COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/howard_mmc.h @ 902:79fab87ee483

Last change on this file since 902:79fab87ee483 was 877:141f9c0db4a3, checked in by Alpar Juttner <alpar@…>, 10 years ago

Unify the sources (#339)

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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_HOWARD_MMC_H
20#define LEMON_HOWARD_MMC_H
21
22/// \ingroup min_mean_cycle
23///
24/// \file
25/// \brief Howard'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 HowardMmc class.
37  ///
38  /// Default traits class of HowardMmc 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 HowardMmcDefaultTraits
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 addBack() 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 HowardMmcDefaultTraits<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 Howard's algorithm for finding a minimum
97  /// mean cycle.
98  ///
99  /// This class implements Howard's policy iteration algorithm for finding
100  /// a directed cycle of minimum mean cost in a digraph
101  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
102  /// This class provides the most efficient algorithm for the
103  /// minimum mean cycle problem, though the best known theoretical
104  /// bound on its running time is exponential.
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 HowardMmcDefaultTraits
111  /// "HowardMmcDefaultTraits<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 = HowardMmcDefaultTraits<GR, CM> >
120#endif
121  class HowardMmc
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 HowardMmcDefaultTraits "default traits class",
146    /// it is \ref lemon::Path "Path<Digraph>".
147    typedef typename TR::Path Path;
148
149    /// The \ref HowardMmcDefaultTraits "traits class" of the algorithm
150    typedef TR Traits;
151
152  private:
153
154    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
155
156    // The digraph the algorithm runs on
157    const Digraph &_gr;
158    // The cost of the arcs
159    const CostMap &_cost;
160
161    // Data for the found cycles
162    bool _curr_found, _best_found;
163    LargeCost _curr_cost, _best_cost;
164    int _curr_size, _best_size;
165    Node _curr_node, _best_node;
166
167    Path *_cycle_path;
168    bool _local_path;
169
170    // Internal data used by the algorithm
171    typename Digraph::template NodeMap<Arc> _policy;
172    typename Digraph::template NodeMap<bool> _reached;
173    typename Digraph::template NodeMap<int> _level;
174    typename Digraph::template NodeMap<LargeCost> _dist;
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> > _in_arcs;
182
183    // Queue used for BFS search
184    std::vector<Node> _queue;
185    int _qfront, _qback;
186
187    Tolerance _tolerance;
188
189    // Infinite constant
190    const LargeCost INF;
191
192  public:
193
194    /// \name Named Template Parameters
195    /// @{
196
197    template <typename T>
198    struct SetLargeCostTraits : public Traits {
199      typedef T LargeCost;
200      typedef lemon::Tolerance<T> Tolerance;
201    };
202
203    /// \brief \ref named-templ-param "Named parameter" for setting
204    /// \c LargeCost type.
205    ///
206    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
207    /// type. It is used for internal computations in the algorithm.
208    template <typename T>
209    struct SetLargeCost
210      : public HowardMmc<GR, CM, SetLargeCostTraits<T> > {
211      typedef HowardMmc<GR, CM, SetLargeCostTraits<T> > Create;
212    };
213
214    template <typename T>
215    struct SetPathTraits : public Traits {
216      typedef T Path;
217    };
218
219    /// \brief \ref named-templ-param "Named parameter" for setting
220    /// \c %Path type.
221    ///
222    /// \ref named-templ-param "Named parameter" for setting the \c %Path
223    /// type of the found cycles.
224    /// It must conform to the \ref lemon::concepts::Path "Path" concept
225    /// and it must have an \c addBack() function.
226    template <typename T>
227    struct SetPath
228      : public HowardMmc<GR, CM, SetPathTraits<T> > {
229      typedef HowardMmc<GR, CM, SetPathTraits<T> > Create;
230    };
231
232    /// @}
233
234  protected:
235
236    HowardMmc() {}
237
238  public:
239
240    /// \brief Constructor.
