // Make heap of the candidate list (approximating a partial sort)
kpeter@648
   559
        make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@648
   560
                   _sort_func );
kpeter@648
   561
kpeter@648
   562
        // Pop the first element of the heap
kpeter@648
   563
        _in_arc = _candidates[0];
kpeter@648
   564
        pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@648
   565
                  _sort_func );
kpeter@648
   566
        _curr_length = std::min(_head_length, _curr_length - 1);
kpeter@648
   567
        return true;
kpeter@648
   568
      }
kpeter@648
   569
kpeter@648
   570
    }; //class AlteringListPivotRule
kpeter@648
   571
kpeter@648
   572
  public:
kpeter@648
   573
kpeter@652
   574
    /// \brief Constructor.
kpeter@648
   575
    ///
kpeter@652
   576
    /// Constructor.
kpeter@648
   577
    ///
kpeter@650
   578
    /// \param graph The digraph the algorithm runs on.
kpeter@652
   579
    NetworkSimplex(const GR& graph) :
kpeter@652
   580
      _graph(graph),
kpeter@652
   581
      _plower(NULL), _pupper(NULL), _pcost(NULL),
kpeter@652
   582
      _psupply(NULL), _pstsup(false),
kpeter@650
   583
      _flow_map(NULL), _potential_map(NULL),
kpeter@648
   584
      _local_flow(false), _local_potential(false),
kpeter@650
   585
      _node_id(graph)
kpeter@652
   586
    {
kpeter@652
   587
      LEMON_ASSERT(std::numeric_limits<Value>::is_integer &&
kpeter@652
   588
                   std::numeric_limits<Value>::is_signed,
kpeter@652
   589
        "The value type of NetworkSimplex must be a signed integer");
kpeter@652
   590
    }
kpeter@648
   591
kpeter@648
   592
    /// Destructor.
kpeter@648
   593
    ~NetworkSimplex() {
kpeter@650
   594
      if (_local_flow) delete _flow_map;
kpeter@650
   595
      if (_local_potential) delete _potential_map;
kpeter@648
   596
    }
kpeter@648
   597
kpeter@652
   598
    /// \brief Set the lower bounds on the arcs.
kpeter@652
   599
    ///
kpeter@652
   600
    /// This function sets the lower bounds on the arcs.
kpeter@652
   601
    /// If neither this function nor \ref boundMaps() is used before
kpeter@652
   602
    /// calling \ref run(), the lower bounds will be set to zero
kpeter@652
   603
    /// on all arcs.
kpeter@652
   604
    ///
kpeter@652
   605
    /// \param map An arc map storing the lower bounds.
kpeter@652
   606
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   607
    /// of the algorithm.
kpeter@652
   608
    ///
kpeter@652
   609
    /// \return <tt>(*this)</tt>
kpeter@652
   610
    template <typename LOWER>
kpeter@652
   611
    NetworkSimplex& lowerMap(const LOWER& map) {
kpeter@652
   612
      delete _plower;
kpeter@652
   613
      _plower = new ValueArcMap(_graph);
kpeter@652
   614
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@652
   615
        (*_plower)[a] = map[a];
kpeter@652
   616
      }
kpeter@652
   617
      return *this;
kpeter@652
   618
    }
kpeter@652
   619
kpeter@652
   620
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@652
   621
    ///
kpeter@652
   622
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@652
   623
    /// If none of the functions \ref upperMap(), \ref capacityMap()
kpeter@652
   624
    /// and \ref boundMaps() is used before calling \ref run(),
kpeter@652
   625
    /// the upper bounds (capacities) will be set to
kpeter@652
   626
    /// \c std::numeric_limits<Value>::max() on all arcs.
kpeter@652
   627
    ///
kpeter@652
   628
    /// \param map An arc map storing the upper bounds.
kpeter@652
   629
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   630
    /// of the algorithm.
kpeter@652
   631
    ///
kpeter@652
   632
    /// \return <tt>(*this)</tt>
kpeter@652
   633
    template<typename UPPER>
kpeter@652
   634
    NetworkSimplex& upperMap(const UPPER& map) {
kpeter@652
   635
      delete _pupper;
kpeter@652
   636
      _pupper = new ValueArcMap(_graph);
kpeter@652
   637
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@652
   638
        (*_pupper)[a] = map[a];
kpeter@652
   639
      }
kpeter@652
   640
      return *this;
kpeter@652
   641
    }
kpeter@652
   642
kpeter@652
   643
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@652
   644
    ///
kpeter@652
   645
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@652
   646
    /// It is just an alias for \ref upperMap().
kpeter@652
   647
    ///
kpeter@652
   648
    /// \return <tt>(*this)</tt>
kpeter@652
   649
    template<typename CAP>
kpeter@652
   650
    NetworkSimplex& capacityMap(const CAP& map) {
kpeter@652
   651
      return upperMap(map);
kpeter@652
   652
    }
kpeter@652
   653
kpeter@652
   654
    /// \brief Set the lower and upper bounds on the arcs.
kpeter@652
   655
    ///
kpeter@652
   656
    /// This function sets the lower and upper bounds on the arcs.
kpeter@652
   657
    /// If neither this function nor \ref lowerMap() is used before
kpeter@652
   658
    /// calling \ref run(), the lower bounds will be set to zero
kpeter@652
   659
    /// on all arcs.
