COIN-OR::LEMON - Graph Library

source: lemon/lemon/howard.h @ 816:e746fb14e680

Last change on this file since 816:e746fb14e680 was 816:e746fb14e680, checked in by Peter Kovacs <kpeter@…>, 12 years ago

Add tolerance() functions for MMC classes (#179)

File size: 17.8 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    /// \brief Set the tolerance used by the algorithm.
277    ///
278    /// This function sets the tolerance object used by the algorithm.
279    ///
280    /// \return <tt>(*this)</tt>
281    Howard& tolerance(const Tolerance& tolerance) {
282      _tolerance = tolerance;
283      return *this;
284    }
285
286    /// \brief Return a const reference to the tolerance.
287    ///
288    /// This function returns a const reference to the tolerance object
289    /// used by the algorithm.
290    const Tolerance& tolerance() const {
291      return _tolerance;
292    }
293
294    /// \name Execution control
295    /// The simplest way to execute the algorithm is to call the \ref run()
296    /// function.\n
297    /// If you only need the minimum mean length, you may call
298    /// \ref findMinMean().
299
300    /// @{
301
302    /// \brief Run the algorithm.
303    ///
304    /// This function runs the algorithm.
305    /// It can be called more than once (e.g. if the underlying digraph
306    /// and/or the arc lengths have been modified).
307    ///
308    /// \return \c true if a directed cycle exists in the digraph.
309    ///
310    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
311    /// \code
312    ///   return mmc.findMinMean() && mmc.findCycle();
313    /// \endcode
314    bool run() {
315      return findMinMean() && findCycle();
316    }
317
318    /// \brief Find the minimum cycle mean.
319    ///
320    /// This function finds the minimum mean length of the directed
321    /// cycles in the digraph.
322    ///
323    /// \return \c true if a directed cycle exists in the digraph.
324    bool findMinMean() {
325      // Initialize and find strongly connected components
326      init();
327      findComponents();
328     
329      // Find the minimum cycle mean in the components
330      for (int comp = 0; comp < _comp_num; ++comp) {
331        // Find the minimum mean cycle in the current component
332        if (!buildPolicyGraph(comp)) continue;
333        while (true) {
334          findPolicyCycle();
335          if (!computeNodeDistances()) break;
336        }
337        // Update the best cycle (global minimum mean cycle)
338        if ( _curr_found && (!_best_found ||
339             _curr_length * _best_size < _best_length * _curr_size) ) {
340          _best_found = true;
341          _best_length = _curr_length;
342          _best_size = _curr_size;
343          _best_node = _curr_node;
344        }
345      }
346      return _best_found;
347    }
348
349    /// \brief Find a minimum mean directed cycle.
350    ///
351    /// This function finds a directed cycle of minimum mean length
352    /// in the digraph using the data computed by findMinMean().
353    ///
354    /// \return \c true if a directed cycle exists in the digraph.
355    ///
356    /// \pre \ref findMinMean() must be called before using this function.
357    bool findCycle() {
358      if (!_best_found) return false;
359      _cycle_path->addBack(_policy[_best_node]);
360      for ( Node v = _best_node;
361            (v = _gr.target(_policy[v])) != _best_node; ) {
362        _cycle_path->addBack(_policy[v]);
363      }
364      return true;
365    }
366
367    /// @}
368
369    /// \name Query Functions
370    /// The results of the algorithm can be obtained using these
371    /// functions.\n
372    /// The algorithm should be executed before using them.
373
374    /// @{
375
376    /// \brief Return the total length of the found cycle.
377    ///
378    /// This function returns the total length of the found cycle.
379    ///
380    /// \pre \ref run() or \ref findMinMean() must be called before
381    /// using this function.
382    LargeValue cycleLength() const {
383      return _best_length;
384    }
385
386    /// \brief Return the number of arcs on the found cycle.
387    ///
388    /// This function returns the number of arcs on the found cycle.
389    ///
390    /// \pre \ref run() or \ref findMinMean() must be called before
391    /// using this function.
392    int cycleArcNum() const {
393      return _best_size;
394    }
395
396    /// \brief Return the mean length of the found cycle.
397    ///
398    /// This function returns the mean length of the found cycle.
399    ///
400    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
401    /// following code.
402    /// \code
403    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
404    /// \endcode
405    ///
406    /// \pre \ref run() or \ref findMinMean() must be called before
407    /// using this function.
408    double cycleMean() const {
409      return static_cast<double>(_best_length) / _best_size;
410    }
411
412    /// \brief Return the found cycle.
413    ///
414    /// This function returns a const reference to the path structure
415    /// storing the found cycle.
416    ///
417    /// \pre \ref run() or \ref findCycle() must be called before using
418    /// this function.
419    const Path& cycle() const {
420      return *_cycle_path;
421    }
422
423    ///@}
424
425  private:
426
427    // Initialize
428    void init() {
429      if (!_cycle_path) {
