lemon/hartmann_orlin_mmc.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sat, 16 Mar 2013 16:20:41 +0100
changeset 1070 ee9bac10f58e
parent 879 38213abd2911
child 1049 7bf489cf624e
permissions -rw-r--r--
Debug checking for capacity bounds in min cost flow algorithms (#454)
alpar@877
     1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@766
     2
 *
alpar@877
     3
 * This file is a part of LEMON, a generic C++ optimization library.
kpeter@766
     4
 *
alpar@877
     5
 * Copyright (C) 2003-2010
kpeter@766
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@766
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@766
     8
 *
kpeter@766
     9
 * Permission to use, modify and distribute this software is granted
kpeter@766
    10
 * provided that this copyright notice appears in all copies. For
kpeter@766
    11
 * precise terms see the accompanying LICENSE file.
kpeter@766
    12
 *
kpeter@766
    13
 * This software is provided "AS IS" with no warranty of any kind,
kpeter@766
    14
 * express or implied, and with no claim as to its suitability for any
kpeter@766
    15
 * purpose.
kpeter@766
    16
 *
kpeter@766
    17
 */
kpeter@766
    18
kpeter@864
    19
#ifndef LEMON_HARTMANN_ORLIN_MMC_H
kpeter@864
    20
#define LEMON_HARTMANN_ORLIN_MMC_H
kpeter@766
    21
kpeter@768
    22
/// \ingroup min_mean_cycle
kpeter@766
    23
///
kpeter@766
    24
/// \file
kpeter@766
    25
/// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.
kpeter@766
    26
kpeter@766
    27
#include <vector>
kpeter@766
    28
#include <limits>
kpeter@766
    29
#include <lemon/core.h>
kpeter@766
    30
#include <lemon/path.h>
kpeter@766
    31
#include <lemon/tolerance.h>
kpeter@766
    32
#include <lemon/connectivity.h>
kpeter@766
    33
kpeter@766
    34
namespace lemon {
kpeter@766
    35
kpeter@864
    36
  /// \brief Default traits class of HartmannOrlinMmc class.
kpeter@766
    37
  ///
kpeter@864
    38
  /// Default traits class of HartmannOrlinMmc class.
kpeter@766
    39
  /// \tparam GR The type of the digraph.
kpeter@864
    40
  /// \tparam CM The type of the cost map.
kpeter@879
    41
  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
kpeter@766
    42
#ifdef DOXYGEN
kpeter@864
    43
  template <typename GR, typename CM>
kpeter@766
    44
#else
kpeter@864
    45
  template <typename GR, typename CM,
kpeter@864
    46
    bool integer = std::numeric_limits<typename CM::Value>::is_integer>
kpeter@766
    47
#endif
kpeter@864
    48
  struct HartmannOrlinMmcDefaultTraits
kpeter@766
    49
  {
kpeter@766
    50
    /// The type of the digraph
kpeter@766
    51
    typedef GR Digraph;
kpeter@864
    52
    /// The type of the cost map
kpeter@864
    53
    typedef CM CostMap;
kpeter@864
    54
    /// The type of the arc costs
kpeter@864
    55
    typedef typename CostMap::Value Cost;
kpeter@766
    56
kpeter@864
    57
    /// \brief The large cost type used for internal computations
kpeter@766
    58
    ///
kpeter@864
    59
    /// The large cost type used for internal computations.
kpeter@864
    60
    /// It is \c long \c long if the \c Cost type is integer,
kpeter@766
    61
    /// otherwise it is \c double.
kpeter@864
    62
    /// \c Cost must be convertible to \c LargeCost.
kpeter@864
    63
    typedef double LargeCost;
kpeter@766
    64
kpeter@766
    65
    /// The tolerance type used for internal computations
kpeter@864
    66
    typedef lemon::Tolerance<LargeCost> Tolerance;
kpeter@766
    67
kpeter@766
    68
    /// \brief The path type of the found cycles
kpeter@766
    69
    ///
kpeter@766
    70
    /// The path type of the found cycles.
kpeter@766
    71
    /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@772
    72
    /// and it must have an \c addFront() function.
