COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/karp_mmc.h @ 942:2b6bffe0e7e8

Last change on this file since 942:2b6bffe0e7e8 was 877:141f9c0db4a3, checked in by Alpar Juttner <alpar@…>, 10 years ago

Unify the sources (#339)

File size: 17.1 KB
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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_KARP_MMC_H
20#define LEMON_KARP_MMC_H
21
22/// \ingroup min_mean_cycle
23///
24/// \file
25/// \brief Karp'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 KarpMmc class.
37  ///
38  /// Default traits class of KarpMmc 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 KarpMmcDefaultTraits
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 KarpMmcDefaultTraits<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 Karp's algorithm for finding a minimum
97  /// mean cycle.
98  ///
99  /// This class implements Karp's algorithm for finding a directed
100  /// cycle of minimum mean cost in a digraph
101  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
102  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
103  ///
104  /// \tparam GR The type of the digraph the algorithm runs on.
105  /// \tparam CM The type of the cost map. The default
106  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
107  /// \tparam TR The traits class that defines various types used by the
108  /// algorithm. By default, it is \ref KarpMmcDefaultTraits
109  /// "KarpMmcDefaultTraits<GR, CM>".
110  /// In most cases, this parameter should not be set directly,
111  /// consider to use the named template parameters instead.
112#ifdef DOXYGEN
113  template <typename GR, typename CM, typename TR>
114#else
115  template < typename GR,
116             typename CM = typename GR::template ArcMap<int>,
117             typename TR = KarpMmcDefaultTraits<GR, CM> >
118#endif
119  class KarpMmc
120  {
121  public:
122
123    /// The type of the digraph
124    typedef typename TR::Digraph Digraph;
125    /// The type of the cost map
126    typedef typename TR::CostMap CostMap;
127    /// The type of the arc costs
128    typedef typename TR::Cost Cost;
129
130    /// \brief The large cost type
131    ///
132    /// The large cost type used for internal computations.
133    /// By default, it is \c long \c long if the \c Cost type is integer,
134    /// otherwise it is \c double.
135    typedef typename TR::LargeCost LargeCost;
136
137    /// The tolerance type
138    typedef typename TR::Tolerance Tolerance;
139
140    /// \brief The path type of the found cycles
141    ///
142    /// The path type of the found cycles.
143    /// Using the \ref KarpMmcDefaultTraits "default traits class",
144    /// it is \ref lemon::Path "Path<Digraph>".
145    typedef typename TR::Path Path;
146
147    /// The \ref KarpMmcDefaultTraits "traits class" of the algorithm
148    typedef TR Traits;
149
150  private:
151
152    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
153
154    // Data sturcture for path data
155    struct PathData
156    {
157      LargeCost dist;
158      Arc pred;
159      PathData(LargeCost d, Arc p = INVALID) :
160        dist(d), pred(p) {}
161    };
162
163    typedef typename Digraph::template NodeMap<std::vector<PathData> >
164      PathDataNodeMap;
165
166  private:
167
168    // The digraph the algorithm runs on
169    const Digraph &_gr;
170    // The cost of the arcs
171    const CostMap &_cost;
172
173    // Data for storing the strongly connected components
174    int _comp_num;
175    typename Digraph::template NodeMap<int> _comp;
176    std::vector<std::vector<Node> > _comp_nodes;
177    std::vector<Node>* _nodes;
178    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
179
180    // Data for the found cycle
181    LargeCost _cycle_cost;
182    int _cycle_size;
183    Node _cycle_node;
184
185    Path *_cycle_path;
186    bool _local_path;
187
188    // Node map for storing path data
189    PathDataNodeMap _data;
190    // The processed nodes in the last round
191    std::vector<Node> _process;
192
193    Tolerance _tolerance;
194
195    // Infinite constant
196    const LargeCost INF;
197
198  public:
199
200    /// \name Named Template Parameters
201    /// @{
202
203    template <typename T>
204    struct SetLargeCostTraits : public Traits {
205      typedef T LargeCost;
206      typedef lemon::Tolerance<T> Tolerance;
207    };
208
209    /// \brief \ref named-templ-param "Named parameter" for setting
210    /// \c LargeCost type.
