COIN-OR::LEMON - Graph Library

source: lemon/lemon/hartmann_orlin_mmc.h @ 1369:9fd86ec2cb81

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2013
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
19#ifndef LEMON_HARTMANN_ORLIN_MMC_H
20#define LEMON_HARTMANN_ORLIN_MMC_H
21
22/// \ingroup min_mean_cycle
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
36  /// \brief Default traits class of HartmannOrlinMmc class.
37  ///
38  /// Default traits class of HartmannOrlinMmc class.
39  /// \tparam GR The type of the digraph.
40  /// \tparam CM The type of the cost map.
41  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
42#ifdef DOXYGEN
43  template <typename GR, typename CM>
44#else
45  template <typename GR, typename CM,
46    bool integer = std::numeric_limits<typename CM::Value>::is_integer>
47#endif
48  struct HartmannOrlinMmcDefaultTraits
49  {
50    /// The type of the digraph
51    typedef GR Digraph;
52    /// The type of the cost map
53    typedef CM CostMap;
54    /// The type of the arc costs
55    typedef typename CostMap::Value Cost;
56
57    /// \brief The large cost type used for internal computations
58    ///
59    /// The large cost type used for internal computations.
60    /// It is \c long \c long if the \c Cost type is integer,
61    /// otherwise it is \c double.
62    /// \c Cost must be convertible to \c LargeCost.
63    typedef double LargeCost;
64
65    /// The tolerance type used for internal computations
66    typedef lemon::Tolerance<LargeCost> Tolerance;
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
72    /// and it must have an \c addFront() function.
73    typedef lemon::Path<Digraph> Path;
74  };
75
76  // Default traits class for integer cost types
77  template <typename GR, typename CM>
78  struct HartmannOrlinMmcDefaultTraits<GR, CM, true>
79  {
80    typedef GR Digraph;
81    typedef CM CostMap;
82    typedef typename CostMap::Value Cost;
83#ifdef LEMON_HAVE_LONG_LONG
84    typedef long long LargeCost;
85#else
86    typedef long LargeCost;
87#endif
88    typedef lemon::Tolerance<LargeCost> Tolerance;
89    typedef lemon::Path<Digraph> Path;
90  };
91
92
93  /// \addtogroup min_mean_cycle
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
100  /// a directed cycle of minimum mean cost in a digraph
101  /// \cite hartmann93finding, \cite dasdan98minmeancycle.
102  /// This method is based on \ref KarpMmc "Karp"'s original algorithm, but
103  /// applies an early termination scheme. It makes the algorithm
104  /// significantly faster for some problem instances, but slower for others.
105  /// The algorithm runs in time O(nm) and uses space O(n<sup>2</sup>+m).
106  ///
107  /// \tparam GR The type of the digraph the algorithm runs on.
108  /// \tparam CM The type of the cost map. The default
109  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
110  /// \tparam TR The traits class that defines various types used by the
111  /// algorithm. By default, it is \ref HartmannOrlinMmcDefaultTraits
112  /// "HartmannOrlinMmcDefaultTraits<GR, CM>".
113  /// In most cases, this parameter should not be set directly,
114  /// consider to use the named template parameters instead.
115#ifdef DOXYGEN
116  template <typename GR, typename CM, typename TR>
117#else
118  template < typename GR,
119             typename CM = typename GR::template ArcMap<int>,
120             typename TR = HartmannOrlinMmcDefaultTraits<GR, CM> >
121#endif
122  class HartmannOrlinMmc
123  {
124  public:
125
126    /// The type of the digraph
127    typedef typename TR::Digraph Digraph;
128    /// The type of the cost map
129    typedef typename TR::CostMap CostMap;
130    /// The type of the arc costs
131    typedef typename TR::Cost Cost;
132
133    /// \brief The large cost type
134    ///
135    /// The large cost type used for internal computations.
136    /// By default, it is \c long \c long if the \c Cost type is integer,
137    /// otherwise it is \c double.