kpeter@766
    73
    typedef lemon::Path<Digraph> Path;
kpeter@766
    74
  };
kpeter@766
    75
kpeter@864
    76
  // Default traits class for integer cost types
kpeter@864
    77
  template <typename GR, typename CM>
kpeter@864
    78
  struct HartmannOrlinMmcDefaultTraits<GR, CM, true>
kpeter@766
    79
  {
kpeter@766
    80
    typedef GR Digraph;
kpeter@864
    81
    typedef CM CostMap;
kpeter@864
    82
    typedef typename CostMap::Value Cost;
kpeter@766
    83
#ifdef LEMON_HAVE_LONG_LONG
kpeter@864
    84
    typedef long long LargeCost;
kpeter@766
    85
#else
kpeter@864
    86
    typedef long LargeCost;
kpeter@766
    87
#endif
kpeter@864
    88
    typedef lemon::Tolerance<LargeCost> Tolerance;
kpeter@766
    89
    typedef lemon::Path<Digraph> Path;
kpeter@766
    90
  };
kpeter@766
    91
kpeter@766
    92
kpeter@768
    93
  /// \addtogroup min_mean_cycle
kpeter@766
    94
  /// @{
kpeter@766
    95
kpeter@766
    96
  /// \brief Implementation of the Hartmann-Orlin algorithm for finding
kpeter@766
    97
  /// a minimum mean cycle.
kpeter@766
    98
  ///
kpeter@766
    99
  /// This class implements the Hartmann-Orlin algorithm for finding
kpeter@864
   100
  /// a directed cycle of minimum mean cost in a digraph
kpeter@1002
   101
  /// \ref hartmann93finding, \ref dasdan98minmeancycle.
kpeter@879
   102
  /// It is an improved version of \ref KarpMmc "Karp"'s original algorithm,
kpeter@766
   103
  /// it applies an efficient early termination scheme.
kpeter@768
   104
  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
kpeter@766
   105
  ///
kpeter@766
   106
  /// \tparam GR The type of the digraph the algorithm runs on.
kpeter@864
   107
  /// \tparam CM The type of the cost map. The default
kpeter@766
   108
  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
kpeter@825
   109
  /// \tparam TR The traits class that defines various types used by the
kpeter@864
   110
  /// algorithm. By default, it is \ref HartmannOrlinMmcDefaultTraits
kpeter@864
   111
  /// "HartmannOrlinMmcDefaultTraits<GR, CM>".
kpeter@825
   112
  /// In most cases, this parameter should not be set directly,
kpeter@825
   113
  /// consider to use the named template parameters instead.
kpeter@766
   114
#ifdef DOXYGEN
kpeter@864
   115
  template <typename GR, typename CM, typename TR>
kpeter@766
   116
#else
kpeter@766
   117
  template < typename GR,
kpeter@864
   118
             typename CM = typename GR::template ArcMap<int>,
kpeter@864
   119
             typename TR = HartmannOrlinMmcDefaultTraits<GR, CM> >
kpeter@766
   120
#endif
kpeter@864
   121
  class HartmannOrlinMmc
kpeter@766
   122
  {
kpeter@766
   123
  public:
kpeter@766
   124
kpeter@766
   125
    /// The type of the digraph
kpeter@766
   126
    typedef typename TR::Digraph Digraph;
kpeter@864
   127
    /// The type of the cost map
kpeter@864
   128
    typedef typename TR::CostMap CostMap;
kpeter@864
   129
    /// The type of the arc costs
kpeter@864
   130
    typedef typename TR::Cost Cost;
kpeter@766
   131
kpeter@864
   132
    /// \brief The large cost type
kpeter@766
   133
    ///
kpeter@864
   134
    /// The large cost type used for internal computations.
kpeter@864
   135
    /// By default, it is \c long \c long if the \c Cost type is integer,
kpeter@766
   136
    /// otherwise it is \c double.
kpeter@864
   137
    typedef typename TR::LargeCost LargeCost;
kpeter@766
   138
kpeter@766
   139
    /// The tolerance type
kpeter@766
   140
    typedef typename TR::Tolerance Tolerance;
kpeter@766
   141
kpeter@766
   142
    /// \brief The path type of the found cycles
kpeter@766
   143
    ///
kpeter@766
   144
    /// The path type of the found cycles.
kpeter@864
   145
    /// Using the \ref HartmannOrlinMmcDefaultTraits "default traits class",
kpeter@766
   146
    /// it is \ref lemon::Path "Path<Digraph>".