kpeter@652
   660
    /// If none of the functions \ref upperMap(), \ref capacityMap()
kpeter@652
   661
    /// and \ref boundMaps() is used before calling \ref run(),
kpeter@652
   662
    /// the upper bounds (capacities) will be set to
kpeter@652
   663
    /// \c std::numeric_limits<Value>::max() on all arcs.
kpeter@652
   664
    ///
kpeter@652
   665
    /// \param lower An arc map storing the lower bounds.
kpeter@652
   666
    /// \param upper An arc map storing the upper bounds.
kpeter@652
   667
    ///
kpeter@652
   668
    /// The \c Value type of the maps must be convertible to the
kpeter@652
   669
    /// \c Value type of the algorithm.
kpeter@652
   670
    ///
kpeter@652
   671
    /// \note This function is just a shortcut of calling \ref lowerMap()
kpeter@652
   672
    /// and \ref upperMap() separately.
kpeter@652
   673
    ///
kpeter@652
   674
    /// \return <tt>(*this)</tt>
kpeter@652
   675
    template <typename LOWER, typename UPPER>
kpeter@652
   676
    NetworkSimplex& boundMaps(const LOWER& lower, const UPPER& upper) {
kpeter@652
   677
      return lowerMap(lower).upperMap(upper);
kpeter@652
   678
    }
kpeter@652
   679
kpeter@652
   680
    /// \brief Set the costs of the arcs.
kpeter@652
   681
    ///
kpeter@652
   682
    /// This function sets the costs of the arcs.
kpeter@652
   683
    /// If it is not used before calling \ref run(), the costs
kpeter@652
   684
    /// will be set to \c 1 on all arcs.
kpeter@652
   685
    ///
kpeter@652
   686
    /// \param map An arc map storing the costs.
kpeter@652
   687
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   688
    /// of the algorithm.
kpeter@652
   689
    ///
kpeter@652
   690
    /// \return <tt>(*this)</tt>
kpeter@652
   691
    template<typename COST>
kpeter@652
   692
    NetworkSimplex& costMap(const COST& map) {
kpeter@652
   693
      delete _pcost;
kpeter@652
   694
      _pcost = new ValueArcMap(_graph);
kpeter@652
   695
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@652
   696
        (*_pcost)[a] = map[a];
kpeter@652
   697
      }
kpeter@652
   698
      return *this;
kpeter@652
   699
    }
kpeter@652
   700
kpeter@652
   701
    /// \brief Set the supply values of the nodes.
kpeter@652
   702
    ///
kpeter@652
   703
    /// This function sets the supply values of the nodes.
kpeter@652
   704
    /// If neither this function nor \ref stSupply() is used before
kpeter@652
   705
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@652
   706
    /// (It makes sense only if non-zero lower bounds are given.)
kpeter@652
   707
    ///
kpeter@652
   708
    /// \param map A node map storing the supply values.
kpeter@652
   709
    /// Its \c Value type must be convertible to the \c Value type
kpeter@652
   710
    /// of the algorithm.
kpeter@652
   711
    ///
kpeter@652
   712
    /// \return <tt>(*this)</tt>
kpeter@652
   713
    template<typename SUP>
kpeter@652
   714
    NetworkSimplex& supplyMap(const SUP& map) {
kpeter@652
   715
      delete _psupply;
kpeter@652
   716
      _pstsup = false;
kpeter@652
   717
      _psupply = new ValueNodeMap(_graph);
kpeter@652
   718
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@652
   719
        (*_psupply)[n] = map[n];
kpeter@652
   720
      }
kpeter@652
   721
      return *this;
kpeter@652
   722
    }
kpeter@652
   723
kpeter@652
   724
    /// \brief Set single source and target nodes and a supply value.
kpeter@652
   725
    ///
kpeter@652
   726
    /// This function sets a single source node and a single target node
kpeter@652
   727
    /// and the required flow value.
kpeter@652
   728
    /// If neither this function nor \ref supplyMap() is used before
kpeter@652
   729
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@652
   730
    /// (It makes sense only if non-zero lower bounds are given.)
kpeter@652
   731
    ///
kpeter@652
   732
    /// \param s The source node.
kpeter@652
   733
    /// \param t The target node.
kpeter@652
   734
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@652
   735
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@652
   736
    ///
kpeter@652
   737
    /// \return <tt>(*this)</tt>
kpeter@652
   738
    NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
kpeter@652
   739
      delete _psupply;
kpeter@652
   740
      _psupply = NULL;
kpeter@652
   741
      _pstsup = true;
kpeter@652
   742
      _psource = s;
kpeter@652
   743
      _ptarget = t;
kpeter@652
   744
      _pstflow = k;
kpeter@652
   745
      return *this;
kpeter@652
   746
    }
kpeter@652
   747
kpeter@648
   748
    /// \brief Set the flow map.
kpeter@648
   749
    ///
kpeter@648
   750
    /// This function sets the flow map.
kpeter@652
   751
    /// If it is not used before calling \ref run(), an instance will
kpeter@652
   752
    /// be allocated automatically. The destructor deallocates this
kpeter@652
   753
    /// automatically allocated map, of course.
kpeter@648
   754
    ///
kpeter@648
   755
    /// \return <tt>(*this)</tt>
kpeter@652
   756
    NetworkSimplex& flowMap(FlowMap& map) {
kpeter@648
   757
      if (_local_flow) {
kpeter@650
   758
        delete _flow_map;
kpeter@648
   759
        _local_flow = false;
kpeter@648
   760
      }
kpeter@650
   761
      _flow_map = &map;
kpeter@648
   762
      return *this;
kpeter@648
   763
    }
kpeter@648
   764
kpeter@648
   765
    /// \brief Set the potential map.
