lemon/karp.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sat, 20 Feb 2010 18:39:03 +0100
changeset 839 f3bc4e9b5f3a
parent 771 8452ca46e29a
child 825 75e6020b19b1
permissions -rw-r--r--
New heuristics for MCF algorithms (#340)
and some implementation improvements.

- A useful heuristic is added to NetworkSimplex to make the
initial pivots faster.
- A powerful global update heuristic is added to CostScaling
and the implementation is reworked with various improvements.
- Better relabeling in CostScaling to improve numerical stability
and make the code faster.
- A small improvement is made in CapacityScaling for better
delta computation.
- Add notes to the classes about the usage of vector<char> instead
of vector<bool> for efficiency reasons.
kpeter@765
     1
/* -*- C++ -*-
kpeter@765
     2
 *
kpeter@765
     3
 * This file is a part of LEMON, a generic C++ optimization library
kpeter@765
     4
 *
kpeter@765
     5
 * Copyright (C) 2003-2008
kpeter@765
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@765
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@765
     8
 *
kpeter@765
     9
 * Permission to use, modify and distribute this software is granted
kpeter@765
    10
 * provided that this copyright notice appears in all copies. For
kpeter@765
    11
 * precise terms see the accompanying LICENSE file.
kpeter@765
    12
 *
kpeter@765
    13
 * This software is provided "AS IS" with no warranty of any kind,
kpeter@765
    14
 * express or implied, and with no claim as to its suitability for any
kpeter@765
    15
 * purpose.
kpeter@765
    16
 *
kpeter@765
    17
 */
kpeter@765
    18
kpeter@765
    19
#ifndef LEMON_KARP_H
kpeter@765
    20
#define LEMON_KARP_H
kpeter@765
    21
kpeter@768
    22
/// \ingroup min_mean_cycle
kpeter@765
    23
///
kpeter@765
    24
/// \file
kpeter@765
    25
/// \brief Karp's algorithm for finding a minimum mean cycle.
kpeter@765
    26
kpeter@765
    27
#include <vector>
kpeter@765
    28
#include <limits>
kpeter@765
    29
#include <lemon/core.h>
kpeter@765
    30
#include <lemon/path.h>
kpeter@765
    31
#include <lemon/tolerance.h>
kpeter@765
    32
#include <lemon/connectivity.h>
kpeter@765
    33
kpeter@765
    34
namespace lemon {
kpeter@765
    35
kpeter@765
    36
  /// \brief Default traits class of Karp algorithm.
kpeter@765
    37
  ///
kpeter@765
    38
  /// Default traits class of Karp algorithm.
kpeter@765
    39
  /// \tparam GR The type of the digraph.
kpeter@765
    40
  /// \tparam LEN The type of the length map.
kpeter@765
    41
  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
kpeter@765
    42
#ifdef DOXYGEN
kpeter@765
    43
  template <typename GR, typename LEN>
kpeter@765
    44
#else
kpeter@765
    45
  template <typename GR, typename LEN,
kpeter@765
    46
    bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
kpeter@765
    47
#endif
kpeter@765
    48
  struct KarpDefaultTraits
kpeter@765
    49
  {
kpeter@765
    50
    /// The type of the digraph
kpeter@765
    51
    typedef GR Digraph;
kpeter@765
    52
    /// The type of the length map
kpeter@765
    53
    typedef LEN LengthMap;
kpeter@765
    54
    /// The type of the arc lengths
kpeter@765
    55
    typedef typename LengthMap::Value Value;
kpeter@765
    56
kpeter@765
    57
    /// \brief The large value type used for internal computations
kpeter@765
    58
    ///
kpeter@765
    59
    /// The large value type used for internal computations.
kpeter@765
    60
    /// It is \c long \c long if the \c Value type is integer,
kpeter@765
    61
    /// otherwise it is \c double.
kpeter@765
    62
    /// \c Value must be convertible to \c LargeValue.
kpeter@765
    63
    typedef double LargeValue;
kpeter@765
    64
kpeter@765
    65
    /// The tolerance type used for internal computations
kpeter@765
    66
    typedef lemon::Tolerance<LargeValue> Tolerance;
kpeter@765
    67
kpeter@765
    68
    /// \brief The path type of the found cycles
kpeter@765
    69
    ///
kpeter@765
    70
    /// The path type of the found cycles.