kpeter@766
   147
    typedef typename TR::Path Path;
kpeter@766
   148
kpeter@864
   149
    /// The \ref HartmannOrlinMmcDefaultTraits "traits class" of the algorithm
kpeter@766
   150
    typedef TR Traits;
kpeter@766
   151
kpeter@766
   152
  private:
kpeter@766
   153
kpeter@766
   154
    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@766
   155
kpeter@766
   156
    // Data sturcture for path data
kpeter@766
   157
    struct PathData
kpeter@766
   158
    {
kpeter@864
   159
      LargeCost dist;
kpeter@766
   160
      Arc pred;
kpeter@864
   161
      PathData(LargeCost d, Arc p = INVALID) :
kpeter@767
   162
        dist(d), pred(p) {}
kpeter@766
   163
    };
kpeter@766
   164
kpeter@766
   165
    typedef typename Digraph::template NodeMap<std::vector<PathData> >
kpeter@766
   166
      PathDataNodeMap;
kpeter@766
   167
kpeter@766
   168
  private:
kpeter@766
   169
kpeter@766
   170
    // The digraph the algorithm runs on
kpeter@766
   171
    const Digraph &_gr;
kpeter@864
   172
    // The cost of the arcs
kpeter@864
   173
    const CostMap &_cost;
kpeter@766
   174
kpeter@766
   175
    // Data for storing the strongly connected components
kpeter@766
   176
    int _comp_num;
kpeter@766
   177
    typename Digraph::template NodeMap<int> _comp;
kpeter@766
   178
    std::vector<std::vector<Node> > _comp_nodes;
kpeter@766
   179
    std::vector<Node>* _nodes;
kpeter@766
   180
    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
kpeter@766
   181
kpeter@766
   182
    // Data for the found cycles
kpeter@766
   183
    bool _curr_found, _best_found;
kpeter@864
   184
    LargeCost _curr_cost, _best_cost;
kpeter@766
   185
    int _curr_size, _best_size;
kpeter@766
   186
    Node _curr_node, _best_node;
kpeter@766
   187
    int _curr_level, _best_level;
kpeter@766
   188
kpeter@766
   189
    Path *_cycle_path;
kpeter@766
   190
    bool _local_path;
kpeter@766
   191
kpeter@766
   192
    // Node map for storing path data
kpeter@766
   193
    PathDataNodeMap _data;
kpeter@766
   194
    // The processed nodes in the last round
kpeter@766
   195
    std::vector<Node> _process;
kpeter@766
   196
kpeter@766
   197
    Tolerance _tolerance;
kpeter@766
   198
kpeter@767
   199
    // Infinite constant
kpeter@864
   200
    const LargeCost INF;
kpeter@767
   201
kpeter@766
   202
  public:
kpeter@766
   203
kpeter@766
   204
    /// \name Named Template Parameters
kpeter@766
   205
    /// @{
kpeter@766
   206
kpeter@766
   207
    template <typename T>
kpeter@864
   208
    struct SetLargeCostTraits : public Traits {
kpeter@864
   209
      typedef T LargeCost;
kpeter@766
   210
      typedef lemon::Tolerance<T> Tolerance;
kpeter@766
   211
    };
kpeter@766
   212
kpeter@766
   213
    /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@864
   214
    /// \c LargeCost type.
kpeter@766
   215
    ///
kpeter@864
   216
    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
kpeter@766
   217
    /// type. It is used for internal computations in the algorithm.
kpeter@766
   218
    template <typename T>
kpeter@864
   219
    struct SetLargeCost
kpeter@864
   220
      : public HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > {
kpeter@864
   221
      typedef HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > Create;
kpeter@766
   222
    };
kpeter@766
   223
kpeter@766
   224
    template <typename T>
kpeter@766
   225
    struct SetPathTraits : public Traits {
kpeter@766
   226
      typedef T Path;
kpeter@766
   227
    };
kpeter@766
   228
kpeter@766
   229
    /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@766
   230
    /// \c %Path type.
kpeter@766
   231
    ///
kpeter@766
   232
    /// \ref named-templ-param "Named parameter" for setting the \c %Path
kpeter@766
   233
    /// type of the found cycles.