211    ///
212    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
213    /// type. It is used for internal computations in the algorithm.
214    template <typename T>
215    struct SetLargeCost
216      : public KarpMmc<GR, CM, SetLargeCostTraits<T> > {
217      typedef KarpMmc<GR, CM, SetLargeCostTraits<T> > Create;
218    };
219
220    template <typename T>
221    struct SetPathTraits : public Traits {
222      typedef T Path;
223    };
224
225    /// \brief \ref named-templ-param "Named parameter" for setting
226    /// \c %Path type.
227    ///
228    /// \ref named-templ-param "Named parameter" for setting the \c %Path
229    /// type of the found cycles.
230    /// It must conform to the \ref lemon::concepts::Path "Path" concept
231    /// and it must have an \c addFront() function.
232    template <typename T>
233    struct SetPath
234      : public KarpMmc<GR, CM, SetPathTraits<T> > {
235      typedef KarpMmc<GR, CM, SetPathTraits<T> > Create;
236    };
237
238    /// @}
239
240  protected:
241
242    KarpMmc() {}
243
244  public:
245
246    /// \brief Constructor.
247    ///
248    /// The constructor of the class.
249    ///
250    /// \param digraph The digraph the algorithm runs on.
251    /// \param cost The costs of the arcs.
252    KarpMmc( const Digraph &digraph,
253             const CostMap &cost ) :
254      _gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),
255      _cycle_cost(0), _cycle_size(1), _cycle_node(INVALID),
256      _cycle_path(NULL), _local_path(false), _data(digraph),
257      INF(std::numeric_limits<LargeCost>::has_infinity ?
258          std::numeric_limits<LargeCost>::infinity() :
259          std::numeric_limits<LargeCost>::max())
260    {}
261
262    /// Destructor.
263    ~KarpMmc() {
264      if (_local_path) delete _cycle_path;
265    }
266
267    /// \brief Set the path structure for storing the found cycle.
268    ///
269    /// This function sets an external path structure for storing the
270    /// found cycle.
271    ///
272    /// If you don't call this function before calling \ref run() or
273    /// \ref findCycleMean(), it will allocate a local \ref Path "path"
274    /// structure. The destuctor deallocates this automatically
275    /// allocated object, of course.
276    ///
277    /// \note The algorithm calls only the \ref lemon::Path::addFront()
278    /// "addFront()" function of the given path structure.
279    ///
280    /// \return <tt>(*this)</tt>
281    KarpMmc& cycle(Path &path) {
282      if (_local_path) {
283        delete _cycle_path;
284        _local_path = false;
285      }
286      _cycle_path = &path;
287      return *this;
288    }
289
290    /// \brief Set the tolerance used by the algorithm.
291    ///
292    /// This function sets the tolerance object used by the algorithm.
293    ///
294    /// \return <tt>(*this)</tt>
295    KarpMmc& tolerance(const Tolerance& tolerance) {
296      _tolerance = tolerance;
297      return *this;
298    }
299
300    /// \brief Return a const reference to the tolerance.
301    ///
302    /// This function returns a const reference to the tolerance object
303    /// used by the algorithm.
304    const Tolerance& tolerance() const {
305      return _tolerance;
306    }
307
308    /// \name Execution control
309    /// The simplest way to execute the algorithm is to call the \ref run()
310    /// function.\n
311    /// If you only need the minimum mean cost, you may call
312    /// \ref findCycleMean().
313
314    /// @{
315
316    /// \brief Run the algorithm.
317    ///
318    /// This function runs the algorithm.
319    /// It can be called more than once (e.g. if the underlying digraph
320    /// and/or the arc costs have been modified).
321    ///
322    /// \return \c true if a directed cycle exists in the digraph.