kpeter@648
   766
    ///
kpeter@652
   767
    /// This function sets the potential map, which is used for storing
kpeter@652
   768
    /// the dual solution.
kpeter@652
   769
    /// If it is not used before calling \ref run(), an instance will
kpeter@652
   770
    /// be allocated automatically. The destructor deallocates this
kpeter@652
   771
    /// automatically allocated map, of course.
kpeter@648
   772
    ///
kpeter@648
   773
    /// \return <tt>(*this)</tt>
kpeter@652
   774
    NetworkSimplex& potentialMap(PotentialMap& map) {
kpeter@648
   775
      if (_local_potential) {
kpeter@650
   776
        delete _potential_map;
kpeter@648
   777
        _local_potential = false;
kpeter@648
   778
      }
kpeter@650
   779
      _potential_map = &map;
kpeter@648
   780
      return *this;
kpeter@648
   781
    }
kpeter@648
   782
kpeter@652
   783
    /// \name Execution Control
kpeter@652
   784
    /// The algorithm can be executed using \ref run().
kpeter@652
   785
kpeter@648
   786
    /// @{
kpeter@648
   787
kpeter@648
   788
    /// \brief Run the algorithm.
kpeter@648
   789
    ///
kpeter@648
   790
    /// This function runs the algorithm.
kpeter@652
   791
    /// The paramters can be specified using \ref lowerMap(),
kpeter@652
   792
    /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(), 
kpeter@652
   793
    /// \ref costMap(), \ref supplyMap() and \ref stSupply()
kpeter@652
   794
    /// functions. For example,
kpeter@652
   795
    /// \code
kpeter@652
   796
    ///   NetworkSimplex<ListDigraph> ns(graph);
kpeter@652
   797
    ///   ns.boundMaps(lower, upper).costMap(cost)
kpeter@652
   798
    ///     .supplyMap(sup).run();
kpeter@652
   799
    /// \endcode
kpeter@648
   800
    ///
kpeter@652
   801
    /// \param pivot_rule The pivot rule that will be used during the
kpeter@652
   802
    /// algorithm. For more information see \ref PivotRule.
kpeter@648
   803
    ///
kpeter@648
   804
    /// \return \c true if a feasible flow can be found.
kpeter@652
   805
    bool run(PivotRule pivot_rule = BLOCK_SEARCH) {
kpeter@648
   806
      return init() && start(pivot_rule);
kpeter@648
   807
    }
kpeter@648
   808
kpeter@648
   809
    /// @}
kpeter@648
   810
kpeter@648
   811
    /// \name Query Functions
kpeter@648
   812
    /// The results of the algorithm can be obtained using these
kpeter@648
   813
    /// functions.\n
kpeter@652
   814
    /// The \ref run() function must be called before using them.
kpeter@652
   815
kpeter@648
   816
    /// @{
kpeter@648
   817
kpeter@652
   818
    /// \brief Return the total cost of the found flow.
kpeter@652
   819
    ///
kpeter@652
   820
    /// This function returns the total cost of the found flow.
kpeter@652
   821
    /// The complexity of the function is \f$ O(e) \f$.
kpeter@652
   822
    ///
kpeter@652
   823
    /// \note The return type of the function can be specified as a
kpeter@652
   824
    /// template parameter. For example,
kpeter@652
   825
    /// \code
kpeter@652
   826
    ///   ns.totalCost<double>();
kpeter@652
   827
    /// \endcode
kpeter@652
   828
    /// It is useful if the total cost cannot be stored in the \c Value
kpeter@652
   829
    /// type of the algorithm, which is the default return type of the
kpeter@652
   830
    /// function.
kpeter@652
   831
    ///
kpeter@652
   832
    /// \pre \ref run() must be called before using this function.
kpeter@652
   833
    template <typename Num>
kpeter@652
   834
    Num totalCost() const {
kpeter@652
   835
      Num c = 0;
kpeter@652
   836
      if (_pcost) {
kpeter@652
   837
        for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@652
   838
          c += (*_flow_map)[e] * (*_pcost)[e];
kpeter@652
   839
      } else {
kpeter@652
   840
        for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@652
   841
          c += (*_flow_map)[e];
kpeter@652
   842
      }
kpeter@652
   843
      return c;
kpeter@652
   844
    }
kpeter@652
   845
kpeter@652
   846
#ifndef DOXYGEN
kpeter@652
   847
    Value totalCost() const {
kpeter@652
   848
      return totalCost<Value>();
kpeter@652
   849
    }
kpeter@652
   850
#endif
kpeter@652
   851
kpeter@652
   852
    /// \brief Return the flow on the given arc.
kpeter@652
   853
    ///
kpeter@652
   854
    /// This function returns the flow on the given arc.
kpeter@652
   855
    ///
kpeter@652
   856
    /// \pre \ref run() must be called before using this function.
kpeter@652
   857
    Value flow(const Arc& a) const {
kpeter@652
   858
      return (*_flow_map)[a];
kpeter@652
   859
    }
kpeter@652
   860
kpeter@648
   861
    /// \brief Return a const reference to the flow map.
kpeter@648
   862
    ///
kpeter@648
   863
    /// This function returns a const reference to an arc map storing
kpeter@648
   864
    /// the found flow.