kpeter@765
    71
    /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@772
    72
    /// and it must have an \c addFront() function.
kpeter@765
    73
    typedef lemon::Path<Digraph> Path;
kpeter@765
    74
  };
kpeter@765
    75
kpeter@765
    76
  // Default traits class for integer value types
kpeter@765
    77
  template <typename GR, typename LEN>
kpeter@765
    78
  struct KarpDefaultTraits<GR, LEN, true>
kpeter@765
    79
  {
kpeter@765
    80
    typedef GR Digraph;
kpeter@765
    81
    typedef LEN LengthMap;
kpeter@765
    82
    typedef typename LengthMap::Value Value;
kpeter@765
    83
#ifdef LEMON_HAVE_LONG_LONG
kpeter@765
    84
    typedef long long LargeValue;
kpeter@765
    85
#else
kpeter@765
    86
    typedef long LargeValue;
kpeter@765
    87
#endif
kpeter@765
    88
    typedef lemon::Tolerance<LargeValue> Tolerance;
kpeter@765
    89
    typedef lemon::Path<Digraph> Path;
kpeter@765
    90
  };
kpeter@765
    91
kpeter@765
    92
kpeter@768
    93
  /// \addtogroup min_mean_cycle
kpeter@765
    94
  /// @{
kpeter@765
    95
kpeter@765
    96
  /// \brief Implementation of Karp's algorithm for finding a minimum
kpeter@765
    97
  /// mean cycle.
kpeter@765
    98
  ///
kpeter@765
    99
  /// This class implements Karp's algorithm for finding a directed
kpeter@771
   100
  /// cycle of minimum mean length (cost) in a digraph
kpeter@771
   101
  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
kpeter@768
   102
  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
kpeter@765
   103
  ///
kpeter@765
   104
  /// \tparam GR The type of the digraph the algorithm runs on.
kpeter@765
   105
  /// \tparam LEN The type of the length map. The default
kpeter@765
   106
  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
kpeter@765
   107
#ifdef DOXYGEN
kpeter@765
   108
  template <typename GR, typename LEN, typename TR>
kpeter@765
   109
#else
kpeter@765
   110
  template < typename GR,
kpeter@765
   111
             typename LEN = typename GR::template ArcMap<int>,
kpeter@765
   112
             typename TR = KarpDefaultTraits<GR, LEN> >
kpeter@765
   113
#endif
kpeter@765
   114
  class Karp
kpeter@765
   115
  {
kpeter@765
   116
  public:
kpeter@765
   117
kpeter@765
   118
    /// The type of the digraph
kpeter@765
   119
    typedef typename TR::Digraph Digraph;
kpeter@765
   120
    /// The type of the length map
kpeter@765
   121
    typedef typename TR::LengthMap LengthMap;
kpeter@765
   122
    /// The type of the arc lengths
kpeter@765
   123
    typedef typename TR::Value Value;
kpeter@765
   124
kpeter@765
   125
    /// \brief The large value type
kpeter@765
   126
    ///
kpeter@765
   127
    /// The large value type used for internal computations.
kpeter@765
   128
    /// Using the \ref KarpDefaultTraits "default traits class",
kpeter@765
   129
    /// it is \c long \c long if the \c Value type is integer,
kpeter@765
   130
    /// otherwise it is \c double.
kpeter@765
   131
    typedef typename TR::LargeValue LargeValue;
kpeter@765
   132
kpeter@765
   133
    /// The tolerance type
kpeter@765
   134
    typedef typename TR::Tolerance Tolerance;
kpeter@765
   135
kpeter@765
   136
    /// \brief The path type of the found cycles
kpeter@765
   137
    ///
kpeter@765
   138
    /// The path type of the found cycles.
kpeter@765
   139
    /// Using the \ref KarpDefaultTraits "default traits class",
kpeter@765
   140
    /// it is \ref lemon::Path "Path<Digraph>".
