COIN-OR::LEMON - Graph Library

source: lemon/lemon/howard.h @ 815:0a42883c8221

Last change on this file since 815:0a42883c8221 was 815:0a42883c8221, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Separate group for the min mean cycle classes (#179)

File size: 17.3 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_HOWARD_H
20#define LEMON_HOWARD_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 Howard class.
37  ///
38  /// Default traits class of Howard class.
39  /// \tparam GR The type of the digraph.
40  /// \tparam LEN The type of the length map.
41  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
42#ifdef DOXYGEN
43  template <typename GR, typename LEN>
44#else
45  template <typename GR, typename LEN,
46    bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
47#endif
48  struct HowardDefaultTraits
49  {
50    /// The type of the digraph
51    typedef GR Digraph;
52    /// The type of the length map
53    typedef LEN LengthMap;
54    /// The type of the arc lengths
55    typedef typename LengthMap::Value Value;
56
57    /// \brief The large value type used for internal computations
58    ///
59    /// The large value type used for internal computations.
60    /// It is \c long \c long if the \c Value type is integer,
61    /// otherwise it is \c double.
62    /// \c Value must be convertible to \c LargeValue.
63    typedef double LargeValue;
64
65    /// The tolerance type used for internal computations
66    typedef lemon::Tolerance<LargeValue> 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 value types
77  template <typename GR, typename LEN>
78  struct HowardDefaultTraits<GR, LEN, true>
79  {
80    typedef GR Digraph;
81    typedef LEN LengthMap;
82    typedef typename LengthMap::Value Value;
83#ifdef LEMON_HAVE_LONG_LONG
84    typedef long long LargeValue;
85#else
86    typedef long LargeValue;
87#endif
88    typedef lemon::Tolerance<LargeValue> 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 length (cost) in a digraph.
101  /// This class provides the most efficient algorithm for the
102  /// minimum mean cycle problem, though the best known theoretical
103  /// bound on its running time is exponential.
104  ///
105  /// \tparam GR The type of the digraph the algorithm runs on.
106  /// \tparam LEN The type of the length map. The default
107  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
108#ifdef DOXYGEN
109  template <typename GR, typename LEN, typename TR>
110#else
111  template < typename GR,
112             typename LEN = typename GR::template ArcMap<int>,
113             typename TR = HowardDefaultTraits<GR, LEN> >
114#endif
115  class Howard
116  {
117  public:
118 
119    /// The type of the digraph
120    typedef typename TR::Digraph Digraph;
121    /// The type of the length map
122    typedef typename TR::LengthMap LengthMap;
123    /// The type of the arc lengths
124    typedef typename TR::Value Value;
125
126    /// \brief The large value type
127    ///
128    /// The large value type used for internal computations.
129    /// Using the \ref HowardDefaultTraits "default traits class",
130    /// it is \c long \c long if the \c Value type is integer,
131    /// otherwise it is \c double.
132    typedef typename TR::LargeValue LargeValue;
133
134    /// The tolerance type
135    typedef typename TR::Tolerance Tolerance;
136
137    /// \brief The path type of the found cycles
138    ///
139    /// The path type of the found cycles.
140    /// Using the \ref HowardDefaultTraits "default traits class",
141    /// it is \ref lemon::Path "Path<Digraph>".
142    typedef typename TR::Path Path;
143
144    /// The \ref HowardDefaultTraits "traits class" of the algorithm
145    typedef TR Traits;
146
147  private:
148
149    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
150 
151    // The digraph the algorithm runs on
152    const Digraph &_gr;
153    // The length of the arcs
154    const LengthMap &_length;
155
156    // Data for the found cycles
157    bool _curr_found, _best_found;
158    LargeValue _curr_length, _best_length;
159    int _curr_size, _best_size;
160    Node _curr_node, _best_node;
161
162    Path *_cycle_path;
163    bool _local_path;
164
165    // Internal data used by the algorithm
166    typename Digraph::template NodeMap<Arc> _policy;
167    typename Digraph::template NodeMap<bool> _reached;
168    typename Digraph::template NodeMap<int> _level;
169    typename Digraph::template NodeMap<LargeValue> _dist;
170
171    // Data for storing the strongly connected components
172    int _comp_num;
173    typename Digraph::template NodeMap<int> _comp;
174    std::vector<std::vector<Node> > _comp_nodes;
175    std::vector<Node>* _nodes;
176    typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
177   
178    // Queue used for BFS search
179    std::vector<Node> _queue;
180    int _qfront, _qback;
181
182    Tolerance _tolerance;
183 
184    // Infinite constant
185    const LargeValue INF;
186
187  public:
188 
189    /// \name Named Template Parameters
190    /// @{
191
192    template <typename T>
193    struct SetLargeValueTraits : public Traits {
194      typedef T LargeValue;
195      typedef lemon::Tolerance<T> Tolerance;
196    };
197
198    /// \brief \ref named-templ-param "Named parameter" for setting
199    /// \c LargeValue type.