138    typedef typename TR::LargeCost LargeCost;
139
140    /// The tolerance type
141    typedef typename TR::Tolerance Tolerance;
142
143    /// \brief The path type of the found cycles
144    ///
145    /// The path type of the found cycles.
146    /// Using the \ref lemon::HartmannOrlinMmcDefaultTraits
147    /// "default traits class",
148    /// it is \ref lemon::Path "Path<Digraph>".
149    typedef typename TR::Path Path;
150
151    /// \brief The
152    /// \ref lemon::HartmannOrlinMmcDefaultTraits "traits class"
153    /// of the algorithm
154    typedef TR Traits;
155
156  private:
157
158    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
159
160    // Data sturcture for path data
161    struct PathData
162    {
163      LargeCost dist;
164      Arc pred;
165      PathData(LargeCost d, Arc p = INVALID) :
166        dist(d), pred(p) {}
167    };
168
169    typedef typename Digraph::template NodeMap<std::vector<PathData> >
170      PathDataNodeMap;
171
172  private:
173
174    // The digraph the algorithm runs on
175    const Digraph &_gr;
176    // The cost of the arcs
177    const CostMap &_cost;
178
179    // Data for storing the strongly connected components
180    int _comp_num;
181    typename Digraph::template NodeMap<int> _comp;
182    std::vector<std::vector<Node> > _comp_nodes;
183    std::vector<Node>* _nodes;
184    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
185
186    // Data for the found cycles
187    bool _curr_found, _best_found;
188    LargeCost _curr_cost, _best_cost;
189    int _curr_size, _best_size;
190    Node _curr_node, _best_node;
191    int _curr_level, _best_level;
192
193    Path *_cycle_path;
194    bool _local_path;
195
196    // Node map for storing path data
197    PathDataNodeMap _data;
198    // The processed nodes in the last round
199    std::vector<Node> _process;
200
201    Tolerance _tolerance;
202
203    // Infinite constant
204    const LargeCost INF;
205
206  public:
207
208    /// \name Named Template Parameters
209    /// @{
210
211    template <typename T>
212    struct SetLargeCostTraits : public Traits {
213      typedef T LargeCost;
214      typedef lemon::Tolerance<T> Tolerance;
215    };
216
217    /// \brief \ref named-templ-param "Named parameter" for setting
218    /// \c LargeCost type.
219    ///
220    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
221    /// type. It is used for internal computations in the algorithm.
222    template <typename T>
223    struct SetLargeCost
224      : public HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > {
225      typedef HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > Create;
226    };
227
228    template <typename T>
229    struct SetPathTraits : public Traits {
230      typedef T Path;
231    };
232
233    /// \brief \ref named-templ-param "Named parameter" for setting
234    /// \c %Path type.
235    ///
236    /// \ref named-templ-param "Named parameter" for setting the \c %Path
237    /// type of the found cycles.
238    /// It must conform to the \ref lemon::concepts::Path "Path" concept
239    /// and it must have an \c addFront() function.
240    template <typename T>
241    struct SetPath
242      : public HartmannOrlinMmc<GR, CM, SetPathTraits<T> > {
243      typedef HartmannOrlinMmc<GR, CM, SetPathTraits<T> > Create;
244    };
245
246    /// @}
247
248  protected:
249
250    HartmannOrlinMmc() {}
251
252  public:
253
254    /// \brief Constructor.
255    ///
256    /// The constructor of the class.
257    ///
258    /// \param digraph The digraph the algorithm runs on.
259    /// \param cost The costs of the arcs.
260    HartmannOrlinMmc( const Digraph &digraph,
261                      const CostMap &cost ) :
262      _gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),
263      _best_found(false), _best_cost(0), _best_size(1),
264      _cycle_path(NULL), _local_path(false), _data(digraph),
265      INF(std::numeric_limits<LargeCost>::has_infinity ?
266          std::numeric_limits<LargeCost>::infinity() :
267          std::numeric_limits<LargeCost>::max())
268    {}
269
270    /// Destructor.