kpeter@765
   141
    typedef typename TR::Path Path;
kpeter@765
   142
kpeter@765
   143
    /// The \ref KarpDefaultTraits "traits class" of the algorithm
kpeter@765
   144
    typedef TR Traits;
kpeter@765
   145
kpeter@765
   146
  private:
kpeter@765
   147
kpeter@765
   148
    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@765
   149
kpeter@765
   150
    // Data sturcture for path data
kpeter@765
   151
    struct PathData
kpeter@765
   152
    {
kpeter@765
   153
      LargeValue dist;
kpeter@765
   154
      Arc pred;
kpeter@767
   155
      PathData(LargeValue d, Arc p = INVALID) :
kpeter@767
   156
        dist(d), pred(p) {}
kpeter@765
   157
    };
kpeter@765
   158
kpeter@765
   159
    typedef typename Digraph::template NodeMap<std::vector<PathData> >
kpeter@765
   160
      PathDataNodeMap;
kpeter@765
   161
kpeter@765
   162
  private:
kpeter@765
   163
kpeter@765
   164
    // The digraph the algorithm runs on
kpeter@765
   165
    const Digraph &_gr;
kpeter@765
   166
    // The length of the arcs
kpeter@765
   167
    const LengthMap &_length;
kpeter@765
   168
kpeter@765
   169
    // Data for storing the strongly connected components
kpeter@765
   170
    int _comp_num;
kpeter@765
   171
    typename Digraph::template NodeMap<int> _comp;
kpeter@765
   172
    std::vector<std::vector<Node> > _comp_nodes;
kpeter@765
   173
    std::vector<Node>* _nodes;
kpeter@765
   174
    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
kpeter@765
   175
kpeter@765
   176
    // Data for the found cycle
kpeter@765
   177
    LargeValue _cycle_length;
kpeter@765
   178
    int _cycle_size;
kpeter@765
   179
    Node _cycle_node;
kpeter@765
   180
kpeter@765
   181
    Path *_cycle_path;
kpeter@765
   182
    bool _local_path;
kpeter@765
   183
kpeter@765
   184
    // Node map for storing path data
kpeter@765
   185
    PathDataNodeMap _data;
kpeter@765
   186
    // The processed nodes in the last round
kpeter@765
   187
    std::vector<Node> _process;
kpeter@765
   188
kpeter@765
   189
    Tolerance _tolerance;
kpeter@767
   190
    
kpeter@767
   191
    // Infinite constant
kpeter@767
   192
    const LargeValue INF;
kpeter@765
   193
kpeter@765
   194
  public:
kpeter@765
   195
kpeter@765
   196
    /// \name Named Template Parameters
kpeter@765
   197
    /// @{
kpeter@765
   198
kpeter@765
   199
    template <typename T>
kpeter@765
   200
    struct SetLargeValueTraits : public Traits {
kpeter@765
   201
      typedef T LargeValue;
kpeter@765
   202
      typedef lemon::Tolerance<T> Tolerance;
kpeter@765
   203
    };
kpeter@765
   204
kpeter@765
   205
    /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@765
   206
    /// \c LargeValue type.
kpeter@765
   207
    ///
kpeter@765
   208
    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
kpeter@765
   209
    /// type. It is used for internal computations in the algorithm.
kpeter@765
   210
    template <typename T>
kpeter@765
   211
    struct SetLargeValue
kpeter@765
   212
      : public Karp<GR, LEN, SetLargeValueTraits<T> > {
kpeter@765
   213
      typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create;
kpeter@765
   214
    };
kpeter@765
   215
kpeter@765
   216
    template <typename T>
kpeter@765
   217
    struct SetPathTraits : public Traits {
kpeter@765
   218
      typedef T Path;
kpeter@765
   219
    };
kpeter@765
   220
kpeter@765
   221
    /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@765
   222
    /// \c %Path type.
kpeter@765
   223
    ///
kpeter@765
   224
    /// \ref named-templ-param "Named parameter" for setting the \c %Path
kpeter@765
   225
    /// type of the found cycles.
kpeter@765
   226
    /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@765
   227
    /// and it must have an \c addFront() function.
kpeter@765
   228
    template <typename T>
kpeter@765
   229
    struct SetPath
kpeter@765
   230
      : public Karp<GR, LEN, SetPathTraits<T> > {
kpeter@765
   231
      typedef Karp<GR, LEN, SetPathTraits<T> > Create;
kpeter@765
   232
    };
kpeter@765
   233
kpeter@765
   234
    /// @}
kpeter@765
   235
kpeter@765
   236
  public:
kpeter@765
   237
kpeter@765
   238
    /// \brief Constructor.
kpeter@765
   239
    ///
kpeter@765
   240
    /// The constructor of the class.
