COIN-OR::LEMON - Graph Library

source: lemon/lemon/hartmann_orlin_mmc.h @ 1221:1c978b5bcc65

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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) 2003-2010
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(ne) and uses space O(n<sup>2</sup>+e).
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 HartmannOrlinMmcDefaultTraits "default traits class",
147    /// it is \ref lemon::Path "Path<Digraph>".
148    typedef typename TR::Path Path;
149
150    /// The \ref HartmannOrlinMmcDefaultTraits "traits class" of the algorithm
151    typedef TR Traits;
152
153  private:
154
155    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
156
157    // Data sturcture for path data
158    struct PathData
159    {
160      LargeCost dist;
161      Arc pred;
162      PathData(LargeCost d, Arc p = INVALID) :
163        dist(d), pred(p) {}
164    };
165
166    typedef typename Digraph::template NodeMap<std::vector<PathData> >
167      PathDataNodeMap;
168
169  private:
170
171    // The digraph the algorithm runs on
172    const Digraph &_gr;
173    // The cost of the arcs
174    const CostMap &_cost;
175
176    // Data for storing the strongly connected components
177    int _comp_num;
178    typename Digraph::template NodeMap<int> _comp;
179    std::vector<std::vector<Node> > _comp_nodes;
180    std::vector<Node>* _nodes;
181    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
182
183    // Data for the found cycles
184    bool _curr_found, _best_found;
185    LargeCost _curr_cost, _best_cost;
186    int _curr_size, _best_size;
187    Node _curr_node, _best_node;
188    int _curr_level, _best_level;
189
190    Path *_cycle_path;
191    bool _local_path;
192
193    // Node map for storing path data
194    PathDataNodeMap _data;
195    // The processed nodes in the last round
196    std::vector<Node> _process;
197
198    Tolerance _tolerance;
199
200    // Infinite constant
201    const LargeCost INF;
202
203  public:
204
205    /// \name Named Template Parameters
206    /// @{
207
208    template <typename T>
209    struct SetLargeCostTraits : public Traits {
210      typedef T LargeCost;
211      typedef lemon::Tolerance<T> Tolerance;
212    };
213
214    /// \brief \ref named-templ-param "Named parameter" for setting
215    /// \c LargeCost type.
216    ///
217    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
218    /// type. It is used for internal computations in the algorithm.
219    template <typename T>
220    struct SetLargeCost
221      : public HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > {
222      typedef HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > Create;
223    };
224
225    template <typename T>
226    struct SetPathTraits : public Traits {
227      typedef T Path;
228    };
229
230    /// \brief \ref named-templ-param "Named parameter" for setting
231    /// \c %Path type.
232    ///
233    /// \ref named-templ-param "Named parameter" for setting the \c %Path
234    /// type of the found cycles.
235    /// It must conform to the \ref lemon::concepts::Path "Path" concept
236    /// and it must have an \c addFront() function.
237    template <typename T>
238    struct SetPath
239      : public HartmannOrlinMmc<GR, CM, SetPathTraits<T> > {
240      typedef HartmannOrlinMmc<GR, CM, SetPathTraits<T> > Create;
241    };
242
243    /// @}
244
245  protected:
246
247    HartmannOrlinMmc() {}
248
249  public:
250
251    /// \brief Constructor.
252    ///
253    /// The constructor of the class.
254    ///
255    /// \param digraph The digraph the algorithm runs on.
256    /// \param cost The costs of the arcs.
257    HartmannOrlinMmc( const Digraph &digraph,
258                      const CostMap &cost ) :
259      _gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),
260      _best_found(false), _best_cost(0), _best_size(1),
261      _cycle_path(NULL), _local_path(false), _data(digraph),
262      INF(std::numeric_limits<LargeCost>::has_infinity ?
263          std::numeric_limits<LargeCost>::infinity() :
264          std::numeric_limits<LargeCost>::max())
265    {}
266
267    /// Destructor.