430        _local_path = true;
431        _cycle_path = new Path;
432      }
433      _queue.resize(countNodes(_gr));
434      _best_found = false;
435      _best_length = 0;
436      _best_size = 1;
437      _cycle_path->clear();
438    }
439   
440    // Find strongly connected components and initialize _comp_nodes
441    // and _in_arcs
442    void findComponents() {
443      _comp_num = stronglyConnectedComponents(_gr, _comp);
444      _comp_nodes.resize(_comp_num);
445      if (_comp_num == 1) {
446        _comp_nodes[0].clear();
447        for (NodeIt n(_gr); n != INVALID; ++n) {
448          _comp_nodes[0].push_back(n);
449          _in_arcs[n].clear();
450          for (InArcIt a(_gr, n); a != INVALID; ++a) {
451            _in_arcs[n].push_back(a);
452          }
453        }
454      } else {
455        for (int i = 0; i < _comp_num; ++i)
456          _comp_nodes[i].clear();
457        for (NodeIt n(_gr); n != INVALID; ++n) {
458          int k = _comp[n];
459          _comp_nodes[k].push_back(n);
460          _in_arcs[n].clear();
461          for (InArcIt a(_gr, n); a != INVALID; ++a) {
462            if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
463          }
464        }
465      }
466    }
467
468    // Build the policy graph in the given strongly connected component
469    // (the out-degree of every node is 1)
470    bool buildPolicyGraph(int comp) {
471      _nodes = &(_comp_nodes[comp]);
472      if (_nodes->size() < 1 ||
473          (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
474        return false;
475      }
476      for (int i = 0; i < int(_nodes->size()); ++i) {
477        _dist[(*_nodes)[i]] = INF;
478      }
479      Node u, v;
480      Arc e;
481      for (int i = 0; i < int(_nodes->size()); ++i) {
482        v = (*_nodes)[i];
483        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
484          e = _in_arcs[v][j];
485          u = _gr.source(e);
486          if (_length[e] < _dist[u]) {
487            _dist[u] = _length[e];
488            _policy[u] = e;
489          }
490        }
491      }
492      return true;
493    }
494
495    // Find the minimum mean cycle in the policy graph
496    void findPolicyCycle() {
497      for (int i = 0; i < int(_nodes->size()); ++i) {
498        _level[(*_nodes)[i]] = -1;
499      }
500      LargeValue clength;
501      int csize;
502      Node u, v;
503      _curr_found = false;
504      for (int i = 0; i < int(_nodes->size()); ++i) {
505        u = (*_nodes)[i];
506        if (_level[u] >= 0) continue;
507        for (; _level[u] < 0; u = _gr.target(_policy[u])) {
508          _level[u] = i;
509        }
510        if (_level[u] == i) {
511          // A cycle is found
512          clength = _length[_policy[u]];
513          csize = 1;
514          for (v = u; (v = _gr.target(_policy[v])) != u; ) {
515            clength += _length[_policy[v]];
516            ++csize;
517          }
518          if ( !_curr_found ||
519               (clength * _curr_size < _curr_length * csize) ) {
520            _curr_found = true;
521            _curr_length = clength;
522            _curr_size = csize;
523            _curr_node = u;
524          }
525        }
526      }
527    }
528
529    // Contract the policy graph and compute node distances
530    bool computeNodeDistances() {
531      // Find the component of the main cycle and compute node distances
532      // using reverse BFS
533      for (int i = 0; i < int(_nodes->size()); ++i) {
534        _reached[(*_nodes)[i]] = false;
535      }
536      _qfront = _qback = 0;
537      _queue[0] = _curr_node;
538      _reached[_curr_node] = true;
539      _dist[_curr_node] = 0;
540      Node u, v;
541      Arc e;
542      while (_qfront <= _qback) {
543        v = _queue[_qfront++];
544        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
545          e = _in_arcs[v][j];
546          u = _gr.source(e);
547          if (_policy[u] == e && !_reached[u]) {
548            _reached[u] = true;
549            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
550            _queue[++_qback] = u;
551          }
552        }
553      }
554
555      // Connect all other nodes to this component and compute node
556      // distances using reverse BFS
557      _qfront = 0;
558      while (_qback < int(_nodes->size())-1) {
559        v = _queue[_qfront++];
560        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
561          e = _in_arcs[v][j];
562          u = _gr.source(e);
563          if (!_reached[u]) {
564            _reached[u] = true;
565            _policy[u] = e;
566            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
567            _queue[++_qback] = u;
568          }
569        }
570      }
571
572      // Improve node distances
573      bool improved = false;
574      for (int i = 0; i < int(_nodes->size()); ++i) {
575        v = (*_nodes)[i];
576        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
577          e = _in_arcs[v][j];
578          u = _gr.source(e);
579          LargeValue delta = _dist[v] + _length[e] * _curr_size - _curr_length;
580          if (_tolerance.less(delta, _dist[u])) {
581            _dist[u] = delta;
582            _policy[u] = e;
583            improved = true;
584          }
585        }
586      }
587      return improved;
588    }
589
590  }; //class Howard
591
592  ///@}
593
594} //namespace lemon
595
596#endif //LEMON_HOWARD_H
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