kpeter@766
   234
    /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@766
   235
    /// and it must have an \c addFront() function.
kpeter@766
   236
    template <typename T>
kpeter@766
   237
    struct SetPath
kpeter@864
   238
      : public HartmannOrlinMmc<GR, CM, SetPathTraits<T> > {
kpeter@864
   239
      typedef HartmannOrlinMmc<GR, CM, SetPathTraits<T> > Create;
kpeter@766
   240
    };
kpeter@766
   241
kpeter@766
   242
    /// @}
kpeter@766
   243
kpeter@863
   244
  protected:
kpeter@863
   245
kpeter@864
   246
    HartmannOrlinMmc() {}
kpeter@863
   247
kpeter@766
   248
  public:
kpeter@766
   249
kpeter@766
   250
    /// \brief Constructor.
kpeter@766
   251
    ///
kpeter@766
   252
    /// The constructor of the class.
kpeter@766
   253
    ///
kpeter@766
   254
    /// \param digraph The digraph the algorithm runs on.
kpeter@864
   255
    /// \param cost The costs of the arcs.
kpeter@864
   256
    HartmannOrlinMmc( const Digraph &digraph,
kpeter@864
   257
                      const CostMap &cost ) :
kpeter@864
   258
      _gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),
kpeter@864
   259
      _best_found(false), _best_cost(0), _best_size(1),
kpeter@767
   260
      _cycle_path(NULL), _local_path(false), _data(digraph),
kpeter@864
   261
      INF(std::numeric_limits<LargeCost>::has_infinity ?
kpeter@864
   262
          std::numeric_limits<LargeCost>::infinity() :
kpeter@864
   263
          std::numeric_limits<LargeCost>::max())
kpeter@766
   264
    {}
kpeter@766
   265
kpeter@766
   266
    /// Destructor.
kpeter@864
   267
    ~HartmannOrlinMmc() {
kpeter@766
   268
      if (_local_path) delete _cycle_path;
kpeter@766
   269
    }
kpeter@766
   270
kpeter@766
   271
    /// \brief Set the path structure for storing the found cycle.
kpeter@766
   272
    ///
kpeter@766
   273
    /// This function sets an external path structure for storing the
kpeter@766
   274
    /// found cycle.
kpeter@766
   275
    ///
kpeter@766
   276
    /// If you don't call this function before calling \ref run() or
kpeter@864
   277
    /// \ref findCycleMean(), it will allocate a local \ref Path "path"
kpeter@766
   278
    /// structure. The destuctor deallocates this automatically
kpeter@766
   279
    /// allocated object, of course.
kpeter@766
   280
    ///
kpeter@766
   281
    /// \note The algorithm calls only the \ref lemon::Path::addFront()
kpeter@766
   282
    /// "addFront()" function of the given path structure.
kpeter@766
   283
    ///
kpeter@766
   284
    /// \return <tt>(*this)</tt>
kpeter@864
   285
    HartmannOrlinMmc& cycle(Path &path) {
kpeter@766
   286
      if (_local_path) {
kpeter@766
   287
        delete _cycle_path;
kpeter@766
   288
        _local_path = false;
kpeter@766
   289
      }
kpeter@766
   290
      _cycle_path = &path;
kpeter@766
   291
      return *this;
kpeter@766
   292
    }
kpeter@766
   293
kpeter@769
   294
    /// \brief Set the tolerance used by the algorithm.
kpeter@769
   295
    ///
kpeter@769
   296
    /// This function sets the tolerance object used by the algorithm.
kpeter@769
   297
    ///
kpeter@769
   298
    /// \return <tt>(*this)</tt>
kpeter@864
   299
    HartmannOrlinMmc& tolerance(const Tolerance& tolerance) {
kpeter@769
   300
      _tolerance = tolerance;
kpeter@769
   301
      return *this;
kpeter@769
   302
    }
kpeter@769
   303
kpeter@769
   304
    /// \brief Return a const reference to the tolerance.
kpeter@769
   305
    ///
kpeter@769
   306
    /// This function returns a const reference to the tolerance object
kpeter@769
   307
    /// used by the algorithm.
