COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/hartmann_orlin_mmc.h @ 880:38213abd2911

Last change on this file since 880:38213abd2911 was 880:38213abd2911, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Small doc fixes and improvements (#359)

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[877]1/* -*- mode: C++; indent-tabs-mode: nil; -*-
[766]2 *
[877]3 * This file is a part of LEMON, a generic C++ optimization library.
[766]4 *
[877]5 * Copyright (C) 2003-2010
[766]6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
[864]19#ifndef LEMON_HARTMANN_ORLIN_MMC_H
20#define LEMON_HARTMANN_ORLIN_MMC_H
[766]21
[768]22/// \ingroup min_mean_cycle
[766]23///
24/// \file
25/// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.
26
27#include <vector>
28#include <limits>
29#include <lemon/core.h>
30#include <lemon/path.h>
31#include <lemon/tolerance.h>
32#include <lemon/connectivity.h>
33
34namespace lemon {
35
[864]36  /// \brief Default traits class of HartmannOrlinMmc class.
[766]37  ///
[864]38  /// Default traits class of HartmannOrlinMmc class.
[766]39  /// \tparam GR The type of the digraph.
[864]40  /// \tparam CM The type of the cost map.
[880]41  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
[766]42#ifdef DOXYGEN
[864]43  template <typename GR, typename CM>
[766]44#else
[864]45  template <typename GR, typename CM,
46    bool integer = std::numeric_limits<typename CM::Value>::is_integer>
[766]47#endif
[864]48  struct HartmannOrlinMmcDefaultTraits
[766]49  {
50    /// The type of the digraph
51    typedef GR Digraph;
[864]52    /// The type of the cost map
53    typedef CM CostMap;
54    /// The type of the arc costs
55    typedef typename CostMap::Value Cost;
[766]56
[864]57    /// \brief The large cost type used for internal computations
[766]58    ///
[864]59    /// The large cost type used for internal computations.
60    /// It is \c long \c long if the \c Cost type is integer,
[766]61    /// otherwise it is \c double.
[864]62    /// \c Cost must be convertible to \c LargeCost.
63    typedef double LargeCost;
[766]64
65    /// The tolerance type used for internal computations
[864]66    typedef lemon::Tolerance<LargeCost> Tolerance;
[766]67
68    /// \brief The path type of the found cycles
69    ///
70    /// The path type of the found cycles.
71    /// It must conform to the \ref lemon::concepts::Path "Path" concept
[772]72    /// and it must have an \c addFront() function.
[766]73    typedef lemon::Path<Digraph> Path;
74  };
75
[864]76  // Default traits class for integer cost types
77  template <typename GR, typename CM>
78  struct HartmannOrlinMmcDefaultTraits<GR, CM, true>
[766]79  {
80    typedef GR Digraph;
[864]81    typedef CM CostMap;
82    typedef typename CostMap::Value Cost;
[766]83#ifdef LEMON_HAVE_LONG_LONG
[864]84    typedef long long LargeCost;
[766]85#else
[864]86    typedef long LargeCost;
[766]87#endif
[864]88    typedef lemon::Tolerance<LargeCost> Tolerance;
[766]89    typedef lemon::Path<Digraph> Path;
90  };
91
92
[768]93  /// \addtogroup min_mean_cycle
[766]94  /// @{
95
96  /// \brief Implementation of the Hartmann-Orlin algorithm for finding
97  /// a minimum mean cycle.
98  ///
99  /// This class implements the Hartmann-Orlin algorithm for finding
[864]100  /// a directed cycle of minimum mean cost in a digraph
[771]101  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
[880]102  /// It is an improved version of \ref KarpMmc "Karp"'s original algorithm,
[766]103  /// it applies an efficient early termination scheme.
[768]104  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
[766]105  ///
106  /// \tparam GR The type of the digraph the algorithm runs on.
[864]107  /// \tparam CM The type of the cost map. The default
[766]108  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
[825]109  /// \tparam TR The traits class that defines various types used by the
[864]110  /// algorithm. By default, it is \ref HartmannOrlinMmcDefaultTraits
111  /// "HartmannOrlinMmcDefaultTraits<GR, CM>".
[825]112  /// In most cases, this parameter should not be set directly,
113  /// consider to use the named template parameters instead.