200    ///
201    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
202    /// type. It is used for internal computations in the algorithm.
203    template <typename T>
204    struct SetLargeValue
205      : public Howard<GR, LEN, SetLargeValueTraits<T> > {
206      typedef Howard<GR, LEN, SetLargeValueTraits<T> > Create;
207    };
208
209    template <typename T>
210    struct SetPathTraits : public Traits {
211      typedef T Path;
212    };
213
214    /// \brief \ref named-templ-param "Named parameter" for setting
215    /// \c %Path type.
216    ///
217    /// \ref named-templ-param "Named parameter" for setting the \c %Path
218    /// type of the found cycles.
219    /// It must conform to the \ref lemon::concepts::Path "Path" concept
220    /// and it must have an \c addBack() function.
221    template <typename T>
222    struct SetPath
223      : public Howard<GR, LEN, SetPathTraits<T> > {
224      typedef Howard<GR, LEN, SetPathTraits<T> > Create;
225    };
226   
227    /// @}
228
229  public:
230
231    /// \brief Constructor.
232    ///
233    /// The constructor of the class.
234    ///
235    /// \param digraph The digraph the algorithm runs on.
236    /// \param length The lengths (costs) of the arcs.
237    Howard( const Digraph &digraph,
238            const LengthMap &length ) :
239      _gr(digraph), _length(length), _best_found(false),
240      _best_length(0), _best_size(1), _cycle_path(NULL), _local_path(false),
241      _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
242      _comp(digraph), _in_arcs(digraph),
243      INF(std::numeric_limits<LargeValue>::has_infinity ?
244          std::numeric_limits<LargeValue>::infinity() :
245          std::numeric_limits<LargeValue>::max())
246    {}
247
248    /// Destructor.
249    ~Howard() {
250      if (_local_path) delete _cycle_path;
251    }
252
253    /// \brief Set the path structure for storing the found cycle.
254    ///
255    /// This function sets an external path structure for storing the
256    /// found cycle.
257    ///
258    /// If you don't call this function before calling \ref run() or
259    /// \ref findMinMean(), it will allocate a local \ref Path "path"
260    /// structure. The destuctor deallocates this automatically
261    /// allocated object, of course.
262    ///
263    /// \note The algorithm calls only the \ref lemon::Path::addBack()
264    /// "addBack()" function of the given path structure.
265    ///
266    /// \return <tt>(*this)</tt>
267    Howard& cycle(Path &path) {
268      if (_local_path) {
269        delete _cycle_path;
270        _local_path = false;
271      }
272      _cycle_path = &path;
273      return *this;
274    }
275
276    /// \name Execution control
277    /// The simplest way to execute the algorithm is to call the \ref run()
278    /// function.\n
279    /// If you only need the minimum mean length, you may call
280    /// \ref findMinMean().
281
282    /// @{
283
284    /// \brief Run the algorithm.
285    ///
286    /// This function runs the algorithm.
287    /// It can be called more than once (e.g. if the underlying digraph
288    /// and/or the arc lengths have been modified).
289    ///
290    /// \return \c true if a directed cycle exists in the digraph.
291    ///
292    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
293    /// \code
294    ///   return mmc.findMinMean() && mmc.findCycle();
295    /// \endcode
296    bool run() {
297      return findMinMean() && findCycle();
298    }
299
300    /// \brief Find the minimum cycle mean.
301    ///
302    /// This function finds the minimum mean length of the directed
303    /// cycles in the digraph.