271    ~HartmannOrlinMmc() {
272      if (_local_path) delete _cycle_path;
273    }
274
275    /// \brief Set the path structure for storing the found cycle.
276    ///
277    /// This function sets an external path structure for storing the
278    /// found cycle.
279    ///
280    /// If you don't call this function before calling \ref run() or
281    /// \ref findCycleMean(), a local \ref Path "path" structure
282    /// will be allocated. The destuctor deallocates this automatically
283    /// allocated object, of course.
284    ///
285    /// \note The algorithm calls only the \ref lemon::Path::addFront()
286    /// "addFront()" function of the given path structure.
287    ///
288    /// \return <tt>(*this)</tt>
289    HartmannOrlinMmc& cycle(Path &path) {
290      if (_local_path) {
291        delete _cycle_path;
292        _local_path = false;
293      }
294      _cycle_path = &path;
295      return *this;
296    }
297
298    /// \brief Set the tolerance used by the algorithm.
299    ///
300    /// This function sets the tolerance object used by the algorithm.
301    ///
302    /// \return <tt>(*this)</tt>
303    HartmannOrlinMmc& tolerance(const Tolerance& tolerance) {
304      _tolerance = tolerance;
305      return *this;
306    }
307
308    /// \brief Return a const reference to the tolerance.
309    ///
310    /// This function returns a const reference to the tolerance object
311    /// used by the algorithm.
312    const Tolerance& tolerance() const {
313      return _tolerance;
314    }
315
316    /// \name Execution control
317    /// The simplest way to execute the algorithm is to call the \ref run()
318    /// function.\n
319    /// If you only need the minimum mean cost, you may call
320    /// \ref findCycleMean().
321
322    /// @{
323
324    /// \brief Run the algorithm.
325    ///
326    /// This function runs the algorithm.
327    /// It can be called more than once (e.g. if the underlying digraph
328    /// and/or the arc costs have been modified).
329    ///
330    /// \return \c true if a directed cycle exists in the digraph.
331    ///
332    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
333    /// \code
334    ///   return mmc.findCycleMean() && mmc.findCycle();
335    /// \endcode
336    bool run() {
337      return findCycleMean() && findCycle();
338    }
339
340    /// \brief Find the minimum cycle mean.
341    ///
342    /// This function finds the minimum mean cost of the directed
343    /// cycles in the digraph.
344    ///
345    /// \return \c true if a directed cycle exists in the digraph.
346    bool findCycleMean() {
347      // Initialization and find strongly connected components
348      init();
349      findComponents();
350
351      // Find the minimum cycle mean in the components
352      for (int comp = 0; comp < _comp_num; ++comp) {
353        if (!initComponent(comp)) continue;
354        processRounds();
355
356        // Update the best cycle (global minimum mean cycle)
357        if ( _curr_found && (!_best_found ||
358             _curr_cost * _best_size < _best_cost * _curr_size) ) {
359          _best_found = true;
360          _best_cost = _curr_cost;
361          _best_size = _curr_size;
362          _best_node = _curr_node;
363          _best_level = _curr_level;
364        }
365      }
366      return _best_found;
367    }
368
369    /// \brief Find a minimum mean directed cycle.
370    ///
371    /// This function finds a directed cycle of minimum mean cost
372    /// in the digraph using the data computed by findCycleMean().
373    ///
374    /// \return \c true if a directed cycle exists in the digraph.
375    ///
376    /// \pre \ref findCycleMean() must be called before using this function.