323    ///
324    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
325    /// \code
326    ///   return mmc.findCycleMean() && mmc.findCycle();
327    /// \endcode
328    bool run() {
329      return findCycleMean() && findCycle();
330    }
331
332    /// \brief Find the minimum cycle mean.
333    ///
334    /// This function finds the minimum mean cost of the directed
335    /// cycles in the digraph.
336    ///
337    /// \return \c true if a directed cycle exists in the digraph.
338    bool findCycleMean() {
339      // Initialization and find strongly connected components
340      init();
341      findComponents();
342
343      // Find the minimum cycle mean in the components
344      for (int comp = 0; comp < _comp_num; ++comp) {
345        if (!initComponent(comp)) continue;
346        processRounds();
347        updateMinMean();
348      }
349      return (_cycle_node != INVALID);
350    }
351
352    /// \brief Find a minimum mean directed cycle.
353    ///
354    /// This function finds a directed cycle of minimum mean cost
355    /// in the digraph using the data computed by findCycleMean().
356    ///
357    /// \return \c true if a directed cycle exists in the digraph.
358    ///
359    /// \pre \ref findCycleMean() must be called before using this function.
360    bool findCycle() {
361      if (_cycle_node == INVALID) return false;
362      IntNodeMap reached(_gr, -1);
363      int r = _data[_cycle_node].size();
364      Node u = _cycle_node;
365      while (reached[u] < 0) {
366        reached[u] = --r;
367        u = _gr.source(_data[u][r].pred);
368      }
369      r = reached[u];
370      Arc e = _data[u][r].pred;
371      _cycle_path->addFront(e);
372      _cycle_cost = _cost[e];
373      _cycle_size = 1;
374      Node v;
375      while ((v = _gr.source(e)) != u) {
376        e = _data[v][--r].pred;
377        _cycle_path->addFront(e);
378        _cycle_cost += _cost[e];
379        ++_cycle_size;
380      }
381      return true;
382    }
383
384    /// @}
385
386    /// \name Query Functions
387    /// The results of the algorithm can be obtained using these
388    /// functions.\n
389    /// The algorithm should be executed before using them.
390
391    /// @{
392
393    /// \brief Return the total cost of the found cycle.
394    ///
395    /// This function returns the total cost of the found cycle.
396    ///
397    /// \pre \ref run() or \ref findCycleMean() must be called before
398    /// using this function.
399    Cost cycleCost() const {
400      return static_cast<Cost>(_cycle_cost);
401    }
402
403    /// \brief Return the number of arcs on the found cycle.
404    ///
405    /// This function returns the number of arcs on the found cycle.
406    ///
407    /// \pre \ref run() or \ref findCycleMean() must be called before
408    /// using this function.
409    int cycleSize() const {
410      return _cycle_size;
411    }
412
413    /// \brief Return the mean cost of the found cycle.
414    ///
415    /// This function returns the mean cost of the found cycle.
416    ///
417    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
418    /// following code.
419    /// \code
420    ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
421    /// \endcode
422    ///
423    /// \pre \ref run() or \ref findCycleMean() must be called before
424    /// using this function.
425    double cycleMean() const {
426      return static_cast<double>(_cycle_cost) / _cycle_size;
427    }
428
429    /// \brief Return the found cycle.
430    ///
431    /// This function returns a const reference to the path structure
432    /// storing the found cycle.
433    ///
434    /// \pre \ref run() or \ref findCycle() must be called before using
435    /// this function.