kpeter@769
   308
    const Tolerance& tolerance() const {
kpeter@769
   309
      return _tolerance;
kpeter@769
   310
    }
kpeter@769
   311
kpeter@766
   312
    /// \name Execution control
kpeter@766
   313
    /// The simplest way to execute the algorithm is to call the \ref run()
kpeter@766
   314
    /// function.\n
kpeter@864
   315
    /// If you only need the minimum mean cost, you may call
kpeter@864
   316
    /// \ref findCycleMean().
kpeter@766
   317
kpeter@766
   318
    /// @{
kpeter@766
   319
kpeter@766
   320
    /// \brief Run the algorithm.
kpeter@766
   321
    ///
kpeter@766
   322
    /// This function runs the algorithm.
kpeter@766
   323
    /// It can be called more than once (e.g. if the underlying digraph
kpeter@864
   324
    /// and/or the arc costs have been modified).
kpeter@766
   325
    ///
kpeter@766
   326
    /// \return \c true if a directed cycle exists in the digraph.
kpeter@766
   327
    ///
kpeter@766
   328
    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
kpeter@766
   329
    /// \code
kpeter@864
   330
    ///   return mmc.findCycleMean() && mmc.findCycle();
kpeter@766
   331
    /// \endcode
kpeter@766
   332
    bool run() {
kpeter@864
   333
      return findCycleMean() && findCycle();
kpeter@766
   334
    }
kpeter@766
   335
kpeter@766
   336
    /// \brief Find the minimum cycle mean.
kpeter@766
   337
    ///
kpeter@864
   338
    /// This function finds the minimum mean cost of the directed
kpeter@766
   339
    /// cycles in the digraph.
kpeter@766
   340
    ///
kpeter@766
   341
    /// \return \c true if a directed cycle exists in the digraph.
kpeter@864
   342
    bool findCycleMean() {
kpeter@766
   343
      // Initialization and find strongly connected components
kpeter@766
   344
      init();
kpeter@766
   345
      findComponents();
alpar@877
   346
kpeter@766
   347
      // Find the minimum cycle mean in the components
kpeter@766
   348
      for (int comp = 0; comp < _comp_num; ++comp) {
kpeter@766
   349
        if (!initComponent(comp)) continue;
kpeter@766
   350
        processRounds();
alpar@877
   351
kpeter@766
   352
        // Update the best cycle (global minimum mean cycle)
alpar@877
   353
        if ( _curr_found && (!_best_found ||
kpeter@864
   354
             _curr_cost * _best_size < _best_cost * _curr_size) ) {
kpeter@766
   355
          _best_found = true;
kpeter@864
   356
          _best_cost = _curr_cost;
kpeter@766
   357
          _best_size = _curr_size;
kpeter@766
   358
          _best_node = _curr_node;
kpeter@766
   359
          _best_level = _curr_level;
kpeter@766
   360
        }
kpeter@766
   361
      }
kpeter@766
   362
      return _best_found;
kpeter@766
   363
    }
kpeter@766
   364
kpeter@766
   365
    /// \brief Find a minimum mean directed cycle.
kpeter@766
   366
    ///
kpeter@864
   367
    /// This function finds a directed cycle of minimum mean cost
kpeter@864
   368
    /// in the digraph using the data computed by findCycleMean().
kpeter@766
   369
    ///
kpeter@766
   370
    /// \return \c true if a directed cycle exists in the digraph.
kpeter@766
   371
    ///
kpeter@864
   372
    /// \pre \ref findCycleMean() must be called before using this function.
kpeter@766
   373
    bool findCycle() {
kpeter@766
   374
      if (!_best_found) return false;
kpeter@766
   375
      IntNodeMap reached(_gr, -1);
kpeter@766
   376
      int r = _best_level + 1;
kpeter@766
   377
      Node u = _best_node;
kpeter@766
   378
      while (reached[u] < 0) {
kpeter@766
   379
        reached[u] = --r;
kpeter@766
   380
        u = _gr.source(_data[u][r].pred);
kpeter@766
   381
      }
kpeter@766
   382
      r = reached[u];
kpeter@766
   383
      Arc e = _data[u][r].pred;
kpeter@766
   384
      _cycle_path->addFront(e);
kpeter@864
   385
      _best_cost = _cost[e];
kpeter@766
   386
      _best_size = 1;
kpeter@766
   387
      Node v;
kpeter@766
   388
      while ((v = _gr.source(e)) != u) {
kpeter@766
   389
        e = _data[v][--r].pred;
kpeter@766
   390
        _cycle_path->addFront(e);
kpeter@864
   391
        _best_cost += _cost[e];
kpeter@766
   392
        ++_best_size;
kpeter@766
   393
      }
kpeter@766
   394
      return true;
kpeter@766
   395
    }
kpeter@766
   396
kpeter@766
   397
    /// @}
kpeter@766
   398
kpeter@766
   399
    /// \name Query Functions
kpeter@766
   400
    /// The results of the algorithm can be obtained using these
kpeter@766
   401
    /// functions.\n
kpeter@766
   402
    /// The algorithm should be executed before using them.