kpeter@765
   241
    ///
kpeter@765
   242
    /// \param digraph The digraph the algorithm runs on.
kpeter@765
   243
    /// \param length The lengths (costs) of the arcs.
kpeter@765
   244
    Karp( const Digraph &digraph,
kpeter@765
   245
          const LengthMap &length ) :
kpeter@765
   246
      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
kpeter@765
   247
      _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
kpeter@767
   248
      _cycle_path(NULL), _local_path(false), _data(digraph),
kpeter@767
   249
      INF(std::numeric_limits<LargeValue>::has_infinity ?
kpeter@767
   250
          std::numeric_limits<LargeValue>::infinity() :
kpeter@767
   251
          std::numeric_limits<LargeValue>::max())
kpeter@765
   252
    {}
kpeter@765
   253
kpeter@765
   254
    /// Destructor.
kpeter@765
   255
    ~Karp() {
kpeter@765
   256
      if (_local_path) delete _cycle_path;
kpeter@765
   257
    }
kpeter@765
   258
kpeter@765
   259
    /// \brief Set the path structure for storing the found cycle.
kpeter@765
   260
    ///
kpeter@765
   261
    /// This function sets an external path structure for storing the
kpeter@765
   262
    /// found cycle.
kpeter@765
   263
    ///
kpeter@765
   264
    /// If you don't call this function before calling \ref run() or
kpeter@765
   265
    /// \ref findMinMean(), it will allocate a local \ref Path "path"
kpeter@765
   266
    /// structure. The destuctor deallocates this automatically
kpeter@765
   267
    /// allocated object, of course.
kpeter@765
   268
    ///
kpeter@765
   269
    /// \note The algorithm calls only the \ref lemon::Path::addFront()
kpeter@765
   270
    /// "addFront()" function of the given path structure.
kpeter@765
   271
    ///
kpeter@765
   272
    /// \return <tt>(*this)</tt>
kpeter@765
   273
    Karp& cycle(Path &path) {
kpeter@765
   274
      if (_local_path) {
kpeter@765
   275
        delete _cycle_path;
kpeter@765
   276
        _local_path = false;
kpeter@765
   277
      }
kpeter@765
   278
      _cycle_path = &path;
kpeter@765
   279
      return *this;
kpeter@765
   280
    }
kpeter@765
   281
kpeter@769
   282
    /// \brief Set the tolerance used by the algorithm.
kpeter@769
   283
    ///
kpeter@769
   284
    /// This function sets the tolerance object used by the algorithm.
kpeter@769
   285
    ///
kpeter@769
   286
    /// \return <tt>(*this)</tt>
kpeter@769
   287
    Karp& tolerance(const Tolerance& tolerance) {
kpeter@769
   288
      _tolerance = tolerance;
kpeter@769
   289
      return *this;
kpeter@769
   290
    }
kpeter@769
   291
kpeter@769
   292
    /// \brief Return a const reference to the tolerance.
kpeter@769
   293
    ///
kpeter@769
   294
    /// This function returns a const reference to the tolerance object
kpeter@769
   295
    /// used by the algorithm.
kpeter@769
   296
    const Tolerance& tolerance() const {
kpeter@769
   297
      return _tolerance;
kpeter@769
   298
    }
kpeter@769
   299
kpeter@765
   300
    /// \name Execution control
kpeter@765
   301
    /// The simplest way to execute the algorithm is to call the \ref run()
kpeter@765
   302
    /// function.\n
kpeter@765
   303
    /// If you only need the minimum mean length, you may call
kpeter@765
   304
    /// \ref findMinMean().
kpeter@765
   305
kpeter@765
   306
    /// @{
kpeter@765
   307
kpeter@765
   308
    /// \brief Run the algorithm.
kpeter@765
   309
    ///
kpeter@765
   310
    /// This function runs the algorithm.
kpeter@765
   311
    /// It can be called more than once (e.g. if the underlying digraph
kpeter@765
   312
    /// and/or the arc lengths have been modified).
kpeter@765
   313
    ///
kpeter@765
   314
    /// \return \c true if a directed cycle exists in the digraph.
kpeter@765
   315
    ///
kpeter@765
   316
    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
kpeter@765
   317
    /// \code
kpeter@765
   318
    ///   return mmc.findMinMean() && mmc.findCycle();
kpeter@765
   319
    /// \endcode
kpeter@765
   320
    bool run() {
kpeter@765
   321
      return findMinMean() && findCycle();
kpeter@765
   322
    }
kpeter@765
   323
kpeter@765
   324
    /// \brief Find the minimum cycle mean.