268    ~HartmannOrlinMmc() {
269      if (_local_path) delete _cycle_path;
270    }
271
272    /// \brief Set the path structure for storing the found cycle.
273    ///
274    /// This function sets an external path structure for storing the
275    /// found cycle.
276    ///
277    /// If you don't call this function before calling \ref run() or
278    /// \ref findCycleMean(), a local \ref Path "path" structure
279    /// will be allocated. The destuctor deallocates this automatically
280    /// allocated object, of course.
281    ///
282    /// \note The algorithm calls only the \ref lemon::Path::addFront()
283    /// "addFront()" function of the given path structure.
284    ///
285    /// \return <tt>(*this)</tt>
286    HartmannOrlinMmc& cycle(Path &path) {
287      if (_local_path) {
288        delete _cycle_path;
289        _local_path = false;
290      }
291      _cycle_path = &path;
292      return *this;
293    }
294
295    /// \brief Set the tolerance used by the algorithm.
296    ///
297    /// This function sets the tolerance object used by the algorithm.
298    ///
299    /// \return <tt>(*this)</tt>
300    HartmannOrlinMmc& tolerance(const Tolerance& tolerance) {
301      _tolerance = tolerance;
302      return *this;
303    }
304
305    /// \brief Return a const reference to the tolerance.
306    ///
307    /// This function returns a const reference to the tolerance object
308    /// used by the algorithm.
309    const Tolerance& tolerance() const {
310      return _tolerance;
311    }
312
313    /// \name Execution control
314    /// The simplest way to execute the algorithm is to call the \ref run()
315    /// function.\n
316    /// If you only need the minimum mean cost, you may call
317    /// \ref findCycleMean().
318
319    /// @{
320
321    /// \brief Run the algorithm.
322    ///
323    /// This function runs the algorithm.
324    /// It can be called more than once (e.g. if the underlying digraph
325    /// and/or the arc costs have been modified).
326    ///
327    /// \return \c true if a directed cycle exists in the digraph.
328    ///
329    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
330    /// \code
331    ///   return mmc.findCycleMean() && mmc.findCycle();
332    /// \endcode
333    bool run() {
334      return findCycleMean() && findCycle();
335    }
336
337    /// \brief Find the minimum cycle mean.
338    ///
339    /// This function finds the minimum mean cost of the directed
340    /// cycles in the digraph.
341    ///
342    /// \return \c true if a directed cycle exists in the digraph.
343    bool findCycleMean() {
344      // Initialization and find strongly connected components
345      init();
346      findComponents();
347
348      // Find the minimum cycle mean in the components
349      for (int comp = 0; comp < _comp_num; ++comp) {
350        if (!initComponent(comp)) continue;
351        processRounds();
352
353        // Update the best cycle (global minimum mean cycle)
354        if ( _curr_found && (!_best_found ||
355             _curr_cost * _best_size < _best_cost * _curr_size) ) {
356          _best_found = true;
357          _best_cost = _curr_cost;
358          _best_size = _curr_size;
359          _best_node = _curr_node;
360          _best_level = _curr_level;
361        }
362      }
363      return _best_found;
364    }
365
366    /// \brief Find a minimum mean directed cycle.
367    ///
368    /// This function finds a directed cycle of minimum mean cost
369    /// in the digraph using the data computed by findCycleMean().
370    ///
371    /// \return \c true if a directed cycle exists in the digraph.
372    ///
373    /// \pre \ref findCycleMean() must be called before using this function.