kpeter@648
   865
    ///
kpeter@648
   866
    /// \pre \ref run() must be called before using this function.
kpeter@648
   867
    const FlowMap& flowMap() const {
kpeter@650
   868
      return *_flow_map;
kpeter@648
   869
    }
kpeter@648
   870
kpeter@652
   871
    /// \brief Return the potential (dual value) of the given node.
kpeter@652
   872
    ///
kpeter@652
   873
    /// This function returns the potential (dual value) of the
kpeter@652
   874
    /// given node.
kpeter@652
   875
    ///
kpeter@652
   876
    /// \pre \ref run() must be called before using this function.
kpeter@652
   877
    Value potential(const Node& n) const {
kpeter@652
   878
      return (*_potential_map)[n];
kpeter@652
   879
    }
kpeter@652
   880
kpeter@648
   881
    /// \brief Return a const reference to the potential map
kpeter@648
   882
    /// (the dual solution).
kpeter@648
   883
    ///
kpeter@648
   884
    /// This function returns a const reference to a node map storing
kpeter@652
   885
    /// the found potentials, which form the dual solution of the
kpeter@652
   886
    /// \ref min_cost_flow "minimum cost flow" problem.
kpeter@648
   887
    ///
kpeter@648
   888
    /// \pre \ref run() must be called before using this function.
kpeter@648
   889
    const PotentialMap& potentialMap() const {
kpeter@650
   890
      return *_potential_map;
kpeter@648
   891
    }
kpeter@648
   892
kpeter@648
   893
    /// @}
kpeter@648
   894
kpeter@648
   895
  private:
kpeter@648
   896
kpeter@648
   897
    // Initialize internal data structures
kpeter@648
   898
    bool init() {
kpeter@648
   899
      // Initialize result maps
kpeter@650
   900
      if (!_flow_map) {
kpeter@650
   901
        _flow_map = new FlowMap(_graph);
kpeter@648
   902
        _local_flow = true;
kpeter@648
   903
      }
kpeter@650
   904
      if (!_potential_map) {
kpeter@650
   905
        _potential_map = new PotentialMap(_graph);
kpeter@648
   906
        _local_potential = true;
kpeter@648
   907
      }
kpeter@648
   908
kpeter@648
   909
      // Initialize vectors
kpeter@650
   910
      _node_num = countNodes(_graph);
kpeter@650
   911
      _arc_num = countArcs(_graph);
kpeter@648
   912
      int all_node_num = _node_num + 1;
kpeter@650
   913
      int all_arc_num = _arc_num + _node_num;
kpeter@652
   914
      if (_node_num == 0) return false;
kpeter@648
   915
kpeter@650
   916
      _arc_ref.resize(_arc_num);
kpeter@650
   917
      _source.resize(all_arc_num);
kpeter@650
   918
      _target.resize(all_arc_num);
kpeter@648
   919
kpeter@650
   920
      _cap.resize(all_arc_num);
kpeter@650
   921
      _cost.resize(all_arc_num);
kpeter@648
   922
      _supply.resize(all_node_num);
kpeter@650
   923
      _flow.resize(all_arc_num, 0);
kpeter@648
   924
      _pi.resize(all_node_num, 0);
kpeter@648
   925
kpeter@648
   926
      _parent.resize(all_node_num);
kpeter@648
   927
      _pred.resize(all_node_num);
kpeter@650
   928
      _forward.resize(all_node_num);
kpeter@648
   929
      _thread.resize(all_node_num);
kpeter@651
   930
      _rev_thread.resize(all_node_num);
kpeter@651
   931
      _succ_num.resize(all_node_num);
kpeter@651
   932
      _last_succ.resize(all_node_num);
kpeter@650
   933
      _state.resize(all_arc_num, STATE_LOWER);
kpeter@648
   934
kpeter@648
   935
      // Initialize node related data
kpeter@648
   936
      bool valid_supply = true;
kpeter@652
   937
      if (!_pstsup && !_psupply) {
kpeter@652
   938
        _pstsup = true;
kpeter@652
   939
        _psource = _ptarget = NodeIt(_graph);
kpeter@652
   940
        _pstflow = 0;
kpeter@652
   941
      }
kpeter@652
   942
      if (_psupply) {
kpeter@652
   943
        Value sum = 0;
kpeter@648
   944
        int i = 0;
kpeter@650
   945
        for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@648
   946
          _node_id[n] = i;
kpeter@652
   947
          _supply[i] = (*_psupply)[n];
kpeter@648
   948
          sum += _supply[i];
kpeter@648
   949
        }
kpeter@648
   950
        valid_supply = (sum == 0);
kpeter@648
   951
      } else {
kpeter@648
   952
        int i = 0;
kpeter@650
   953
        for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@648
   954
          _node_id[n] = i;
kpeter@648
   955
          _supply[i] = 0;
kpeter@648
   956
        }
kpeter@652
   957
        _supply[_node_id[_psource]] =  _pstflow;
kpeter@652
   958
        _supply[_node_id[_ptarget]]   = -_pstflow;
kpeter@648
   959
      }
kpeter@648
   960
      if (!valid_supply) return false;
kpeter@648
   961
kpeter@648
   962
      // Set data for the artificial root node
kpeter@648
   963
      _root = _node_num;
kpeter@648
   964
      _parent[_root] = -1;
kpeter@648
   965
      _pred[_root] = -1;
kpeter@648
   966
      _thread[_root] = 0;
kpeter@651
   967
      _rev_thread[0] = _root;
kpeter@651
   968
      _succ_num[_root] = all_node_num;
kpeter@651
   969
      _last_succ[_root] = _root - 1;
kpeter@648