kpeter@766
   403
kpeter@766
   404
    /// @{
kpeter@766
   405
kpeter@864
   406
    /// \brief Return the total cost of the found cycle.
kpeter@766
   407
    ///
kpeter@864
   408
    /// This function returns the total cost of the found cycle.
kpeter@766
   409
    ///
kpeter@864
   410
    /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@766
   411
    /// using this function.
kpeter@864
   412
    Cost cycleCost() const {
kpeter@864
   413
      return static_cast<Cost>(_best_cost);
kpeter@766
   414
    }
kpeter@766
   415
kpeter@766
   416
    /// \brief Return the number of arcs on the found cycle.
kpeter@766
   417
    ///
kpeter@766
   418
    /// This function returns the number of arcs on the found cycle.
kpeter@766
   419
    ///
kpeter@864
   420
    /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@766
   421
    /// using this function.
kpeter@864
   422
    int cycleSize() const {
kpeter@766
   423
      return _best_size;
kpeter@766
   424
    }
kpeter@766
   425
kpeter@864
   426
    /// \brief Return the mean cost of the found cycle.
kpeter@766
   427
    ///
kpeter@864
   428
    /// This function returns the mean cost of the found cycle.
kpeter@766
   429
    ///
kpeter@766
   430
    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@766
   431
    /// following code.
kpeter@766
   432
    /// \code
kpeter@864
   433
    ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
kpeter@766
   434
    /// \endcode
kpeter@766
   435
    ///
kpeter@864
   436
    /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@766
   437
    /// using this function.
kpeter@766
   438
    double cycleMean() const {
kpeter@864
   439
      return static_cast<double>(_best_cost) / _best_size;
kpeter@766
   440
    }
kpeter@766
   441
kpeter@766
   442
    /// \brief Return the found cycle.
kpeter@766
   443
    ///
kpeter@766
   444
    /// This function returns a const reference to the path structure
kpeter@766
   445
    /// storing the found cycle.
kpeter@766
   446
    ///
kpeter@766
   447
    /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@766
   448
    /// this function.
kpeter@766
   449
    const Path& cycle() const {
kpeter@766
   450
      return *_cycle_path;
kpeter@766
   451
    }
kpeter@766
   452
kpeter@766
   453
    ///@}
kpeter@766
   454
kpeter@766
   455
  private:
kpeter@766
   456
kpeter@766
   457
    // Initialization
kpeter@766
   458
    void init() {
kpeter@766
   459
      if (!_cycle_path) {
kpeter@766
   460
        _local_path = true;
kpeter@766
   461
        _cycle_path = new Path;
kpeter@766
   462
      }
kpeter@766
   463
      _cycle_path->clear();
kpeter@766
   464
      _best_found = false;
kpeter@864
   465
      _best_cost = 0;
kpeter@766
   466
      _best_size = 1;
kpeter@766
   467
      _cycle_path->clear();
kpeter@766
   468
      for (NodeIt u(_gr); u != INVALID; ++u)
kpeter@766
   469
        _data[u].clear();
kpeter@766
   470
    }
kpeter@766
   471
kpeter@766
   472
    // Find strongly connected components and initialize _comp_nodes
kpeter@766
   473
    // and _out_arcs
kpeter@766
   474
    void findComponents() {
kpeter@766
   475
      _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@766
   476
      _comp_nodes.resize(_comp_num);
kpeter@766
   477
      if (_comp_num == 1) {
kpeter@766
   478
        _comp_nodes[0].clear();
kpeter@766
   479
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@766
   480
          _comp_nodes[0].push_back(n);
kpeter@766
   481
          _out_arcs[n].clear();
kpeter@766
   482
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@766
   483
            _out_arcs[n].push_back(a);
kpeter@766
   484
          }
kpeter@766
   485
        }
kpeter@766
   486
      } else {
kpeter@766
   487
        for (int i = 0; i < _comp_num; ++i)
kpeter@766
   488
          _comp_nodes[i].clear();