377    bool findCycle() {
378      if (!_best_found) return false;
379      IntNodeMap reached(_gr, -1);
380      int r = _best_level + 1;
381      Node u = _best_node;
382      while (reached[u] < 0) {
383        reached[u] = --r;
384        u = _gr.source(_data[u][r].pred);
385      }
386      r = reached[u];
387      Arc e = _data[u][r].pred;
388      _cycle_path->addFront(e);
389      _best_cost = _cost[e];
390      _best_size = 1;
391      Node v;
392      while ((v = _gr.source(e)) != u) {
393        e = _data[v][--r].pred;
394        _cycle_path->addFront(e);
395        _best_cost += _cost[e];
396        ++_best_size;
397      }
398      return true;
399    }
400
401    /// @}
402
403    /// \name Query Functions
404    /// The results of the algorithm can be obtained using these
405    /// functions.\n
406    /// The algorithm should be executed before using them.
407
408    /// @{
409
410    /// \brief Return the total cost of the found cycle.
411    ///
412    /// This function returns the total cost of the found cycle.
413    ///
414    /// \pre \ref run() or \ref findCycleMean() must be called before
415    /// using this function.
416    Cost cycleCost() const {
417      return static_cast<Cost>(_best_cost);
418    }
419
420    /// \brief Return the number of arcs on the found cycle.
421    ///
422    /// This function returns the number of arcs on the found cycle.
423    ///
424    /// \pre \ref run() or \ref findCycleMean() must be called before
425    /// using this function.
426    int cycleSize() const {
427      return _best_size;
428    }
429
430    /// \brief Return the mean cost of the found cycle.
431    ///
432    /// This function returns the mean cost of the found cycle.
433    ///
434    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
435    /// following code.
436    /// \code
437    ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
438    /// \endcode
439    ///
440    /// \pre \ref run() or \ref findCycleMean() must be called before
441    /// using this function.
442    double cycleMean() const {
443      return static_cast<double>(_best_cost) / _best_size;
444    }
445
446    /// \brief Return the found cycle.
447    ///
448    /// This function returns a const reference to the path structure
449    /// storing the found cycle.
450    ///
451    /// \pre \ref run() or \ref findCycle() must be called before using
452    /// this function.
453    const Path& cycle() const {
454      return *_cycle_path;
455    }
456
457    ///@}
458
459  private:
460
461    // Initialization
462    void init() {
463      if (!_cycle_path) {
464        _local_path = true;
465        _cycle_path = new Path;
466      }
467      _cycle_path->clear();
468      _best_found = false;
469      _best_cost = 0;
470      _best_size = 1;
471      _cycle_path->clear();
472      for (NodeIt u(_gr); u != INVALID; ++u)
473        _data[u].clear();
474    }
475
476    // Find strongly connected components and initialize _comp_nodes
477    // and _out_arcs
478    void findComponents() {
479      _comp_num = stronglyConnectedComponents(_gr, _comp);
480      _comp_nodes.resize(_comp_num);
481      if (_comp_num == 1) {
482        _comp_nodes[0].clear();
483        for (NodeIt n(_gr); n != INVALID; ++n) {
484          _comp_nodes[0].push_back(n);
485          _out_arcs[n].clear();
486          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
487            _out_arcs[n].push_back(a);
488          }
489        }
490      } else {
491        for (int i = 0; i < _comp_num; ++i)
492          _comp_nodes[i].clear();
493        for (NodeIt n(_gr); n != INVALID; ++n) {
494          int k = _comp[n];
495          _comp_nodes[k].push_back(n);
496          _out_arcs[n].clear();
497          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
498            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
499          }
500        }
501      }
502    }
503
504    // Initialize path data for the current component
505    bool initComponent(int comp) {
506      _nodes = &(_comp_nodes[comp]);
507      int n = _nodes->size();
508      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
509        return false;
510      }
511      for (int i = 0; i < n; ++i) {
512        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
513      }
514      return true;
515    }
516
517    // Process all rounds of computing path data for the current component.
518    // _data[v][k] is the cost of a shortest directed walk from the root
519    // node to node v containing exactly k arcs.