   970
      _supply[_root] = 0;
kpeter@648
   971
      _pi[_root] = 0;
kpeter@648
   972
kpeter@648
   973
      // Store the arcs in a mixed order
kpeter@648
   974
      int k = std::max(int(sqrt(_arc_num)), 10);
kpeter@648
   975
      int i = 0;
kpeter@650
   976
      for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@650
   977
        _arc_ref[i] = e;
kpeter@648
   978
        if ((i += k) >= _arc_num) i = (i % k) + 1;
kpeter@648
   979
      }
kpeter@648
   980
kpeter@648
   981
      // Initialize arc maps
kpeter@652
   982
      if (_pupper && _pcost) {
kpeter@652
   983
        for (int i = 0; i != _arc_num; ++i) {
kpeter@652
   984
          Arc e = _arc_ref[i];
kpeter@652
   985
          _source[i] = _node_id[_graph.source(e)];
kpeter@652
   986
          _target[i] = _node_id[_graph.target(e)];
kpeter@652
   987
          _cap[i] = (*_pupper)[e];
kpeter@652
   988
          _cost[i] = (*_pcost)[e];
kpeter@652
   989
        }
kpeter@652
   990
      } else {
kpeter@652
   991
        for (int i = 0; i != _arc_num; ++i) {
kpeter@652
   992
          Arc e = _arc_ref[i];
kpeter@652
   993
          _source[i] = _node_id[_graph.source(e)];
kpeter@652
   994
          _target[i] = _node_id[_graph.target(e)];
kpeter@652
   995
        }
kpeter@652
   996
        if (_pupper) {
kpeter@652
   997
          for (int i = 0; i != _arc_num; ++i)
kpeter@652
   998
            _cap[i] = (*_pupper)[_arc_ref[i]];
kpeter@652
   999
        } else {
kpeter@652
  1000
          Value val = std::numeric_limits<Value>::max();
kpeter@652
  1001
          for (int i = 0; i != _arc_num; ++i)
kpeter@652
  1002
            _cap[i] = val;
kpeter@652
  1003
        }
kpeter@652
  1004
        if (_pcost) {
kpeter@652
  1005
          for (int i = 0; i != _arc_num; ++i)
kpeter@652
  1006
            _cost[i] = (*_pcost)[_arc_ref[i]];
kpeter@652
  1007
        } else {
kpeter@652
  1008
          for (int i = 0; i != _arc_num; ++i)
kpeter@652
  1009
            _cost[i] = 1;
kpeter@652
  1010
        }
kpeter@648
  1011
      }
kpeter@648
  1012
kpeter@648
  1013
      // Remove non-zero lower bounds
kpeter@652
  1014
      if (_plower) {
kpeter@648
  1015
        for (int i = 0; i != _arc_num; ++i) {
kpeter@652
  1016
          Value c = (*_plower)[_arc_ref[i]];
kpeter@648
  1017
          if (c != 0) {
kpeter@648
  1018
            _cap[i] -= c;
kpeter@648
  1019
            _supply[_source[i]] -= c;
kpeter@648
  1020
            _supply[_target[i]] += c;
kpeter@648
  1021
          }
kpeter@648
  1022
        }
kpeter@648
  1023
      }
kpeter@648
  1024
kpeter@648
  1025
      // Add artificial arcs and initialize the spanning tree data structure
kpeter@652
  1026
      Value max_cap = std::numeric_limits<Value>::max();
kpeter@652
  1027
      Value max_cost = std::numeric_limits<Value>::max() / 4;
kpeter@648
  1028
      for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@648
  1029
        _thread[u] = u + 1;
kpeter@651
  1030
        _rev_thread[u + 1] = u;
kpeter@651
  1031
        _succ_num[u] = 1;
kpeter@651
  1032
        _last_succ[u] = u;
kpeter@648
  1033
        _parent[u] = _root;
kpeter@648
  1034
        _pred[u] = e;
kpeter@648
  1035
        if (_supply[u] >= 0) {
kpeter@648
  1036
          _flow[e] = _supply[u];
kpeter@648
  1037
          _forward[u] = true;
kpeter@648
  1038
          _pi[u] = -max_cost;
kpeter@648
  1039
        } else {
kpeter@648
  1040
          _flow[e] = -_supply[u];
kpeter@648
  1041
          _forward[u] = false;
kpeter@648
  1042
          _pi[u] = max_cost;
kpeter@648
  1043
        }
kpeter@648
  1044
        _cost[e] = max_cost;
kpeter@648
  1045
        _cap[e] = max_cap;
kpeter@648
  1046
        _state[e] = STATE_TREE;
kpeter@648
  1047
      }
kpeter@648
  1048
kpeter@648
  1049
      return true;
kpeter@648
  1050
    }
kpeter@648
  1051
kpeter@648
  1052
    // Find the join node
kpeter@648
  1053
    void findJoinNode() {
kpeter@650
  1054
      int u = _source[in_arc];
kpeter@650
  1055
      int v = _target[in_arc];
kpeter@648
  1056
      while (u != v) {
kpeter@651
  1057
        if (_succ_num[u] < _succ_num[v]) {
kpeter@651
  1058
          u = _parent[u];
kpeter@651
  1059
        } else {
kpeter@651
  1060
          v = _parent[v];
kpeter@651
  1061
        }
kpeter@648
  1062
      }
kpeter@648
  1063
      join = u;
kpeter@648
  1064
    }
kpeter@648
  1065
kpeter@648
  1066
    // Find the leaving arc of the cycle and returns true if the
kpeter@648
  1067
    // leaving arc is not the same as the entering arc
kpeter@648
  1068
    bool findLeavingArc() {
kpeter@648
  1069
      // Initialize first and second nodes according to the direction
kpeter@648
  1070
      // of the cycle
kpeter@650
  1071
      if (_state[in_arc] == STATE_LOWER) {
kpeter@650
  1072
        first  = _source[in_arc];
kpeter@650
  1073
        second = _target[in_arc];
kpeter@648
  1074
      } else {
kpeter@650
  1075
        first  = _target[in_arc];