436    const Path& cycle() const {
437      return *_cycle_path;
438    }
439
440    ///@}
441
442  private:
443
444    // Initialization
445    void init() {
446      if (!_cycle_path) {
447        _local_path = true;
448        _cycle_path = new Path;
449      }
450      _cycle_path->clear();
451      _cycle_cost = 0;
452      _cycle_size = 1;
453      _cycle_node = INVALID;
454      for (NodeIt u(_gr); u != INVALID; ++u)
455        _data[u].clear();
456    }
457
458    // Find strongly connected components and initialize _comp_nodes
459    // and _out_arcs
460    void findComponents() {
461      _comp_num = stronglyConnectedComponents(_gr, _comp);
462      _comp_nodes.resize(_comp_num);
463      if (_comp_num == 1) {
464        _comp_nodes[0].clear();
465        for (NodeIt n(_gr); n != INVALID; ++n) {
466          _comp_nodes[0].push_back(n);
467          _out_arcs[n].clear();
468          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
469            _out_arcs[n].push_back(a);
470          }
471        }
472      } else {
473        for (int i = 0; i < _comp_num; ++i)
474          _comp_nodes[i].clear();
475        for (NodeIt n(_gr); n != INVALID; ++n) {
476          int k = _comp[n];
477          _comp_nodes[k].push_back(n);
478          _out_arcs[n].clear();
479          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
480            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
481          }
482        }
483      }
484    }
485
486    // Initialize path data for the current component
487    bool initComponent(int comp) {
488      _nodes = &(_comp_nodes[comp]);
489      int n = _nodes->size();
490      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
491        return false;
492      }
493      for (int i = 0; i < n; ++i) {
494        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
495      }
496      return true;
497    }
498
499    // Process all rounds of computing path data for the current component.
500    // _data[v][k] is the cost of a shortest directed walk from the root
501    // node to node v containing exactly k arcs.
502    void processRounds() {
503      Node start = (*_nodes)[0];
504      _data[start][0] = PathData(0);
505      _process.clear();
506      _process.push_back(start);
507
508      int k, n = _nodes->size();
509      for (k = 1; k <= n && int(_process.size()) < n; ++k) {
510        processNextBuildRound(k);
511      }
512      for ( ; k <= n; ++k) {
513        processNextFullRound(k);
514      }
515    }
516
517    // Process one round and rebuild _process
518    void processNextBuildRound(int k) {
519      std::vector<Node> next;
520      Node u, v;
521      Arc e;
522      LargeCost d;
523      for (int i = 0; i < int(_process.size()); ++i) {
524        u = _process[i];
525        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
526          e = _out_arcs[u][j];
527          v = _gr.target(e);
528          d = _data[u][k-1].dist + _cost[e];
529          if (_tolerance.less(d, _data[v][k].dist)) {
530            if (_data[v][k].dist == INF) next.push_back(v);
531            _data[v][k] = PathData(d, e);
532          }
533        }
534      }
535      _process.swap(next);
536    }
537
538    // Process one round using _nodes instead of _process
539    void processNextFullRound(int k) {
540      Node u, v;
541      Arc e;
542      LargeCost d;
543      for (int i = 0; i < int(_nodes->size()); ++i) {
544        u = (*_nodes)[i];
545        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
546          e = _out_arcs[u][j];
547          v = _gr.target(e);
548          d = _data[u][k-1].dist + _cost[e];
549          if (_tolerance.less(d, _data[v][k].dist)) {
550            _data[v][k] = PathData(d, e);
551          }
552        }
553      }
554    }
555
556    // Update the minimum cycle mean
557    void updateMinMean() {
558      int n = _nodes->size();
559      for (int i = 0; i < n; ++i) {
560        Node u = (*_nodes)[i];
561        if (_data[u][n].dist == INF) continue;
562        LargeCost cost, max_cost = 0;
563        int size, max_size = 1;
564        bool found_curr = false;
565        for (int k = 0; k < n; ++k) {
566          if (_data[u][k].dist == INF) continue;
567          cost = _data[u][n].dist - _data[u][k].dist;
568          size = n - k;
569          if (!found_curr || cost * max_size > max_cost * size) {
570            found_curr = true;
571            max_cost = cost;
572            max_size = size;
573          }
574        }
575        if ( found_curr && (_cycle_node == INVALID ||
576             max_cost * _cycle_size < _cycle_cost * max_size) ) {
577          _cycle_cost = max_cost;
578          _cycle_size = max_size;
579          _cycle_node = u;
580        }
581      }
582    }
583
584  }; //class KarpMmc
585
586  ///@}
587
588} //namespace lemon
589
590#endif //LEMON_KARP_MMC_H
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