kpeter@765
   325
    ///
kpeter@765
   326
    /// This function finds the minimum mean length of the directed
kpeter@765
   327
    /// cycles in the digraph.
kpeter@765
   328
    ///
kpeter@765
   329
    /// \return \c true if a directed cycle exists in the digraph.
kpeter@765
   330
    bool findMinMean() {
kpeter@765
   331
      // Initialization and find strongly connected components
kpeter@765
   332
      init();
kpeter@765
   333
      findComponents();
kpeter@765
   334
      
kpeter@765
   335
      // Find the minimum cycle mean in the components
kpeter@765
   336
      for (int comp = 0; comp < _comp_num; ++comp) {
kpeter@765
   337
        if (!initComponent(comp)) continue;
kpeter@765
   338
        processRounds();
kpeter@765
   339
        updateMinMean();
kpeter@765
   340
      }
kpeter@765
   341
      return (_cycle_node != INVALID);
kpeter@765
   342
    }
kpeter@765
   343
kpeter@765
   344
    /// \brief Find a minimum mean directed cycle.
kpeter@765
   345
    ///
kpeter@765
   346
    /// This function finds a directed cycle of minimum mean length
kpeter@765
   347
    /// in the digraph using the data computed by findMinMean().
kpeter@765
   348
    ///
kpeter@765
   349
    /// \return \c true if a directed cycle exists in the digraph.
kpeter@765
   350
    ///
kpeter@765
   351
    /// \pre \ref findMinMean() must be called before using this function.
kpeter@765
   352
    bool findCycle() {
kpeter@765
   353
      if (_cycle_node == INVALID) return false;
kpeter@765
   354
      IntNodeMap reached(_gr, -1);
kpeter@765
   355
      int r = _data[_cycle_node].size();
kpeter@765
   356
      Node u = _cycle_node;
kpeter@765
   357
      while (reached[u] < 0) {
kpeter@765
   358
        reached[u] = --r;
kpeter@765
   359
        u = _gr.source(_data[u][r].pred);
kpeter@765
   360
      }
kpeter@765
   361
      r = reached[u];
kpeter@765
   362
      Arc e = _data[u][r].pred;
kpeter@765
   363
      _cycle_path->addFront(e);
kpeter@765
   364
      _cycle_length = _length[e];
kpeter@765
   365
      _cycle_size = 1;
kpeter@765
   366
      Node v;
kpeter@765
   367
      while ((v = _gr.source(e)) != u) {
kpeter@765
   368
        e = _data[v][--r].pred;
kpeter@765
   369
        _cycle_path->addFront(e);
kpeter@765
   370
        _cycle_length += _length[e];
kpeter@765
   371
        ++_cycle_size;
kpeter@765
   372
      }
kpeter@765
   373
      return true;
kpeter@765
   374
    }
kpeter@765
   375
kpeter@765
   376
    /// @}
kpeter@765
   377
kpeter@765
   378
    /// \name Query Functions
kpeter@765
   379
    /// The results of the algorithm can be obtained using these
kpeter@765
   380
    /// functions.\n
kpeter@765
   381
    /// The algorithm should be executed before using them.
kpeter@765
   382
kpeter@765
   383
    /// @{
kpeter@765
   384
kpeter@765
   385
    /// \brief Return the total length of the found cycle.
kpeter@765
   386
    ///
kpeter@765
   387
    /// This function returns the total length of the found cycle.
kpeter@765
   388
    ///
kpeter@765
   389
    /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@765
   390
    /// using this function.
kpeter@765
   391
    LargeValue cycleLength() const {
kpeter@765
   392
      return _cycle_length;
kpeter@765
   393
    }
kpeter@765
   394
kpeter@765
   395
    /// \brief Return the number of arcs on the found cycle.
kpeter@765
   396
    ///
kpeter@765
   397
    /// This function returns the number of arcs on the found cycle.
kpeter@765
   398
    ///
kpeter@765
   399
    /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@765
   400
    /// using this function.
kpeter@765
   401
    int cycleArcNum() const {
kpeter@765
   402
      return _cycle_size;
kpeter@765
   403
    }
kpeter@765
   404
kpeter@765
   405
    /// \brief Return the mean length of the found cycle.