kpeter@650
  1076
        second = _source[in_arc];
kpeter@648
  1077
      }
kpeter@650
  1078
      delta = _cap[in_arc];
kpeter@648
  1079
      int result = 0;
kpeter@652
  1080
      Value d;
kpeter@648
  1081
      int e;
kpeter@648
  1082
kpeter@648
  1083
      // Search the cycle along the path form the first node to the root
kpeter@648
  1084
      for (int u = first; u != join; u = _parent[u]) {
kpeter@648
  1085
        e = _pred[u];
kpeter@648
  1086
        d = _forward[u] ? _flow[e] : _cap[e] - _flow[e];
kpeter@648
  1087
        if (d < delta) {
kpeter@648
  1088
          delta = d;
kpeter@648
  1089
          u_out = u;
kpeter@648
  1090
          result = 1;
kpeter@648
  1091
        }
kpeter@648
  1092
      }
kpeter@648
  1093
      // Search the cycle along the path form the second node to the root
kpeter@648
  1094
      for (int u = second; u != join; u = _parent[u]) {
kpeter@648
  1095
        e = _pred[u];
kpeter@648
  1096
        d = _forward[u] ? _cap[e] - _flow[e] : _flow[e];
kpeter@648
  1097
        if (d <= delta) {
kpeter@648
  1098
          delta = d;
kpeter@648
  1099
          u_out = u;
kpeter@648
  1100
          result = 2;
kpeter@648
  1101
        }
kpeter@648
  1102
      }
kpeter@648
  1103
kpeter@648
  1104
      if (result == 1) {
kpeter@648
  1105
        u_in = first;
kpeter@648
  1106
        v_in = second;
kpeter@648
  1107
      } else {
kpeter@648
  1108
        u_in = second;
kpeter@648
  1109
        v_in = first;
kpeter@648
  1110
      }
kpeter@648
  1111
      return result != 0;
kpeter@648
  1112
    }
kpeter@648
  1113
kpeter@648
  1114
    // Change _flow and _state vectors
kpeter@648
  1115
    void changeFlow(bool change) {
kpeter@648
  1116
      // Augment along the cycle
kpeter@648
  1117
      if (delta > 0) {
kpeter@652
  1118
        Value val = _state[in_arc] * delta;
kpeter@650
  1119
        _flow[in_arc] += val;
kpeter@650
  1120
        for (int u = _source[in_arc]; u != join; u = _parent[u]) {
kpeter@648
  1121
          _flow[_pred[u]] += _forward[u] ? -val : val;
kpeter@648
  1122
        }
kpeter@650
  1123
        for (int u = _target[in_arc]; u != join; u = _parent[u]) {
kpeter@648
  1124
          _flow[_pred[u]] += _forward[u] ? val : -val;
kpeter@648
  1125
        }
kpeter@648
  1126
      }
kpeter@648
  1127
      // Update the state of the entering and leaving arcs
kpeter@648
  1128
      if (change) {
kpeter@650
  1129
        _state[in_arc] = STATE_TREE;
kpeter@648
  1130
        _state[_pred[u_out]] =
kpeter@648
  1131
          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
kpeter@648
  1132
      } else {
kpeter@650
  1133
        _state[in_arc] = -_state[in_arc];
kpeter@648
  1134
      }
kpeter@648
  1135
    }
kpeter@648
  1136
kpeter@651
  1137
    // Update the tree structure
kpeter@651
  1138
    void updateTreeStructure() {
kpeter@651
  1139
      int u, w;
kpeter@651
  1140
      int old_rev_thread = _rev_thread[u_out];
kpeter@651
  1141
      int old_succ_num = _succ_num[u_out];
kpeter@651
  1142
      int old_last_succ = _last_succ[u_out];
kpeter@648
  1143
      v_out = _parent[u_out];
kpeter@648
  1144
kpeter@651
  1145
      u = _last_succ[u_in];  // the last successor of u_in
kpeter@651
  1146
      right = _thread[u];    // the node after it
kpeter@651
  1147
kpeter@651
  1148
      // Handle the case when old_rev_thread equals to v_in
kpeter@651
  1149
      // (it also means that join and v_out coincide)
kpeter@651
  1150
      if (old_rev_thread == v_in) {
kpeter@651
  1151
        last = _thread[_last_succ[u_out]];
kpeter@651
  1152
      } else {
kpeter@651
  1153
        last = _thread[v_in];
kpeter@648
  1154
      }
kpeter@648
  1155
kpeter@651
  1156
      // Update _thread and _parent along the stem nodes (i.e. the nodes
kpeter@651
  1157
      // between u_in and u_out, whose parent have to be changed)
kpeter@648
  1158
      _thread[v_in] = stem = u_in;
kpeter@651
  1159
      _dirty_revs.clear();
kpeter@651
  1160
      _dirty_revs.push_back(v_in);
kpeter@648
  1161
      par_stem = v_in;
kpeter@648
  1162
      while (stem != u_out) {
kpeter@651
  1163
        // Insert the next stem node into the thread list
kpeter@651
  1164
        new_stem = _parent[stem];
kpeter@651
  1165
        _thread[u] = new_stem;
kpeter@651
  1166
        _dirty_revs.push_back(u);
kpeter@648
  1167
kpeter@651
  1168
        // Remove the subtree of stem from the thread list
kpeter@651
  1169
        w = _rev_thread[stem];
kpeter@651
  1170
        _thread[w] = right;
kpeter@651
  1171
        _rev_thread[right] = w;
kpeter@648
  1172
kpeter@651
  1173
        // Change the parent node and shift stem nodes
kpeter@648
  1174
        _parent[stem] = par_stem;
kpeter@648
  1175
        par_stem = stem;
kpeter@648
  1176
        stem = new_stem;
kpeter@648
  1177
kpeter@651
  1178
        // Update u and right
kpeter@651
  1179
        u = _last_succ[stem] == _last_succ[par_stem] ?