kpeter@766
   489
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@766
   490
          int k = _comp[n];
kpeter@766
   491
          _comp_nodes[k].push_back(n);
kpeter@766
   492
          _out_arcs[n].clear();
kpeter@766
   493
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@766
   494
            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
kpeter@766
   495
          }
kpeter@766
   496
        }
kpeter@766
   497
      }
kpeter@766
   498
    }
kpeter@766
   499
kpeter@766
   500
    // Initialize path data for the current component
kpeter@766
   501
    bool initComponent(int comp) {
kpeter@766
   502
      _nodes = &(_comp_nodes[comp]);
kpeter@766
   503
      int n = _nodes->size();
kpeter@766
   504
      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@766
   505
        return false;
alpar@877
   506
      }
kpeter@766
   507
      for (int i = 0; i < n; ++i) {
kpeter@767
   508
        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
kpeter@766
   509
      }
kpeter@766
   510
      return true;
kpeter@766
   511
    }
kpeter@766
   512
kpeter@766
   513
    // Process all rounds of computing path data for the current component.
kpeter@864
   514
    // _data[v][k] is the cost of a shortest directed walk from the root
kpeter@766
   515
    // node to node v containing exactly k arcs.
kpeter@766
   516
    void processRounds() {
kpeter@766
   517
      Node start = (*_nodes)[0];
kpeter@767
   518
      _data[start][0] = PathData(0);
kpeter@766
   519
      _process.clear();
kpeter@766
   520
      _process.push_back(start);
kpeter@766
   521
kpeter@766
   522
      int k, n = _nodes->size();
kpeter@766
   523
      int next_check = 4;
kpeter@766
   524
      bool terminate = false;
kpeter@766
   525
      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
kpeter@766
   526
        processNextBuildRound(k);
kpeter@766
   527
        if (k == next_check || k == n) {
kpeter@766
   528
          terminate = checkTermination(k);
kpeter@766
   529
          next_check = next_check * 3 / 2;
kpeter@766
   530
        }
kpeter@766
   531
      }
kpeter@766
   532
      for ( ; k <= n && !terminate; ++k) {
kpeter@766
   533
        processNextFullRound(k);
kpeter@766
   534
        if (k == next_check || k == n) {
kpeter@766
   535
          terminate = checkTermination(k);
kpeter@766
   536
          next_check = next_check * 3 / 2;
kpeter@766
   537
        }
kpeter@766
   538
      }
kpeter@766
   539
    }
kpeter@766
   540
kpeter@766
   541
    // Process one round and rebuild _process
kpeter@766
   542
    void processNextBuildRound(int k) {
kpeter@766
   543
      std::vector<Node> next;
kpeter@766
   544
      Node u, v;
kpeter@766
   545
      Arc e;
kpeter@864
   546
      LargeCost d;
kpeter@766
   547
      for (int i = 0; i < int(_process.size()); ++i) {
kpeter@766
   548
        u = _process[i];
kpeter@766
   549
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@766
   550
          e = _out_arcs[u][j];
kpeter@766
   551
          v = _gr.target(e);
kpeter@864
   552
          d = _data[u][k-1].dist + _cost[e];
kpeter@767
   553
          if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@767
   554
            if (_data[v][k].dist == INF) next.push_back(v);
kpeter@767
   555
            _data[v][k] = PathData(d, e);
kpeter@766
   556
          }
kpeter@766
   557
        }
kpeter@766
   558
      }
kpeter@766
   559
      _process.swap(next);
kpeter@766
   560
    }
kpeter@766
   561
kpeter@766
   562
    // Process one round using _nodes instead of _process
kpeter@766
   563
    void processNextFullRound(int k) {
kpeter@766
   564
      Node u, v;
kpeter@766
   565
      Arc e;
kpeter@864
   566
      LargeCost d;
kpeter@766
   567
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@766
   568
        u = (*_nodes)[i];