304    ///
305    /// \return \c true if a directed cycle exists in the digraph.
306    bool findMinMean() {
307      // Initialize and find strongly connected components
308      init();
309      findComponents();
310     
311      // Find the minimum cycle mean in the components
312      for (int comp = 0; comp < _comp_num; ++comp) {
313        // Find the minimum mean cycle in the current component
314        if (!buildPolicyGraph(comp)) continue;
315        while (true) {
316          findPolicyCycle();
317          if (!computeNodeDistances()) break;
318        }
319        // Update the best cycle (global minimum mean cycle)
320        if ( _curr_found && (!_best_found ||
321             _curr_length * _best_size < _best_length * _curr_size) ) {
322          _best_found = true;
323          _best_length = _curr_length;
324          _best_size = _curr_size;
325          _best_node = _curr_node;
326        }
327      }
328      return _best_found;
329    }
330
331    /// \brief Find a minimum mean directed cycle.
332    ///
333    /// This function finds a directed cycle of minimum mean length
334    /// in the digraph using the data computed by findMinMean().
335    ///
336    /// \return \c true if a directed cycle exists in the digraph.
337    ///
338    /// \pre \ref findMinMean() must be called before using this function.
339    bool findCycle() {
340      if (!_best_found) return false;
341      _cycle_path->addBack(_policy[_best_node]);
342      for ( Node v = _best_node;
343            (v = _gr.target(_policy[v])) != _best_node; ) {
344        _cycle_path->addBack(_policy[v]);
345      }
346      return true;
347    }
348
349    /// @}
350
351    /// \name Query Functions
352    /// The results of the algorithm can be obtained using these
353    /// functions.\n
354    /// The algorithm should be executed before using them.
355
356    /// @{
357
358    /// \brief Return the total length of the found cycle.
359    ///
360    /// This function returns the total length of the found cycle.
361    ///
362    /// \pre \ref run() or \ref findMinMean() must be called before
363    /// using this function.
364    LargeValue cycleLength() const {
365      return _best_length;
366    }
367
368    /// \brief Return the number of arcs on the found cycle.
369    ///
370    /// This function returns the number of arcs on the found cycle.
371    ///
372    /// \pre \ref run() or \ref findMinMean() must be called before
373    /// using this function.
374    int cycleArcNum() const {
375      return _best_size;
376    }
377
378    /// \brief Return the mean length of the found cycle.
379    ///
380    /// This function returns the mean length of the found cycle.
381    ///
382    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
383    /// following code.
384    /// \code
385    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
386    /// \endcode
387    ///
388    /// \pre \ref run() or \ref findMinMean() must be called before
389    /// using this function.
390    double cycleMean() const {
391      return static_cast<double>(_best_length) / _best_size;
392    }
393
394    /// \brief Return the found cycle.
395    ///
396    /// This function returns a const reference to the path structure
397    /// storing the found cycle.
398    ///
399    /// \pre \ref run() or \ref findCycle() must be called before using
400    /// this function.