241    ///
242    /// The constructor of the class.
243    ///
244    /// \param digraph The digraph the algorithm runs on.
245    /// \param cost The costs of the arcs.
246    HowardMmc( const Digraph &digraph,
247               const CostMap &cost ) :
248      _gr(digraph), _cost(cost), _best_found(false),
249      _best_cost(0), _best_size(1), _cycle_path(NULL), _local_path(false),
250      _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
251      _comp(digraph), _in_arcs(digraph),
252      INF(std::numeric_limits<LargeCost>::has_infinity ?
253          std::numeric_limits<LargeCost>::infinity() :
254          std::numeric_limits<LargeCost>::max())
255    {}
256
257    /// Destructor.
258    ~HowardMmc() {
259      if (_local_path) delete _cycle_path;
260    }
261
262    /// \brief Set the path structure for storing the found cycle.
263    ///
264    /// This function sets an external path structure for storing the
265    /// found cycle.
266    ///
267    /// If you don't call this function before calling \ref run() or
268    /// \ref findCycleMean(), it will allocate a local \ref Path "path"
269    /// structure. The destuctor deallocates this automatically
270    /// allocated object, of course.
271    ///
272    /// \note The algorithm calls only the \ref lemon::Path::addBack()
273    /// "addBack()" function of the given path structure.
274    ///
275    /// \return <tt>(*this)</tt>
276    HowardMmc& cycle(Path &path) {
277      if (_local_path) {
278        delete _cycle_path;
279        _local_path = false;
280      }
281      _cycle_path = &path;
282      return *this;
283    }
284
285    /// \brief Set the tolerance used by the algorithm.
286    ///
287    /// This function sets the tolerance object used by the algorithm.
288    ///
289    /// \return <tt>(*this)</tt>
290    HowardMmc& tolerance(const Tolerance& tolerance) {
291      _tolerance = tolerance;
292      return *this;
293    }
294
295    /// \brief Return a const reference to the tolerance.
296    ///
297    /// This function returns a const reference to the tolerance object
298    /// used by the algorithm.
299    const Tolerance& tolerance() const {
300      return _tolerance;
301    }
302
303    /// \name Execution control
304    /// The simplest way to execute the algorithm is to call the \ref run()
305    /// function.\n
306    /// If you only need the minimum mean cost, you may call
307    /// \ref findCycleMean().
308
309    /// @{
310
311    /// \brief Run the algorithm.
312    ///
313    /// This function runs the algorithm.
314    /// It can be called more than once (e.g. if the underlying digraph
315    /// and/or the arc costs have been modified).
316    ///
317    /// \return \c true if a directed cycle exists in the digraph.
318    ///
319    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
320    /// \code
321    ///   return mmc.findCycleMean() && mmc.findCycle();
322    /// \endcode
323    bool run() {
324      return findCycleMean() && findCycle();
325    }
326
327    /// \brief Find the minimum cycle mean.
328    ///
329    /// This function finds the minimum mean cost of the directed
330    /// cycles in the digraph.
331    ///
332    /// \return \c true if a directed cycle exists in the digraph.
333    bool findCycleMean() {
334      // Initialize and find strongly connected components
335      init();
336      findComponents();
337
338      // Find the minimum cycle mean in the components
339      for (int comp = 0; comp < _comp_num; ++comp) {
340        // Find the minimum mean cycle in the current component
341        if (!buildPolicyGraph(comp)) continue;
342        while (true) {
343          findPolicyCycle();
344          if (!computeNodeDistances()) break;
345        }
346        // Update the best cycle (global minimum mean cycle)
347        if ( _curr_found && (!_best_found ||
348             _curr_cost * _best_size < _best_cost * _curr_size) ) {
349          _best_found = true;
350          _best_cost = _curr_cost;
351          _best_size = _curr_size;
352          _best_node = _curr_node;
353        }
354      }
355      return _best_found;
356    }
357
358    /// \brief Find a minimum mean directed cycle.
