COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/hartmann_orlin_mmc.h @ 864:d3ea191c3412

Last change on this file since 864:d3ea191c3412 was 864:d3ea191c3412, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Rename min mean cycle classes and their members (#179)
with respect to the possible introduction of min ratio
cycle algorithms in the future.

The renamed classes:

The renamed members:

File size: 19.3 KB
Line 
1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2008
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::Rea_data "Rea_data" 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  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
102  /// It is an improved version of \ref Karp "Karp"'s original algorithm,
103  /// it applies an efficient early termination scheme.
104  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
105  ///
106  /// \tparam GR The type of the digraph the algorithm runs on.
107  /// \tparam CM The type of the cost map. The default
108  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
109  /// \tparam TR The traits class that defines various types used by the
110  /// algorithm. By default, it is \ref HartmannOrlinMmcDefaultTraits
111  /// "HartmannOrlinMmcDefaultTraits<GR, CM>".
112  /// In most cases, this parameter should not be set directly,
113  /// consider to use the named template parameters instead.
114#ifdef DOXYGEN
115  template <typename GR, typename CM, typename TR>
116#else
117  template < typename GR,
118             typename CM = typename GR::template ArcMap<int>,
119             typename TR = HartmannOrlinMmcDefaultTraits<GR, CM> >
120#endif
121  class HartmannOrlinMmc
122  {
123  public:
124
125    /// The type of the digraph
126    typedef typename TR::Digraph Digraph;
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;
131
132    /// \brief The large cost type
133    ///
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,
136    /// otherwise it is \c double.
137    typedef typename TR::LargeCost LargeCost;
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.
145    /// Using the \ref HartmannOrlinMmcDefaultTraits "default traits class",
146    /// it is \ref lemon::Path "Path<Digraph>".
147    typedef typename TR::Path Path;
148
149    /// The \ref HartmannOrlinMmcDefaultTraits "traits class" of the algorithm
150    typedef TR Traits;
151
152  private:
153
154    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
155
156    // Data sturcture for path data
157    struct PathData
158    {
159      LargeCost dist;
160      Arc pred;
161      PathData(LargeCost d, Arc p = INVALID) :
162        dist(d), pred(p) {}
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;
172    // The cost of the arcs
173    const CostMap &_cost;
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;
184    LargeCost _curr_cost, _best_cost;
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
199    // Infinite constant
200    const LargeCost INF;
201
202  public:
203
204    /// \name Named Template Parameters
205    /// @{
206
207    template <typename T>
208    struct SetLargeCostTraits : public Traits {
209      typedef T LargeCost;
210      typedef lemon::Tolerance<T> Tolerance;
211    };
212
213    /// \brief \ref named-templ-param "Named parameter" for setting
214    /// \c LargeCost type.
215    ///
216    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
217    /// type. It is used for internal computations in the algorithm.
218    template <typename T>
219    struct SetLargeCost
220      : public HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > {
221      typedef HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > Create;
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
238      : public HartmannOrlinMmc<GR, CM, SetPathTraits<T> > {
239      typedef HartmannOrlinMmc<GR, CM, SetPathTraits<T> > Create;
240    };
241
242    /// @}
243
244  protected:
245
246    HartmannOrlinMmc() {}
247
248  public:
249
250    /// \brief Constructor.
251    ///
252    /// The constructor of the class.
253    ///
254    /// \param digraph The digraph the algorithm runs on.
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),
260      _cycle_path(NULL), _local_path(false), _data(digraph),
261      INF(std::numeric_limits<LargeCost>::has_infinity ?
262          std::numeric_limits<LargeCost>::infinity() :
263          std::numeric_limits<LargeCost>::max())
264    {}
265
266    /// Destructor.
267    ~HartmannOrlinMmc() {
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
277    /// \ref findCycleMean(), it will allocate a local \ref Path "path"
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>
285    HartmannOrlinMmc& cycle(Path &path) {
286      if (_local_path) {
287        delete _cycle_path;
288        _local_path = false;
289      }
290      _cycle_path = &path;
291      return *this;
292    }
293
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>
299    HartmannOrlinMmc& tolerance(const Tolerance& tolerance) {
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
312    /// \name Execution control
313    /// The simplest way to execute the algorithm is to call the \ref run()
314    /// function.\n
315    /// If you only need the minimum mean cost, you may call
316    /// \ref findCycleMean().
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
324    /// and/or the arc costs have been modified).
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
330    ///   return mmc.findCycleMean() && mmc.findCycle();
331    /// \endcode
332    bool run() {
333      return findCycleMean() && findCycle();