kpeter@765
   406
    ///
kpeter@765
   407
    /// This function returns the mean length of the found cycle.
kpeter@765
   408
    ///
kpeter@765
   409
    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@765
   410
    /// following code.
kpeter@765
   411
    /// \code
kpeter@765
   412
    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
kpeter@765
   413
    /// \endcode
kpeter@765
   414
    ///
kpeter@765
   415
    /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@765
   416
    /// using this function.
kpeter@765
   417
    double cycleMean() const {
kpeter@765
   418
      return static_cast<double>(_cycle_length) / _cycle_size;
kpeter@765
   419
    }
kpeter@765
   420
kpeter@765
   421
    /// \brief Return the found cycle.
kpeter@765
   422
    ///
kpeter@765
   423
    /// This function returns a const reference to the path structure
kpeter@765
   424
    /// storing the found cycle.
kpeter@765
   425
    ///
kpeter@765
   426
    /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@765
   427
    /// this function.
kpeter@765
   428
    const Path& cycle() const {
kpeter@765
   429
      return *_cycle_path;
kpeter@765
   430
    }
kpeter@765
   431
kpeter@765
   432
    ///@}
kpeter@765
   433
kpeter@765
   434
  private:
kpeter@765
   435
kpeter@765
   436
    // Initialization
kpeter@765
   437
    void init() {
kpeter@765
   438
      if (!_cycle_path) {
kpeter@765
   439
        _local_path = true;
kpeter@765
   440
        _cycle_path = new Path;
kpeter@765
   441
      }
kpeter@765
   442
      _cycle_path->clear();
kpeter@765
   443
      _cycle_length = 0;
kpeter@765
   444
      _cycle_size = 1;
kpeter@765
   445
      _cycle_node = INVALID;
kpeter@765
   446
      for (NodeIt u(_gr); u != INVALID; ++u)
kpeter@765
   447
        _data[u].clear();
kpeter@765
   448
    }
kpeter@765
   449
kpeter@765
   450
    // Find strongly connected components and initialize _comp_nodes
kpeter@765
   451
    // and _out_arcs
kpeter@765
   452
    void findComponents() {
kpeter@765
   453
      _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@765
   454
      _comp_nodes.resize(_comp_num);
kpeter@765
   455
      if (_comp_num == 1) {
kpeter@765
   456
        _comp_nodes[0].clear();
kpeter@765
   457
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@765
   458
          _comp_nodes[0].push_back(n);
kpeter@765
   459
          _out_arcs[n].clear();
kpeter@765
   460
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@765
   461
            _out_arcs[n].push_back(a);
kpeter@765
   462
          }
kpeter@765
   463
        }
kpeter@765
   464
      } else {
kpeter@765
   465
        for (int i = 0; i < _comp_num; ++i)
kpeter@765
   466
          _comp_nodes[i].clear();
kpeter@765
   467
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@765
   468
          int k = _comp[n];
kpeter@765
   469
          _comp_nodes[k].push_back(n);
kpeter@765
   470
          _out_arcs[n].clear();
kpeter@765
   471
          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@765
   472
            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
kpeter@765
   473
          }
kpeter@765
   474
        }
kpeter@765
   475
      }
kpeter@765
   476
    }
kpeter@765
   477
kpeter@765
   478
    // Initialize path data for the current component
kpeter@765
   479
    bool initComponent(int comp) {
kpeter@765
   480
      _nodes = &(_comp_nodes[comp]);
kpeter@765
   481
      int n = _nodes->size();
kpeter@765
   482
      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@765
   483
        return false;
kpeter@765
   484
      }      
kpeter@765
   485
      for (int i = 0; i < n; ++i) {
kpeter@767
   486
        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
kpeter@765
   487
      }
kpeter@765
   488
      return true;
kpeter@765
   489
    }
kpeter@765
   490
kpeter@765
   491
    // Process all rounds of computing path data for the current component.
kpeter@765
   492
    // _data[v][k] is the length of a shortest directed walk from the root
kpeter@765
   493
    // node to node v containing exactly k arcs.
