COIN-OR::LEMON - Graph Library

source: lemon/lemon/howard.h @ 899:cc9e0c15d747

Last change on this file since 899:cc9e0c15d747 was 891:75e6020b19b1, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Add doc for the traits class parameters (#315)

File size: 18.1 KB
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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  /// \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 LEN The type of the length 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 HowardDefaultTraits
111  /// "HowardDefaultTraits<GR, LEN>".
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 LEN, typename TR>
116#else
117  template < typename GR,
118             typename LEN = typename GR::template ArcMap<int>,
119             typename TR = HowardDefaultTraits<GR, LEN> >
120#endif
121  class Howard
122  {
123  public:
124 
125    /// The type of the digraph
126    typedef typename TR::Digraph Digraph;
127    /// The type of the length map
128    typedef typename TR::LengthMap LengthMap;
129    /// The type of the arc lengths
130    typedef typename TR::Value Value;
131
132    /// \brief The large value type
133    ///
134    /// The large value type used for internal computations.
135    /// By default, it is \c long \c long if the \c Value type is integer,
136    /// otherwise it is \c double.
137    typedef typename TR::LargeValue LargeValue;
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 HowardDefaultTraits "default traits class",
146    /// it is \ref lemon::Path "Path<Digraph>".
147    typedef typename TR::Path Path;
148
149    /// The \ref HowardDefaultTraits "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 length of the arcs
159    const LengthMap &_length;
160
161    // Data for the found cycles
162    bool _curr_found, _best_found;
163    LargeValue _curr_length, _best_length;
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<LargeValue> _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 LargeValue INF;
191
192  public:
193 
194    /// \name Named Template Parameters
195    /// @{
196
197    template <typename T>
198    struct SetLargeValueTraits : public Traits {
199      typedef T LargeValue;
200      typedef lemon::Tolerance<T> Tolerance;
201    };
202
203    /// \brief \ref named-templ-param "Named parameter" for setting
204    /// \c LargeValue type.
205    ///
206    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
207    /// type. It is used for internal computations in the algorithm.
208    template <typename T>
209    struct SetLargeValue
210      : public Howard<GR, LEN, SetLargeValueTraits<T> > {
211      typedef Howard<GR, LEN, SetLargeValueTraits<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 Howard<GR, LEN, SetPathTraits<T> > {
229      typedef Howard<GR, LEN, SetPathTraits<T> > Create;
230    };
231   
232    /// @}
233
234  public:
235
236    /// \brief Constructor.
237    ///
238    /// The constructor of the class.
239    ///
240    /// \param digraph The digraph the algorithm runs on.
241    /// \param length The lengths (costs) of the arcs.
242    Howard( const Digraph &digraph,
243            const LengthMap &length ) :
244      _gr(digraph), _length(length), _best_found(false),
245      _best_length(0), _best_size(1), _cycle_path(NULL), _local_path(false),
246      _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
247      _comp(digraph), _in_arcs(digraph),
248      INF(std::numeric_limits<LargeValue>::has_infinity ?
249          std::numeric_limits<LargeValue>::infinity() :
250          std::numeric_limits<LargeValue>::max())
251    {}
252
253    /// Destructor.
254    ~Howard() {
255      if (_local_path) delete _cycle_path;
256    }
257
258    /// \brief Set the path structure for storing the found cycle.
259    ///
260    /// This function sets an external path structure for storing the
261    /// found cycle.
262    ///
263    /// If you don't call this function before calling \ref run() or
264    /// \ref findMinMean(), it will allocate a local \ref Path "path"
265    /// structure. The destuctor deallocates this automatically
266    /// allocated object, of course.
267    ///
268    /// \note The algorithm calls only the \ref lemon::Path::addBack()
269    /// "addBack()" function of the given path structure.
270    ///
271    /// \return <tt>(*this)</tt>
272    Howard& cycle(Path &path) {
273      if (_local_path) {
274        delete _cycle_path;
275        _local_path = false;
276      }
277      _cycle_path = &path;
278      return *this;
279    }
280
281    /// \brief Set the tolerance used by the algorithm.
282    ///
283    /// This function sets the tolerance object used by the algorithm.
284    ///
285    /// \return <tt>(*this)</tt>
286    Howard& tolerance(const Tolerance& tolerance) {
287      _tolerance = tolerance;
288      return *this;
289    }
290
291    /// \brief Return a const reference to the tolerance.
292    ///
293    /// This function returns a const reference to the tolerance object
294    /// used by the algorithm.
295    const Tolerance& tolerance() const {
296      return _tolerance;
297    }
298
299    /// \name Execution control
300    /// The simplest way to execute the algorithm is to call the \ref run()
301    /// function.\n
302    /// If you only need the minimum mean length, you may call
303    /// \ref findMinMean().
304
305    /// @{
306
307    /// \brief Run the algorithm.
308    ///
309    /// This function runs the algorithm.
310    /// It can be called more than once (e.g. if the underlying digraph
311    /// and/or the arc lengths have been modified).
312    ///
313    /// \return \c true if a directed cycle exists in the digraph.
314    ///
315    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
316    /// \code
317    ///   return mmc.findMinMean() && mmc.findCycle();