359    ///
360    /// This function finds a directed cycle of minimum mean cost
361    /// in the digraph using the data computed by findCycleMean().
362    ///
363    /// \return \c true if a directed cycle exists in the digraph.
364    ///
365    /// \pre \ref findCycleMean() must be called before using this function.
366    bool findCycle() {
367      if (!_best_found) return false;
368      _cycle_path->addBack(_policy[_best_node]);
369      for ( Node v = _best_node;
370            (v = _gr.target(_policy[v])) != _best_node; ) {
371        _cycle_path->addBack(_policy[v]);
372      }
373      return true;
374    }
375
376    /// @}
377
378    /// \name Query Functions
379    /// The results of the algorithm can be obtained using these
380    /// functions.\n
381    /// The algorithm should be executed before using them.
382
383    /// @{
384
385    /// \brief Return the total cost of the found cycle.
386    ///
387    /// This function returns the total cost of the found cycle.
388    ///
389    /// \pre \ref run() or \ref findCycleMean() must be called before
390    /// using this function.
391    Cost cycleCost() const {
392      return static_cast<Cost>(_best_cost);
393    }
394
395    /// \brief Return the number of arcs on the found cycle.
396    ///
397    /// This function returns the number of arcs on the found cycle.
398    ///
399    /// \pre \ref run() or \ref findCycleMean() must be called before
400    /// using this function.
401    int cycleSize() const {
402      return _best_size;
403    }
404
405    /// \brief Return the mean cost of the found cycle.
406    ///
407    /// This function returns the mean cost of the found cycle.
408    ///
409    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
410    /// following code.
411    /// \code
412    ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
413    /// \endcode
414    ///
415    /// \pre \ref run() or \ref findCycleMean() must be called before
416    /// using this function.
417    double cycleMean() const {
418      return static_cast<double>(_best_cost) / _best_size;
419    }
420
421    /// \brief Return the found cycle.
422    ///
423    /// This function returns a const reference to the path structure
424    /// storing the found cycle.
425    ///
426    /// \pre \ref run() or \ref findCycle() must be called before using
427    /// this function.
428    const Path& cycle() const {
429      return *_cycle_path;
430    }
431
432    ///@}
433
434  private:
435
436    // Initialize
437    void init() {
438      if (!_cycle_path) {
439        _local_path = true;
440        _cycle_path = new Path;
441      }
442      _queue.resize(countNodes(_gr));
443      _best_found = false;
444      _best_cost = 0;
445      _best_size = 1;
446      _cycle_path->clear();
447    }
448
449    // Find strongly connected components and initialize _comp_nodes
450    // and _in_arcs
451    void findComponents() {
452      _comp_num = stronglyConnectedComponents(_gr, _comp);
453      _comp_nodes.resize(_comp_num);
454      if (_comp_num == 1) {
455        _comp_nodes[0].clear();
456        for (NodeIt n(_gr); n != INVALID; ++n) {
457          _comp_nodes[0].push_back(n);
458          _in_arcs[n].clear();
459          for (InArcIt a(_gr, n); a != INVALID; ++a) {
460            _in_arcs[n].push_back(a);
461          }
462        }
463      } else {
464        for (int i = 0; i < _comp_num; ++i)
465          _comp_nodes[i].clear();
466        for (NodeIt n(_gr); n != INVALID; ++n) {
467          int k = _comp[n];
468          _comp_nodes[k].push_back(n);
469          _in_arcs[n].clear();
470          for (InArcIt a(_gr, n); a != INVALID; ++a) {
471            if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
472          }
473        }
474      }
475    }
476
477    // Build the policy graph in the given strongly connected component
478    // (the out-degree of every node is 1)
479    bool buildPolicyGraph(int comp) {
480      _nodes = &(_comp_nodes[comp]);
481      if (_nodes->size() < 1 ||