kpeter@765
   494
    void processRounds() {
kpeter@765
   495
      Node start = (*_nodes)[0];
kpeter@767
   496
      _data[start][0] = PathData(0);
kpeter@765
   497
      _process.clear();
kpeter@765
   498
      _process.push_back(start);
kpeter@765
   499
kpeter@765
   500
      int k, n = _nodes->size();
kpeter@765
   501
      for (k = 1; k <= n && int(_process.size()) < n; ++k) {
kpeter@765
   502
        processNextBuildRound(k);
kpeter@765
   503
      }
kpeter@765
   504
      for ( ; k <= n; ++k) {
kpeter@765
   505
        processNextFullRound(k);
kpeter@765
   506
      }
kpeter@765
   507
    }
kpeter@765
   508
kpeter@765
   509
    // Process one round and rebuild _process
kpeter@765
   510
    void processNextBuildRound(int k) {
kpeter@765
   511
      std::vector<Node> next;
kpeter@765
   512
      Node u, v;
kpeter@765
   513
      Arc e;
kpeter@765
   514
      LargeValue d;
kpeter@765
   515
      for (int i = 0; i < int(_process.size()); ++i) {
kpeter@765
   516
        u = _process[i];
kpeter@765
   517
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@765
   518
          e = _out_arcs[u][j];
kpeter@765
   519
          v = _gr.target(e);
kpeter@765
   520
          d = _data[u][k-1].dist + _length[e];
kpeter@767
   521
          if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@767
   522
            if (_data[v][k].dist == INF) next.push_back(v);
kpeter@767
   523
            _data[v][k] = PathData(d, e);
kpeter@765
   524
          }
kpeter@765
   525
        }
kpeter@765
   526
      }
kpeter@765
   527
      _process.swap(next);
kpeter@765
   528
    }
kpeter@765
   529
kpeter@765
   530
    // Process one round using _nodes instead of _process
kpeter@765
   531
    void processNextFullRound(int k) {
kpeter@765
   532
      Node u, v;
kpeter@765
   533
      Arc e;
kpeter@765
   534
      LargeValue d;
kpeter@765
   535
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@765
   536
        u = (*_nodes)[i];
kpeter@765
   537
        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@765
   538
          e = _out_arcs[u][j];
kpeter@765
   539
          v = _gr.target(e);
kpeter@765
   540
          d = _data[u][k-1].dist + _length[e];
kpeter@767
   541
          if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@767
   542
            _data[v][k] = PathData(d, e);
kpeter@765
   543
          }
kpeter@765
   544
        }
kpeter@765
   545
      }
kpeter@765
   546
    }
kpeter@765
   547
kpeter@765
   548
    // Update the minimum cycle mean
kpeter@765
   549
    void updateMinMean() {
kpeter@765
   550
      int n = _nodes->size();
kpeter@765
   551
      for (int i = 0; i < n; ++i) {
kpeter@765
   552
        Node u = (*_nodes)[i];
kpeter@767
   553
        if (_data[u][n].dist == INF) continue;
kpeter@765
   554
        LargeValue length, max_length = 0;
kpeter@765
   555
        int size, max_size = 1;
kpeter@765
   556
        bool found_curr = false;
kpeter@765
   557
        for (int k = 0; k < n; ++k) {
kpeter@767
   558
          if (_data[u][k].dist == INF) continue;
kpeter@765
   559
          length = _data[u][n].dist - _data[u][k].dist;
kpeter@765
   560
          size = n - k;
kpeter@765
   561
          if (!found_curr || length * max_size > max_length * size) {
kpeter@765
   562
            found_curr = true;
kpeter@765
   563
            max_length = length;
kpeter@765
   564
            max_size = size;
kpeter@765
   565
          }
kpeter@765
   566
        }
kpeter@765
   567
        if ( found_curr && (_cycle_node == INVALID ||
kpeter@765
   568
             max_length * _cycle_size < _cycle_length * max_size) ) {
kpeter@765
   569
          _cycle_length = max_length;
kpeter@765
   570
          _cycle_size = max_size;
kpeter@765
   571
          _cycle_node = u;
kpeter@765
   572
        }
kpeter@765
   573
      }
kpeter@765
   574
    }
kpeter@765
   575
kpeter@765
   576
  }; //class Karp
kpeter@765
   577
kpeter@765
   578
  ///@}
kpeter@765
   579
kpeter@765
   580
} //namespace lemon
kpeter@765
   581
kpeter@765
   582
#endif //LEMON_KARP_H