[766]114#ifdef DOXYGEN
[864]115  template <typename GR, typename CM, typename TR>
[766]116#else
117  template < typename GR,
[864]118             typename CM = typename GR::template ArcMap<int>,
119             typename TR = HartmannOrlinMmcDefaultTraits<GR, CM> >
[766]120#endif
[864]121  class HartmannOrlinMmc
[766]122  {
123  public:
124
125    /// The type of the digraph
126    typedef typename TR::Digraph Digraph;
[864]127    /// The type of the cost map
128    typedef typename TR::CostMap CostMap;
129    /// The type of the arc costs
130    typedef typename TR::Cost Cost;
[766]131
[864]132    /// \brief The large cost type
[766]133    ///
[864]134    /// The large cost type used for internal computations.
135    /// By default, it is \c long \c long if the \c Cost type is integer,
[766]136    /// otherwise it is \c double.
[864]137    typedef typename TR::LargeCost LargeCost;
[766]138
139    /// The tolerance type
140    typedef typename TR::Tolerance Tolerance;
141
142    /// \brief The path type of the found cycles
143    ///
144    /// The path type of the found cycles.
[864]145    /// Using the \ref HartmannOrlinMmcDefaultTraits "default traits class",
[766]146    /// it is \ref lemon::Path "Path<Digraph>".
147    typedef typename TR::Path Path;
148
[864]149    /// The \ref HartmannOrlinMmcDefaultTraits "traits class" of the algorithm
[766]150    typedef TR Traits;
151
152  private:
153
154    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
155
156    // Data sturcture for path data
157    struct PathData
158    {
[864]159      LargeCost dist;
[766]160      Arc pred;
[864]161      PathData(LargeCost d, Arc p = INVALID) :
[767]162        dist(d), pred(p) {}
[766]163    };
164
165    typedef typename Digraph::template NodeMap<std::vector<PathData> >
166      PathDataNodeMap;
167
168  private:
169
170    // The digraph the algorithm runs on
171    const Digraph &_gr;
[864]172    // The cost of the arcs
173    const CostMap &_cost;
[766]174
175    // Data for storing the strongly connected components
176    int _comp_num;
177    typename Digraph::template NodeMap<int> _comp;
178    std::vector<std::vector<Node> > _comp_nodes;
179    std::vector<Node>* _nodes;
180    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
181
182    // Data for the found cycles
183    bool _curr_found, _best_found;
[864]184    LargeCost _curr_cost, _best_cost;
[766]185    int _curr_size, _best_size;
186    Node _curr_node, _best_node;
187    int _curr_level, _best_level;
188
189    Path *_cycle_path;
190    bool _local_path;
191
192    // Node map for storing path data
193    PathDataNodeMap _data;
194    // The processed nodes in the last round
195    std::vector<Node> _process;
196
197    Tolerance _tolerance;
198
[767]199    // Infinite constant
[864]200    const LargeCost INF;
[767]201
[766]202  public:
203
204    /// \name Named Template Parameters
205    /// @{
206
207    template <typename T>
[864]208    struct SetLargeCostTraits : public Traits {
209      typedef T LargeCost;
[766]210      typedef lemon::Tolerance<T> Tolerance;
211    };
212
213    /// \brief \ref named-templ-param "Named parameter" for setting
[864]214    /// \c LargeCost type.
[766]215    ///
[864]216    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
[766]217    /// type. It is used for internal computations in the algorithm.
218    template <typename T>
[864]219    struct SetLargeCost
220      : public HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > {
221      typedef HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > Create;
[766]222    };
223
224    template <typename T>
225    struct SetPathTraits : public Traits {
226      typedef T Path;
227    };
228
229    /// \brief \ref named-templ-param "Named parameter" for setting
230    /// \c %Path type.
231    ///
232    /// \ref named-templ-param "Named parameter" for setting the \c %Path
233    /// type of the found cycles.
234    /// It must conform to the \ref lemon::concepts::Path "Path" concept
235    /// and it must have an \c addFront() function.
236    template <typename T>
237    struct SetPath
[864]238      : public HartmannOrlinMmc<GR, CM, SetPathTraits<T> > {
239      typedef HartmannOrlinMmc<GR, CM, SetPathTraits<T> > Create;
[766]240    };
241
242    /// @}
243
[863]244  protected:
245
[864]246    HartmannOrlinMmc() {}
[863]247
[766]248  public:
249
250    /// \brief Constructor.
251    ///
252    /// The constructor of the class.