334    }
335
336    /// \brief Find the minimum cycle mean.
337    ///
338    /// This function finds the minimum mean cost of the directed
339    /// cycles in the digraph.
340    ///
341    /// \return \c true if a directed cycle exists in the digraph.
342    bool findCycleMean() {
343      // Initialization and find strongly connected components
344      init();
345      findComponents();
346     
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();
351       
352        // Update the best cycle (global minimum mean cycle)
353        if ( _curr_found && (!_best_found ||
354             _curr_cost * _best_size < _best_cost * _curr_size) ) {
355          _best_found = true;
356          _best_cost = _curr_cost;
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    ///
367    /// This function finds a directed cycle of minimum mean cost
368    /// in the digraph using the data computed by findCycleMean().
369    ///
370    /// \return \c true if a directed cycle exists in the digraph.
371    ///
372    /// \pre \ref findCycleMean() must be called before using this function.
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);
385      _best_cost = _cost[e];
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);
391        _best_cost += _cost[e];
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
406    /// \brief Return the total cost of the found cycle.
407    ///
408    /// This function returns the total cost of the found cycle.
409    ///
410    /// \pre \ref run() or \ref findCycleMean() must be called before
411    /// using this function.
412    Cost cycleCost() const {
413      return static_cast<Cost>(_best_cost);
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    ///
420    /// \pre \ref run() or \ref findCycleMean() must be called before
421    /// using this function.
422    int cycleSize() const {
423      return _best_size;
424    }
425
426    /// \brief Return the mean cost of the found cycle.
427    ///
428    /// This function returns the mean cost of the found cycle.
429    ///
430    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
431    /// following code.
432    /// \code
433    ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
434    /// \endcode
435    ///
436    /// \pre \ref run() or \ref findCycleMean() must be called before
437    /// using this function.
438    double cycleMean() const {
439      return static_cast<double>(_best_cost) / _best_size;
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;
465      _best_cost = 0;
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;
506      }     
507      for (int i = 0; i < n; ++i) {
508        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
509      }
510      return true;
511    }
512
513    // Process all rounds of computing path data for the current component.
514    // _data[v][k] is the cost of a shortest directed walk from the root
515    // node to node v containing exactly k arcs.
516    void processRounds() {
517      Node start = (*_nodes)[0];
518      _data[start][0] = PathData(0);
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;
546      LargeCost d;
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);
552          d = _data[u][k-1].dist + _cost[e];
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);
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;
566      LargeCost d;
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);
572          d = _data[u][k-1].dist + _cost[e];
573          if (_tolerance.less(d, _data[v][k].dist)) {
574            _data[v][k] = PathData(d, e);
575          }
576        }
577      }
578    }
579   
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));
584      typename GR::template NodeMap<LargeCost> pi(_gr);
585      int n = _nodes->size();
586      LargeCost cost;
587      int size;
588      Node u;
589     
590      // Search for cycles that are already found
591      _curr_found = false;
592      for (int i = 0; i < n; ++i) {
593        u = (*_nodes)[i];
594        if (_data[u][k].dist == INF) continue;
595        for (int j = k; j >= 0; --j) {
596          if (level[u].first == i && level[u].second > 0) {
597            // A cycle is found
598            cost = _data[u][level[u].second].dist - _data[u][j].dist;
599            size = level[u].second - j;
600            if (!_curr_found || cost * _curr_size < _curr_cost * size) {
601              _curr_cost = cost;
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);
609          if (j != 0) {
610            u = _gr.source(_data[u][j].pred);
611          }
612        }
613      }
614
615      // If at least one cycle is found, check the optimality condition
616      LargeCost d;
617      if (_curr_found && k < n) {
618        // Find node potentials
619        for (int i = 0; i < n; ++i) {
620          u = (*_nodes)[i];
621          pi[u] = INF;
622          for (int j = 0; j <= k; ++j) {
623            if (_data[u][j].dist < INF) {
624              d = _data[u][j].dist * _curr_size - j * _curr_cost;
625              if (_tolerance.less(d, pi[u])) pi[u] = d;
626            }
627          }
628        }
629
630        // Check the optimality condition for all arcs
631        bool done = true;
632        for (ArcIt a(_gr); a != INVALID; ++a) {
633          if (_tolerance.less(_cost[a] * _curr_size - _curr_cost,
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
644  }; //class HartmannOrlinMmc
645
646  ///@}
647
648} //namespace lemon
649
650#endif //LEMON_HARTMANN_ORLIN_MMC_H
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