401    const Path& cycle() const {
402      return *_cycle_path;
403    }
404
405    ///@}
406
407  private:
408
409    // Initialize
410    void init() {
411      if (!_cycle_path) {
412        _local_path = true;
413        _cycle_path = new Path;
414      }
415      _queue.resize(countNodes(_gr));
416      _best_found = false;
417      _best_length = 0;
418      _best_size = 1;
419      _cycle_path->clear();
420    }
421   
422    // Find strongly connected components and initialize _comp_nodes
423    // and _in_arcs
424    void findComponents() {
425      _comp_num = stronglyConnectedComponents(_gr, _comp);
426      _comp_nodes.resize(_comp_num);
427      if (_comp_num == 1) {
428        _comp_nodes[0].clear();
429        for (NodeIt n(_gr); n != INVALID; ++n) {
430          _comp_nodes[0].push_back(n);
431          _in_arcs[n].clear();
432          for (InArcIt a(_gr, n); a != INVALID; ++a) {
433            _in_arcs[n].push_back(a);
434          }
435        }
436      } else {
437        for (int i = 0; i < _comp_num; ++i)
438          _comp_nodes[i].clear();
439        for (NodeIt n(_gr); n != INVALID; ++n) {
440          int k = _comp[n];
441          _comp_nodes[k].push_back(n);
442          _in_arcs[n].clear();
443          for (InArcIt a(_gr, n); a != INVALID; ++a) {
444            if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
445          }
446        }
447      }
448    }
449
450    // Build the policy graph in the given strongly connected component
451    // (the out-degree of every node is 1)
452    bool buildPolicyGraph(int comp) {
453      _nodes = &(_comp_nodes[comp]);
454      if (_nodes->size() < 1 ||
455          (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
456        return false;
457      }
458      for (int i = 0; i < int(_nodes->size()); ++i) {
459        _dist[(*_nodes)[i]] = INF;
460      }
461      Node u, v;
462      Arc e;
463      for (int i = 0; i < int(_nodes->size()); ++i) {
464        v = (*_nodes)[i];
465        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
466          e = _in_arcs[v][j];
467          u = _gr.source(e);
468          if (_length[e] < _dist[u]) {
469            _dist[u] = _length[e];
470            _policy[u] = e;
471          }
472        }
473      }
474      return true;
475    }
476
477    // Find the minimum mean cycle in the policy graph
478    void findPolicyCycle() {
479      for (int i = 0; i < int(_nodes->size()); ++i) {
480        _level[(*_nodes)[i]] = -1;
481      }
482      LargeValue clength;
483      int csize;
484      Node u, v;
485      _curr_found = false;
486      for (int i = 0; i < int(_nodes->size()); ++i) {
487        u = (*_nodes)[i];
488        if (_level[u] >= 0) continue;
489        for (; _level[u] < 0; u = _gr.target(_policy[u])) {
490          _level[u] = i;
491        }
492        if (_level[u] == i) {
493          // A cycle is found
494          clength = _length[_policy[u]];
495          csize = 1;
496          for (v = u; (v = _gr.target(_policy[v])) != u; ) {
497            clength += _length[_policy[v]];
498            ++csize;
499          }
500          if ( !_curr_found ||
501               (clength * _curr_size < _curr_length * csize) ) {
502            _curr_found = true;
503            _curr_length = clength;
504            _curr_size = csize;
505            _curr_node = u;
506          }
507        }
508      }
509    }
510
511    // Contract the policy graph and compute node distances
512    bool computeNodeDistances() {
513      // Find the component of the main cycle and compute node distances
514      // using reverse BFS
515      for (int i = 0; i < int(_nodes->size()); ++i) {
516        _reached[(*_nodes)[i]] = false;
517      }
518      _qfront = _qback = 0;
519      _queue[0] = _curr_node;
520      _reached[_curr_node] = true;
521      _dist[_curr_node] = 0;
522      Node u, v;
523      Arc e;
524      while (_qfront <= _qback) {
525        v = _queue[_qfront++];
526        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
527          e = _in_arcs[v][j];
528          u = _gr.source(e);
529          if (_policy[u] == e && !_reached[u]) {
530            _reached[u] = true;
531            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
532            _queue[++_qback] = u;
533          }
534        }
535      }
536
537      // Connect all other nodes to this component and compute node
538      // distances using reverse BFS
539      _qfront = 0;
540      while (_qback < int(_nodes->size())-1) {
541        v = _queue[_qfront++];
542        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
543          e = _in_arcs[v][j];
544          u = _gr.source(e);
545          if (!_reached[u]) {
546            _reached[u] = true;
547            _policy[u] = e;
548            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
549            _queue[++_qback] = u;
550          }
551        }
552      }
553
554      // Improve node distances
555      bool improved = false;
556      for (int i = 0; i < int(_nodes->size()); ++i) {
557        v = (*_nodes)[i];
558        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
559          e = _in_arcs[v][j];
560          u = _gr.source(e);
561          LargeValue delta = _dist[v] + _length[e] * _curr_size - _curr_length;
562          if (_tolerance.less(delta, _dist[u])) {
563            _dist[u] = delta;
564            _policy[u] = e;
565            improved = true;
566          }
567        }
568      }
569      return improved;
570    }
571
572  }; //class Howard
573
574  ///@}
575
576} //namespace lemon
577
578#endif //LEMON_HOWARD_H
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