253    ///
254    /// \param digraph The digraph the algorithm runs on.
[864]255    /// \param cost The costs of the arcs.
256    HartmannOrlinMmc( const Digraph &digraph,
257                      const CostMap &cost ) :
258      _gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),
259      _best_found(false), _best_cost(0), _best_size(1),
[767]260      _cycle_path(NULL), _local_path(false), _data(digraph),
[864]261      INF(std::numeric_limits<LargeCost>::has_infinity ?
262          std::numeric_limits<LargeCost>::infinity() :
263          std::numeric_limits<LargeCost>::max())
[766]264    {}
265
266    /// Destructor.
[864]267    ~HartmannOrlinMmc() {
[766]268      if (_local_path) delete _cycle_path;
269    }
270
271    /// \brief Set the path structure for storing the found cycle.
272    ///
273    /// This function sets an external path structure for storing the
274    /// found cycle.
275    ///
276    /// If you don't call this function before calling \ref run() or
[864]277    /// \ref findCycleMean(), it will allocate a local \ref Path "path"
[766]278    /// structure. The destuctor deallocates this automatically
279    /// allocated object, of course.
280    ///
281    /// \note The algorithm calls only the \ref lemon::Path::addFront()
282    /// "addFront()" function of the given path structure.
283    ///
284    /// \return <tt>(*this)</tt>
[864]285    HartmannOrlinMmc& cycle(Path &path) {
[766]286      if (_local_path) {
287        delete _cycle_path;
288        _local_path = false;
289      }
290      _cycle_path = &path;
291      return *this;
292    }
293
[769]294    /// \brief Set the tolerance used by the algorithm.
295    ///
296    /// This function sets the tolerance object used by the algorithm.
297    ///
298    /// \return <tt>(*this)</tt>
[864]299    HartmannOrlinMmc& tolerance(const Tolerance& tolerance) {
[769]300      _tolerance = tolerance;
301      return *this;
302    }
303
304    /// \brief Return a const reference to the tolerance.
305    ///
306    /// This function returns a const reference to the tolerance object
307    /// used by the algorithm.
308    const Tolerance& tolerance() const {
309      return _tolerance;
310    }
311
[766]312    /// \name Execution control
313    /// The simplest way to execute the algorithm is to call the \ref run()
314    /// function.\n
[864]315    /// If you only need the minimum mean cost, you may call
316    /// \ref findCycleMean().
[766]317
318    /// @{
319
320    /// \brief Run the algorithm.
321    ///
322    /// This function runs the algorithm.
323    /// It can be called more than once (e.g. if the underlying digraph
[864]324    /// and/or the arc costs have been modified).
[766]325    ///
326    /// \return \c true if a directed cycle exists in the digraph.
327    ///
328    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
329    /// \code
[864]330    ///   return mmc.findCycleMean() && mmc.findCycle();
[766]331    /// \endcode
332    bool run() {
[864]333      return findCycleMean() && findCycle();
[766]334    }
335
336    /// \brief Find the minimum cycle mean.
337    ///
[864]338    /// This function finds the minimum mean cost of the directed
[766]339    /// cycles in the digraph.
340    ///
341    /// \return \c true if a directed cycle exists in the digraph.
[864]342    bool findCycleMean() {
[766]343      // Initialization and find strongly connected components
344      init();
345      findComponents();
[877]346
[766]347      // Find the minimum cycle mean in the components
348      for (int comp = 0; comp < _comp_num; ++comp) {
349        if (!initComponent(comp)) continue;
350        processRounds();
[877]351
[766]352        // Update the best cycle (global minimum mean cycle)
[877]353        if ( _curr_found && (!_best_found ||
[864]354             _curr_cost * _best_size < _best_cost * _curr_size) ) {
[766]355          _best_found = true;
[864]356          _best_cost = _curr_cost;
[766]357          _best_size = _curr_size;
358          _best_node = _curr_node;
359          _best_level = _curr_level;
360        }
361      }
362      return _best_found;
363    }
364
365    /// \brief Find a minimum mean directed cycle.
366    ///
[864]367    /// This function finds a directed cycle of minimum mean cost
368    /// in the digraph using the data computed by findCycleMean().
[766]369    ///
370    /// \return \c true if a directed cycle exists in the digraph.
371    ///
[864]372    /// \pre \ref findCycleMean() must be called before using this function.