374    bool findCycle() {
375      if (!_best_found) return false;
376      IntNodeMap reached(_gr, -1);
377      int r = _best_level + 1;
378      Node u = _best_node;
379      while (reached[u] < 0) {
380        reached[u] = --r;
381        u = _gr.source(_data[u][r].pred);
382      }
383      r = reached[u];
384      Arc e = _data[u][r].pred;
385      _cycle_path->addFront(e);
386      _best_cost = _cost[e];
387      _best_size = 1;
388      Node v;
389      while ((v = _gr.source(e)) != u) {
390        e = _data[v][--r].pred;
391        _cycle_path->addFront(e);
392        _best_cost += _cost[e];
393        ++_best_size;
394      }
395      return true;
396    }
397
398    /// @}
399
400    /// \name Query Functions
401    /// The results of the algorithm can be obtained using these
402    /// functions.\n
403    /// The algorithm should be executed before using them.
404
405    /// @{
406
407    /// \brief Return the total cost of the found cycle.
408    ///
409    /// This function returns the total cost of the found cycle.
410    ///
411    /// \pre \ref run() or \ref findCycleMean() must be called before
412    /// using this function.
413    Cost cycleCost() const {
414      return static_cast<Cost>(_best_cost);
415    }
416
417    /// \brief Return the number of arcs on the found cycle.
418    ///
419    /// This function returns the number of arcs on the found cycle.
420    ///
421    /// \pre \ref run() or \ref findCycleMean() must be called before
422    /// using this function.
423    int cycleSize() const {
424      return _best_size;
425    }
426
427    /// \brief Return the mean cost of the found cycle.
428    ///
429    /// This function returns the mean cost of the found cycle.
430    ///
431    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
432    /// following code.
433    /// \code
434    ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
435    /// \endcode
436    ///
437    /// \pre \ref run() or \ref findCycleMean() must be called before
438    /// using this function.
439    double cycleMean() const {
440      return static_cast<double>(_best_cost) / _best_size;
441    }
442
443    /// \brief Return the found cycle.
444    ///
445    /// This function returns a const reference to the path structure
446    /// storing the found cycle.
447    ///
448    /// \pre \ref run() or \ref findCycle() must be called before using
449    /// this function.
450    const Path& cycle() const {
451      return *_cycle_path;
452    }
453
454    ///@}
455
456  private:
457
458    // Initialization
459    void init() {
460      if (!_cycle_path) {
461        _local_path = true;
462        _cycle_path = new Path;
463      }
464      _cycle_path->clear();
465      _best_found = false;
466      _best_cost = 0;
467      _best_size = 1;
468      _cycle_path->clear();
469      for (NodeIt u(_gr); u != INVALID; ++u)
470        _data[u].clear();
471    }
472
473    // Find strongly connected components and initialize _comp_nodes
474    // and _out_arcs
475    void findComponents() {
476      _comp_num = stronglyConnectedComponents(_gr, _comp);
477      _comp_nodes.resize(_comp_num);
478      if (_comp_num == 1) {
479        _comp_nodes[0].clear();
480        for (NodeIt n(_gr); n != INVALID; ++n) {
481          _comp_nodes[0].push_back(n);
482          _out_arcs[n].clear();
483          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
484            _out_arcs[n].push_back(a);
485          }
486        }
487      } else {
488        for (int i = 0; i < _comp_num; ++i)
489          _comp_nodes[i].clear();
490        for (NodeIt n(_gr); n != INVALID; ++n) {
491          int k = _comp[n];
492          _comp_nodes[k].push_back(n);
493          _out_arcs[n].clear();
494          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
495            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
496          }
497        }
498      }
499    }
500
501    // Initialize path data for the current component
502    bool initComponent(int comp) {
503      _nodes = &(_comp_nodes[comp]);
504      int n = _nodes->size();
505      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
506        return false;
507      }
508      for (int i = 0; i < n; ++i) {
509        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
510      }
511      return true;
512    }
513
514    // Process all rounds of computing path data for the current component.
515    // _data[v][k] is the cost of a shortest directed walk from the root
516    // node to node v containing exactly k arcs.