kpeter@651
  1180
          _rev_thread[par_stem] : _last_succ[stem];
kpeter@648
  1181
        right = _thread[u];
kpeter@648
  1182
      }
kpeter@648
  1183
      _parent[u_out] = par_stem;
kpeter@648
  1184
      _thread[u] = last;
kpeter@651
  1185
      _rev_thread[last] = u;
kpeter@651
  1186
      _last_succ[u_out] = u;
kpeter@648
  1187
kpeter@651
  1188
      // Remove the subtree of u_out from the thread list except for
kpeter@651
  1189
      // the case when old_rev_thread equals to v_in
kpeter@651
  1190
      // (it also means that join and v_out coincide)
kpeter@651
  1191
      if (old_rev_thread != v_in) {
kpeter@651
  1192
        _thread[old_rev_thread] = right;
kpeter@651
  1193
        _rev_thread[right] = old_rev_thread;
kpeter@651
  1194
      }
kpeter@651
  1195
kpeter@651
  1196
      // Update _rev_thread using the new _thread values
kpeter@651
  1197
      for (int i = 0; i < int(_dirty_revs.size()); ++i) {
kpeter@651
  1198
        u = _dirty_revs[i];
kpeter@651
  1199
        _rev_thread[_thread[u]] = u;
kpeter@651
  1200
      }
kpeter@651
  1201
kpeter@651
  1202
      // Update _pred, _forward, _last_succ and _succ_num for the
kpeter@651
  1203
      // stem nodes from u_out to u_in
kpeter@651
  1204
      int tmp_sc = 0, tmp_ls = _last_succ[u_out];
kpeter@651
  1205
      u = u_out;
kpeter@651
  1206
      while (u != u_in) {
kpeter@651
  1207
        w = _parent[u];
kpeter@651
  1208
        _pred[u] = _pred[w];
kpeter@651
  1209
        _forward[u] = !_forward[w];
kpeter@651
  1210
        tmp_sc += _succ_num[u] - _succ_num[w];
kpeter@651
  1211
        _succ_num[u] = tmp_sc;
kpeter@651
  1212
        _last_succ[w] = tmp_ls;
kpeter@651
  1213
        u = w;
kpeter@651
  1214
      }
kpeter@651
  1215
      _pred[u_in] = in_arc;
kpeter@651
  1216
      _forward[u_in] = (u_in == _source[in_arc]);
kpeter@651
  1217
      _succ_num[u_in] = old_succ_num;
kpeter@651
  1218
kpeter@651
  1219
      // Set limits for updating _last_succ form v_in and v_out
kpeter@651
  1220
      // towards the root
kpeter@651
  1221
      int up_limit_in = -1;
kpeter@651
  1222
      int up_limit_out = -1;
kpeter@651
  1223
      if (_last_succ[join] == v_in) {
kpeter@651
  1224
        up_limit_out = join;
kpeter@648
  1225
      } else {
kpeter@651
  1226
        up_limit_in = join;
kpeter@651
  1227
      }
kpeter@651
  1228
kpeter@651
  1229
      // Update _last_succ from v_in towards the root
kpeter@651
  1230
      for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;
kpeter@651
  1231
           u = _parent[u]) {
kpeter@651
  1232
        _last_succ[u] = _last_succ[u_out];
kpeter@651
  1233
      }
kpeter@651
  1234
      // Update _last_succ from v_out towards the root
kpeter@651
  1235
      if (join != old_rev_thread && v_in != old_rev_thread) {
kpeter@651
  1236
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@651
  1237
             u = _parent[u]) {
kpeter@651
  1238
          _last_succ[u] = old_rev_thread;
kpeter@651
  1239
        }
kpeter@651
  1240
      } else {
kpeter@651
  1241
        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@651
  1242
             u = _parent[u]) {
kpeter@651
  1243
          _last_succ[u] = _last_succ[u_out];
kpeter@651
  1244
        }
kpeter@651
  1245
      }
kpeter@651
  1246
kpeter@651
  1247
      // Update _succ_num from v_in to join
kpeter@651
  1248
      for (u = v_in; u != join; u = _parent[u]) {
kpeter@651
  1249
        _succ_num[u] += old_succ_num;
kpeter@651
  1250
      }
kpeter@651
  1251
      // Update _succ_num from v_out to join
kpeter@651
  1252
      for (u = v_out; u != join; u = _parent[u]) {
kpeter@651
  1253
        _succ_num[u] -= old_succ_num;
kpeter@648
  1254
      }
kpeter@648
  1255
    }
kpeter@648
  1256
kpeter@651
  1257
    // Update potentials
kpeter@651
  1258
    void updatePotential() {
kpeter@652
  1259
      Value sigma = _forward[u_in] ?