[766]373    bool findCycle() {
374      if (!_best_found) return false;
375      IntNodeMap reached(_gr, -1);
376      int r = _best_level + 1;
377      Node u = _best_node;
378      while (reached[u] < 0) {
379        reached[u] = --r;
380        u = _gr.source(_data[u][r].pred);
381      }
382      r = reached[u];
383      Arc e = _data[u][r].pred;
384      _cycle_path->addFront(e);
[864]385      _best_cost = _cost[e];
[766]386      _best_size = 1;
387      Node v;
388      while ((v = _gr.source(e)) != u) {
389        e = _data[v][--r].pred;
390        _cycle_path->addFront(e);
[864]391        _best_cost += _cost[e];
[766]392        ++_best_size;
393      }
394      return true;
395    }
396
397    /// @}
398
399    /// \name Query Functions
400    /// The results of the algorithm can be obtained using these
401    /// functions.\n
402    /// The algorithm should be executed before using them.
403
404    /// @{
405
[864]406    /// \brief Return the total cost of the found cycle.
[766]407    ///
[864]408    /// This function returns the total cost of the found cycle.
[766]409    ///
[864]410    /// \pre \ref run() or \ref findCycleMean() must be called before
[766]411    /// using this function.
[864]412    Cost cycleCost() const {
413      return static_cast<Cost>(_best_cost);
[766]414    }
415
416    /// \brief Return the number of arcs on the found cycle.
417    ///
418    /// This function returns the number of arcs on the found cycle.
419    ///
[864]420    /// \pre \ref run() or \ref findCycleMean() must be called before
[766]421    /// using this function.
[864]422    int cycleSize() const {
[766]423      return _best_size;
424    }
425
[864]426    /// \brief Return the mean cost of the found cycle.
[766]427    ///
[864]428    /// This function returns the mean cost of the found cycle.
[766]429    ///
430    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
431    /// following code.
432    /// \code
[864]433    ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
[766]434    /// \endcode
435    ///
[864]436    /// \pre \ref run() or \ref findCycleMean() must be called before
[766]437    /// using this function.
438    double cycleMean() const {
[864]439      return static_cast<double>(_best_cost) / _best_size;
[766]440    }
441
442    /// \brief Return the found cycle.
443    ///
444    /// This function returns a const reference to the path structure
445    /// storing the found cycle.
446    ///
447    /// \pre \ref run() or \ref findCycle() must be called before using
448    /// this function.
449    const Path& cycle() const {
450      return *_cycle_path;
451    }
452
453    ///@}
454
455  private:
456
457    // Initialization
458    void init() {
459      if (!_cycle_path) {
460        _local_path = true;
461        _cycle_path = new Path;
462      }
463      _cycle_path->clear();
464      _best_found = false;
[864]465      _best_cost = 0;
[766]466      _best_size = 1;
467      _cycle_path->clear();
468      for (NodeIt u(_gr); u != INVALID; ++u)
469        _data[u].clear();
470    }
471
472    // Find strongly connected components and initialize _comp_nodes
473    // and _out_arcs
474    void findComponents() {
475      _comp_num = stronglyConnectedComponents(_gr, _comp);
476      _comp_nodes.resize(_comp_num);
477      if (_comp_num == 1) {
478        _comp_nodes[0].clear();
479        for (NodeIt n(_gr); n != INVALID; ++n) {
480          _comp_nodes[0].push_back(n);
481          _out_arcs[n].clear();
482          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
483            _out_arcs[n].push_back(a);
484          }
485        }
486      } else {
487        for (int i = 0; i < _comp_num; ++i)
488          _comp_nodes[i].clear();
489        for (NodeIt n(_gr); n != INVALID; ++n) {
490          int k = _comp[n];
491          _comp_nodes[k].push_back(n);
492          _out_arcs[n].clear();
493          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
494            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
495          }
496        }
497      }
498    }
499
500    // Initialize path data for the current component
501    bool initComponent(int comp) {
502      _nodes = &(_comp_nodes[comp]);
503      int n = _nodes->size();
504      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
505        return false;
[877]506      }
[766]507      for (int i = 0; i < n; ++i) {
[767]508        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
[766]509      }
510      return true;
511    }
512
513    // Process all rounds of computing path data for the current component.
[864]514    // _data[v][k] is the cost of a shortest directed walk from the root
[766]515    // node to node v containing exactly k arcs.