kpeter@766
   569
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@766
   570
          e = _out_arcs[u][j];
kpeter@766
   571
          v = _gr.target(e);
kpeter@864
   572
          d = _data[u][k-1].dist + _cost[e];
kpeter@767
   573
          if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@767
   574
            _data[v][k] = PathData(d, e);
kpeter@766
   575
          }
kpeter@766
   576
        }
kpeter@766
   577
      }
kpeter@766
   578
    }
alpar@877
   579
kpeter@766
   580
    // Check early termination
kpeter@766
   581
    bool checkTermination(int k) {
kpeter@766
   582
      typedef std::pair<int, int> Pair;
kpeter@766
   583
      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
kpeter@864
   584
      typename GR::template NodeMap<LargeCost> pi(_gr);
kpeter@766
   585
      int n = _nodes->size();
kpeter@864
   586
      LargeCost cost;
kpeter@766
   587
      int size;
kpeter@766
   588
      Node u;
alpar@877
   589
kpeter@766
   590
      // Search for cycles that are already found
kpeter@766
   591
      _curr_found = false;
kpeter@766
   592
      for (int i = 0; i < n; ++i) {
kpeter@766
   593
        u = (*_nodes)[i];
kpeter@767
   594
        if (_data[u][k].dist == INF) continue;
kpeter@766
   595
        for (int j = k; j >= 0; --j) {
kpeter@766
   596
          if (level[u].first == i && level[u].second > 0) {
kpeter@766
   597
            // A cycle is found
kpeter@864
   598
            cost = _data[u][level[u].second].dist - _data[u][j].dist;
kpeter@766
   599
            size = level[u].second - j;
kpeter@864
   600
            if (!_curr_found || cost * _curr_size < _curr_cost * size) {
kpeter@864
   601
              _curr_cost = cost;
kpeter@766
   602
              _curr_size = size;
kpeter@766
   603
              _curr_node = u;
kpeter@766
   604
              _curr_level = level[u].second;
kpeter@766
   605
              _curr_found = true;
kpeter@766
   606
            }
kpeter@766
   607
          }
kpeter@766
   608
          level[u] = Pair(i, j);
deba@795
   609
          if (j != 0) {
alpar@877
   610
            u = _gr.source(_data[u][j].pred);
alpar@877
   611
          }
kpeter@766
   612
        }
kpeter@766
   613
      }
kpeter@766
   614
kpeter@766
   615
      // If at least one cycle is found, check the optimality condition
kpeter@864
   616
      LargeCost d;
kpeter@766
   617
      if (_curr_found && k < n) {
kpeter@766
   618
        // Find node potentials
kpeter@766
   619
        for (int i = 0; i < n; ++i) {
kpeter@766
   620
          u = (*_nodes)[i];
kpeter@767
   621
          pi[u] = INF;
kpeter@766
   622
          for (int j = 0; j <= k; ++j) {
kpeter@767
   623
            if (_data[u][j].dist < INF) {
kpeter@864
   624
              d = _data[u][j].dist * _curr_size - j * _curr_cost;
kpeter@767
   625
              if (_tolerance.less(d, pi[u])) pi[u] = d;
kpeter@766
   626
            }
kpeter@766
   627
          }
kpeter@766
   628
        }
kpeter@766
   629
kpeter@766
   630
        // Check the optimality condition for all arcs
kpeter@766
   631
        bool done = true;
kpeter@766
   632
        for (ArcIt a(_gr); a != INVALID; ++a) {
kpeter@864
   633
          if (_tolerance.less(_cost[a] * _curr_size - _curr_cost,
kpeter@766
   634
                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
kpeter@766
   635
            done = false;
kpeter@766
   636
            break;
kpeter@766
   637
          }
kpeter@766
   638
        }
kpeter@766
   639
        return done;
kpeter@766
   640
      }
kpeter@766
   641
      return (k == n);
kpeter@766
   642
    }
kpeter@766
   643
kpeter@864
   644
  }; //class HartmannOrlinMmc
kpeter@766
   645
kpeter@766
   646
  ///@}
kpeter@766
   647
kpeter@766
   648
} //namespace lemon
kpeter@766
   649
kpeter@864
   650
#endif //LEMON_HARTMANN_ORLIN_MMC_H