482          (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
483        return false;
484      }
485      for (int i = 0; i < int(_nodes->size()); ++i) {
486        _dist[(*_nodes)[i]] = INF;
487      }
488      Node u, v;
489      Arc e;
490      for (int i = 0; i < int(_nodes->size()); ++i) {
491        v = (*_nodes)[i];
492        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
493          e = _in_arcs[v][j];
494          u = _gr.source(e);
495          if (_cost[e] < _dist[u]) {
496            _dist[u] = _cost[e];
497            _policy[u] = e;
498          }
499        }
500      }
501      return true;
502    }
503
504    // Find the minimum mean cycle in the policy graph
505    void findPolicyCycle() {
506      for (int i = 0; i < int(_nodes->size()); ++i) {
507        _level[(*_nodes)[i]] = -1;
508      }
509      LargeCost ccost;
510      int csize;
511      Node u, v;
512      _curr_found = false;
513      for (int i = 0; i < int(_nodes->size()); ++i) {
514        u = (*_nodes)[i];
515        if (_level[u] >= 0) continue;
516        for (; _level[u] < 0; u = _gr.target(_policy[u])) {
517          _level[u] = i;
518        }
519        if (_level[u] == i) {
520          // A cycle is found
521          ccost = _cost[_policy[u]];
522          csize = 1;
523          for (v = u; (v = _gr.target(_policy[v])) != u; ) {
524            ccost += _cost[_policy[v]];
525            ++csize;
526          }
527          if ( !_curr_found ||
528               (ccost * _curr_size < _curr_cost * csize) ) {
529            _curr_found = true;
530            _curr_cost = ccost;
531            _curr_size = csize;
532            _curr_node = u;
533          }
534        }
535      }
536    }
537
538    // Contract the policy graph and compute node distances
539    bool computeNodeDistances() {
540      // Find the component of the main cycle and compute node distances
541      // using reverse BFS
542      for (int i = 0; i < int(_nodes->size()); ++i) {
543        _reached[(*_nodes)[i]] = false;
544      }
545      _qfront = _qback = 0;
546      _queue[0] = _curr_node;
547      _reached[_curr_node] = true;
548      _dist[_curr_node] = 0;
549      Node u, v;
550      Arc e;
551      while (_qfront <= _qback) {
552        v = _queue[_qfront++];
553        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
554          e = _in_arcs[v][j];
555          u = _gr.source(e);
556          if (_policy[u] == e && !_reached[u]) {
557            _reached[u] = true;
558            _dist[u] = _dist[v] + _cost[e] * _curr_size - _curr_cost;
559            _queue[++_qback] = u;
560          }
561        }
562      }
563
564      // Connect all other nodes to this component and compute node
565      // distances using reverse BFS
566      _qfront = 0;
567      while (_qback < int(_nodes->size())-1) {
568        v = _queue[_qfront++];
569        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
570          e = _in_arcs[v][j];
571          u = _gr.source(e);
572          if (!_reached[u]) {
573            _reached[u] = true;
574            _policy[u] = e;
575            _dist[u] = _dist[v] + _cost[e] * _curr_size - _curr_cost;
576            _queue[++_qback] = u;
577          }
578        }
579      }
580
581      // Improve node distances
582      bool improved = false;
583      for (int i = 0; i < int(_nodes->size()); ++i) {
584        v = (*_nodes)[i];
585        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
586          e = _in_arcs[v][j];
587          u = _gr.source(e);
588          LargeCost delta = _dist[v] + _cost[e] * _curr_size - _curr_cost;
589          if (_tolerance.less(delta, _dist[u])) {
590            _dist[u] = delta;
591            _policy[u] = e;
592            improved = true;
593          }
594        }
595      }
596      return improved;
597    }
598
599  }; //class HowardMmc
600
601  ///@}
602
603} //namespace lemon
604
605#endif //LEMON_HOWARD_MMC_H
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