517    void processRounds() {
518      Node start = (*_nodes)[0];
519      _data[start][0] = PathData(0);
520      _process.clear();
521      _process.push_back(start);
522
523      int k, n = _nodes->size();
524      int next_check = 4;
525      bool terminate = false;
526      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
527        processNextBuildRound(k);
528        if (k == next_check || k == n) {
529          terminate = checkTermination(k);
530          next_check = next_check * 3 / 2;
531        }
532      }
533      for ( ; k <= n && !terminate; ++k) {
534        processNextFullRound(k);
535        if (k == next_check || k == n) {
536          terminate = checkTermination(k);
537          next_check = next_check * 3 / 2;
538        }
539      }
540    }
541
542    // Process one round and rebuild _process
543    void processNextBuildRound(int k) {
544      std::vector<Node> next;
545      Node u, v;
546      Arc e;
547      LargeCost d;
548      for (int i = 0; i < int(_process.size()); ++i) {
549        u = _process[i];
550        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
551          e = _out_arcs[u][j];
552          v = _gr.target(e);
553          d = _data[u][k-1].dist + _cost[e];
554          if (_tolerance.less(d, _data[v][k].dist)) {
555            if (_data[v][k].dist == INF) next.push_back(v);
556            _data[v][k] = PathData(d, e);
557          }
558        }
559      }
560      _process.swap(next);
561    }
562
563    // Process one round using _nodes instead of _process
564    void processNextFullRound(int k) {
565      Node u, v;
566      Arc e;
567      LargeCost d;
568      for (int i = 0; i < int(_nodes->size()); ++i) {
569        u = (*_nodes)[i];
570        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
571          e = _out_arcs[u][j];
572          v = _gr.target(e);
573          d = _data[u][k-1].dist + _cost[e];
574          if (_tolerance.less(d, _data[v][k].dist)) {
575            _data[v][k] = PathData(d, e);
576          }
577        }
578      }
579    }
580
581    // Check early termination
582    bool checkTermination(int k) {
583      typedef std::pair<int, int> Pair;
584      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
585      typename GR::template NodeMap<LargeCost> pi(_gr);
586      int n = _nodes->size();
587      LargeCost cost;
588      int size;
589      Node u;
590
591      // Search for cycles that are already found
592      _curr_found = false;
593      for (int i = 0; i < n; ++i) {
594        u = (*_nodes)[i];
595        if (_data[u][k].dist == INF) continue;
596        for (int j = k; j >= 0; --j) {
597          if (level[u].first == i && level[u].second > 0) {
598            // A cycle is found
599            cost = _data[u][level[u].second].dist - _data[u][j].dist;
600            size = level[u].second - j;
601            if (!_curr_found || cost * _curr_size < _curr_cost * size) {
602              _curr_cost = cost;
603              _curr_size = size;
604              _curr_node = u;
605              _curr_level = level[u].second;
606              _curr_found = true;
607            }
608          }
609          level[u] = Pair(i, j);
610          if (j != 0) {
611            u = _gr.source(_data[u][j].pred);
612          }
613        }
614      }
615
616      // If at least one cycle is found, check the optimality condition
617      LargeCost d;
618      if (_curr_found && k < n) {
619        // Find node potentials
620        for (int i = 0; i < n; ++i) {
621          u = (*_nodes)[i];
622          pi[u] = INF;
623          for (int j = 0; j <= k; ++j) {
624            if (_data[u][j].dist < INF) {
625              d = _data[u][j].dist * _curr_size - j * _curr_cost;
626              if (_tolerance.less(d, pi[u])) pi[u] = d;
627            }
628          }
629        }
630
631        // Check the optimality condition for all arcs
632        bool done = true;
633        for (ArcIt a(_gr); a != INVALID; ++a) {
634          if (_tolerance.less(_cost[a] * _curr_size - _curr_cost,
635                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
636            done = false;
637            break;
638          }
639        }
640        return done;
641      }
642      return (k == n);
643    }
644
645  }; //class HartmannOrlinMmc
646
647  ///@}
648
649} //namespace lemon
650
651#endif //LEMON_HARTMANN_ORLIN_MMC_H
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