516    void processRounds() {
517      Node start = (*_nodes)[0];
[767]518      _data[start][0] = PathData(0);
[766]519      _process.clear();
520      _process.push_back(start);
521
522      int k, n = _nodes->size();
523      int next_check = 4;
524      bool terminate = false;
525      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
526        processNextBuildRound(k);
527        if (k == next_check || k == n) {
528          terminate = checkTermination(k);
529          next_check = next_check * 3 / 2;
530        }
531      }
532      for ( ; k <= n && !terminate; ++k) {
533        processNextFullRound(k);
534        if (k == next_check || k == n) {
535          terminate = checkTermination(k);
536          next_check = next_check * 3 / 2;
537        }
538      }
539    }
540
541    // Process one round and rebuild _process
542    void processNextBuildRound(int k) {
543      std::vector<Node> next;
544      Node u, v;
545      Arc e;
[864]546      LargeCost d;
[766]547      for (int i = 0; i < int(_process.size()); ++i) {
548        u = _process[i];
549        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
550          e = _out_arcs[u][j];
551          v = _gr.target(e);
[864]552          d = _data[u][k-1].dist + _cost[e];
[767]553          if (_tolerance.less(d, _data[v][k].dist)) {
554            if (_data[v][k].dist == INF) next.push_back(v);
555            _data[v][k] = PathData(d, e);
[766]556          }
557        }
558      }
559      _process.swap(next);
560    }
561
562    // Process one round using _nodes instead of _process
563    void processNextFullRound(int k) {
564      Node u, v;
565      Arc e;
[864]566      LargeCost d;
[766]567      for (int i = 0; i < int(_nodes->size()); ++i) {
568        u = (*_nodes)[i];
569        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
570          e = _out_arcs[u][j];
571          v = _gr.target(e);
[864]572          d = _data[u][k-1].dist + _cost[e];
[767]573          if (_tolerance.less(d, _data[v][k].dist)) {
574            _data[v][k] = PathData(d, e);
[766]575          }
576        }
577      }
578    }
[877]579
[766]580    // Check early termination
581    bool checkTermination(int k) {
582      typedef std::pair<int, int> Pair;
583      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
[864]584      typename GR::template NodeMap<LargeCost> pi(_gr);
[766]585      int n = _nodes->size();
[864]586      LargeCost cost;
[766]587      int size;
588      Node u;
[877]589
[766]590      // Search for cycles that are already found
591      _curr_found = false;
592      for (int i = 0; i < n; ++i) {
593        u = (*_nodes)[i];
[767]594        if (_data[u][k].dist == INF) continue;
[766]595        for (int j = k; j >= 0; --j) {
596          if (level[u].first == i && level[u].second > 0) {
597            // A cycle is found
[864]598            cost = _data[u][level[u].second].dist - _data[u][j].dist;
[766]599            size = level[u].second - j;
[864]600            if (!_curr_found || cost * _curr_size < _curr_cost * size) {
601              _curr_cost = cost;
[766]602              _curr_size = size;
603              _curr_node = u;
604              _curr_level = level[u].second;
605              _curr_found = true;
606            }
607          }
608          level[u] = Pair(i, j);
[795]609          if (j != 0) {
[877]610            u = _gr.source(_data[u][j].pred);
611          }
[766]612        }
613      }
614
615      // If at least one cycle is found, check the optimality condition
[864]616      LargeCost d;
[766]617      if (_curr_found && k < n) {
618        // Find node potentials
619        for (int i = 0; i < n; ++i) {
620          u = (*_nodes)[i];
[767]621          pi[u] = INF;
[766]622          for (int j = 0; j <= k; ++j) {
[767]623            if (_data[u][j].dist < INF) {
[864]624              d = _data[u][j].dist * _curr_size - j * _curr_cost;
[767]625              if (_tolerance.less(d, pi[u])) pi[u] = d;
[766]626            }
627          }
628        }
629
630        // Check the optimality condition for all arcs
631        bool done = true;
632        for (ArcIt a(_gr); a != INVALID; ++a) {
[864]633          if (_tolerance.less(_cost[a] * _curr_size - _curr_cost,
[766]634                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
635            done = false;
636            break;
637          }
638        }
639        return done;
640      }
641      return (k == n);
642    }
643
[864]644  }; //class HartmannOrlinMmc
[766]645
646  ///@}
647
648} //namespace lemon
649
[864]650#endif //LEMON_HARTMANN_ORLIN_MMC_H
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