kpeter@648
  1260
        _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
kpeter@648
  1261
        _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
kpeter@651
  1262
      if (_succ_num[u_in] > _node_num / 2) {
kpeter@651
  1263
        // Update in the upper subtree (which contains the root)
kpeter@651
  1264
        int before = _rev_thread[u_in];
kpeter@651
  1265
        int after = _thread[_last_succ[u_in]];
kpeter@651
  1266
        _thread[before] = after;
kpeter@651
  1267
        _pi[_root] -= sigma;
kpeter@651
  1268
        for (int u = _thread[_root]; u != _root; u = _thread[u]) {
kpeter@651
  1269
          _pi[u] -= sigma;
kpeter@651
  1270
        }
kpeter@651
  1271
        _thread[before] = u_in;
kpeter@651
  1272
      } else {
kpeter@651
  1273
        // Update in the lower subtree (which has been moved)
kpeter@651
  1274
        int end = _thread[_last_succ[u_in]];
kpeter@651
  1275
        for (int u = u_in; u != end; u = _thread[u]) {
kpeter@651
  1276
          _pi[u] += sigma;
kpeter@651
  1277
        }
kpeter@648
  1278
      }
kpeter@648
  1279
    }
kpeter@648
  1280
kpeter@648
  1281
    // Execute the algorithm
kpeter@652
  1282
    bool start(PivotRule pivot_rule) {
kpeter@648
  1283
      // Select the pivot rule implementation
kpeter@648
  1284
      switch (pivot_rule) {
kpeter@652
  1285
        case FIRST_ELIGIBLE:
kpeter@648
  1286
          return start<FirstEligiblePivotRule>();
kpeter@652
  1287
        case BEST_ELIGIBLE:
kpeter@648
  1288
          return start<BestEligiblePivotRule>();
kpeter@652
  1289
        case BLOCK_SEARCH:
kpeter@648
  1290
          return start<BlockSearchPivotRule>();
kpeter@652
  1291
        case CANDIDATE_LIST:
kpeter@648
  1292
          return start<CandidateListPivotRule>();
kpeter@652
  1293
        case ALTERING_LIST:
kpeter@648
  1294
          return start<AlteringListPivotRule>();
kpeter@648
  1295
      }
kpeter@648
  1296
      return false;
kpeter@648
  1297
    }
kpeter@648
  1298
kpeter@652
  1299
    template <typename PivotRuleImpl>
kpeter@648
  1300
    bool start() {
kpeter@652
  1301
      PivotRuleImpl pivot(*this);
kpeter@648
  1302
kpeter@652
  1303
      // Execute the Network Simplex algorithm
kpeter@648
  1304
      while (pivot.findEnteringArc()) {
kpeter@648
  1305
        findJoinNode();
kpeter@648
  1306
        bool change = findLeavingArc();
kpeter@648
  1307
        changeFlow(change);
kpeter@648
  1308
        if (change) {
kpeter@651
  1309
          updateTreeStructure();
kpeter@651
  1310
          updatePotential();
kpeter@648
  1311
        }
kpeter@648
  1312
      }
kpeter@648
  1313
kpeter@648
  1314
      // Check if the flow amount equals zero on all the artificial arcs
kpeter@648
  1315
      for (int e = _arc_num; e != _arc_num + _node_num; ++e) {
kpeter@648
  1316
        if (_flow[e] > 0) return false;
kpeter@648
  1317
      }
kpeter@648
  1318
kpeter@650
  1319
      // Copy flow values to _flow_map
kpeter@652
  1320
      if (_plower) {
kpeter@648
  1321
        for (int i = 0; i != _arc_num; ++i) {
kpeter@650
  1322
          Arc e = _arc_ref[i];
kpeter@652
  1323
          _flow_map->set(e, (*_plower)[e] + _flow[i]);
kpeter@648
  1324
        }
kpeter@648
  1325
      } else {
kpeter@648
  1326
        for (int i = 0; i != _arc_num; ++i) {
kpeter@650
  1327
          _flow_map->set(_arc_ref[i], _flow[i]);
kpeter@648
  1328
        }
kpeter@648
  1329
      }
kpeter@650
  1330
      // Copy potential values to _potential_map
kpeter@650
  1331
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@650
  1332
        _potential_map->set(n, _pi[_node_id[n]]);
kpeter@648
  1333
      }
kpeter@648
  1334
kpeter@648
  1335
      return true;
kpeter@648
  1336
    }
kpeter@648
  1337
kpeter@648
  1338
  }; //class NetworkSimplex
kpeter@648
  1339
kpeter@648
  1340
  ///@}
kpeter@648
  1341
kpeter@648
  1342
} //namespace lemon
kpeter@648
  1343
kpeter@648
  1344
#endif //LEMON_NETWORK_SIMPLEX_H