520    void processRounds() {
521      Node start = (*_nodes)[0];
522      _data[start][0] = PathData(0);
523      _process.clear();
524      _process.push_back(start);
525
526      int k, n = _nodes->size();
527      int next_check = 4;
528      bool terminate = false;
529      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
530        processNextBuildRound(k);
531        if (k == next_check || k == n) {
532          terminate = checkTermination(k);
533          next_check = next_check * 3 / 2;
534        }
535      }
536      for ( ; k <= n && !terminate; ++k) {
537        processNextFullRound(k);
538        if (k == next_check || k == n) {
539          terminate = checkTermination(k);
540          next_check = next_check * 3 / 2;
541        }
542      }
543    }
544
545    // Process one round and rebuild _process
546    void processNextBuildRound(int k) {
547      std::vector<Node> next;
548      Node u, v;
549      Arc e;
550      LargeCost d;
551      for (int i = 0; i < int(_process.size()); ++i) {
552        u = _process[i];
553        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
554          e = _out_arcs[u][j];
555          v = _gr.target(e);
556          d = _data[u][k-1].dist + _cost[e];
557          if (_tolerance.less(d, _data[v][k].dist)) {
558            if (_data[v][k].dist == INF) next.push_back(v);
559            _data[v][k] = PathData(d, e);
560          }
561        }
562      }
563      _process.swap(next);
564    }
565
566    // Process one round using _nodes instead of _process
567    void processNextFullRound(int k) {
568      Node u, v;
569      Arc e;
570      LargeCost d;
571      for (int i = 0; i < int(_nodes->size()); ++i) {
572        u = (*_nodes)[i];
573        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
574          e = _out_arcs[u][j];
575          v = _gr.target(e);
576          d = _data[u][k-1].dist + _cost[e];
577          if (_tolerance.less(d, _data[v][k].dist)) {
578            _data[v][k] = PathData(d, e);
579          }
580        }
581      }
582    }
583
584    // Check early termination
585    bool checkTermination(int k) {
586      typedef std::pair<int, int> Pair;
587      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
588      typename GR::template NodeMap<LargeCost> pi(_gr);
589      int n = _nodes->size();
590      LargeCost cost;
591      int size;
592      Node u;
593
594      // Search for cycles that are already found
595      _curr_found = false;
596      for (int i = 0; i < n; ++i) {
597        u = (*_nodes)[i];
598        if (_data[u][k].dist == INF) continue;
599        for (int j = k; j >= 0; --j) {
600          if (level[u].first == i && level[u].second > 0) {
601            // A cycle is found
602            cost = _data[u][level[u].second].dist - _data[u][j].dist;
603            size = level[u].second - j;
604            if (!_curr_found || cost * _curr_size < _curr_cost * size) {
605              _curr_cost = cost;
606              _curr_size = size;
607              _curr_node = u;
608              _curr_level = level[u].second;
609              _curr_found = true;
610            }
611          }
612          level[u] = Pair(i, j);
613          if (j != 0) {
614            u = _gr.source(_data[u][j].pred);
615          }
616        }
617      }
618
619      // If at least one cycle is found, check the optimality condition
620      LargeCost d;
621      if (_curr_found && k < n) {
622        // Find node potentials
623        for (int i = 0; i < n; ++i) {
624          u = (*_nodes)[i];
625          pi[u] = INF;
626          for (int j = 0; j <= k; ++j) {
627            if (_data[u][j].dist < INF) {
628              d = _data[u][j].dist * _curr_size - j * _curr_cost;
629              if (_tolerance.less(d, pi[u])) pi[u] = d;
630            }
631          }
632        }
633
634        // Check the optimality condition for all arcs
635        bool done = true;
636        for (ArcIt a(_gr); a != INVALID; ++a) {
637          if (_tolerance.less(_cost[a] * _curr_size - _curr_cost,
638                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
639            done = false;
640            break;
641          }
642        }
643        return done;
644      }
645      return (k == n);
646    }
647
648  }; //class HartmannOrlinMmc
649
650  ///@}
651
652} //namespace lemon
653
654#endif //LEMON_HARTMANN_ORLIN_MMC_H
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