318    /// \endcode
319    bool run() {
320      return findMinMean() && findCycle();
321    }
322
323    /// \brief Find the minimum cycle mean.
324    ///
325    /// This function finds the minimum mean length of the directed
326    /// cycles in the digraph.
327    ///
328    /// \return \c true if a directed cycle exists in the digraph.
329    bool findMinMean() {
330      // Initialize and find strongly connected components
331      init();
332      findComponents();
333     
334      // Find the minimum cycle mean in the components
335      for (int comp = 0; comp < _comp_num; ++comp) {
336        // Find the minimum mean cycle in the current component
337        if (!buildPolicyGraph(comp)) continue;
338        while (true) {
339          findPolicyCycle();
340          if (!computeNodeDistances()) break;
341        }
342        // Update the best cycle (global minimum mean cycle)
343        if ( _curr_found && (!_best_found ||
344             _curr_length * _best_size < _best_length * _curr_size) ) {
345          _best_found = true;
346          _best_length = _curr_length;
347          _best_size = _curr_size;
348          _best_node = _curr_node;
349        }
350      }
351      return _best_found;
352    }
353
354    /// \brief Find a minimum mean directed cycle.
355    ///
356    /// This function finds a directed cycle of minimum mean length
357    /// in the digraph using the data computed by findMinMean().
358    ///
359    /// \return \c true if a directed cycle exists in the digraph.
360    ///
361    /// \pre \ref findMinMean() must be called before using this function.
362    bool findCycle() {
363      if (!_best_found) return false;
364      _cycle_path->addBack(_policy[_best_node]);
365      for ( Node v = _best_node;
366            (v = _gr.target(_policy[v])) != _best_node; ) {
367        _cycle_path->addBack(_policy[v]);
368      }
369      return true;
370    }
371
372    /// @}
373
374    /// \name Query Functions
375    /// The results of the algorithm can be obtained using these
376    /// functions.\n
377    /// The algorithm should be executed before using them.
378
379    /// @{
380
381    /// \brief Return the total length of the found cycle.
382    ///
383    /// This function returns the total length of the found cycle.
384    ///
385    /// \pre \ref run() or \ref findMinMean() must be called before
386    /// using this function.
387    LargeValue cycleLength() const {
388      return _best_length;
389    }
390
391    /// \brief Return the number of arcs on the found cycle.
392    ///
393    /// This function returns the number of arcs on the found cycle.
394    ///
395    /// \pre \ref run() or \ref findMinMean() must be called before
396    /// using this function.
397    int cycleArcNum() const {
398      return _best_size;
399    }
400
401    /// \brief Return the mean length of the found cycle.
402    ///
403    /// This function returns the mean length of the found cycle.
404    ///
405    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
406    /// following code.
407    /// \code
408    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
409    /// \endcode
410    ///
411    /// \pre \ref run() or \ref findMinMean() must be called before
412    /// using this function.
413    double cycleMean() const {
414      return static_cast<double>(_best_length) / _best_size;
415    }
416
417    /// \brief Return the found cycle.
418    ///
419    /// This function returns a const reference to the path structure
420    /// storing the found cycle.
421    ///
422    /// \pre \ref run() or \ref findCycle() must be called before using
423    /// this function.
424    const Path& cycle() const {
425      return *_cycle_path;
426    }
427
428    ///@}
429
430  private:
431
432    // Initialize
433    void init() {
434      if (!_cycle_path) {
435        _local_path = true;
436        _cycle_path = new Path;
437      }
438      _queue.resize(countNodes(_gr));
439      _best_found = false;
440      _best_length = 0;
441      _best_size = 1;
442      _cycle_path->clear();
443    }
444   
445    // Find strongly connected components and initialize _comp_nodes
446    // and _in_arcs
447    void findComponents() {
448      _comp_num = stronglyConnectedComponents(_gr, _comp);
449      _comp_nodes.resize(_comp_num);
450      if (_comp_num == 1) {
451        _comp_nodes[0].clear();
452        for (NodeIt n(_gr); n != INVALID; ++n) {
453          _comp_nodes[0].push_back(n);
454          _in_arcs[n].clear();
455          for (InArcIt a(_gr, n); a != INVALID; ++a) {
456            _in_arcs[n].push_back(a);
457          }
458        }
459      } else {
460        for (int i = 0; i < _comp_num; ++i)
461          _comp_nodes[i].clear();
462        for (NodeIt n(_gr); n != INVALID; ++n) {
463          int k = _comp[n];
464          _comp_nodes[k].push_back(n);
465          _in_arcs[n].clear();
466          for (InArcIt a(_gr, n); a != INVALID; ++a) {
467            if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
468          }
469        }
470      }
471    }
472
473    // Build the policy graph in the given strongly connected component
474    // (the out-degree of every node is 1)
475    bool buildPolicyGraph(int comp) {
476      _nodes = &(_comp_nodes[comp]);
477      if (_nodes->size() < 1 ||
478          (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
479        return false;
480      }
481      for (int i = 0; i < int(_nodes->size()); ++i) {
482        _dist[(*_nodes)[i]] = INF;
483      }
484      Node u, v;
485      Arc e;
486      for (int i = 0; i < int(_nodes->size()); ++i) {
487        v = (*_nodes)[i];
488        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
489          e = _in_arcs[v][j];
490          u = _gr.source(e);
491          if (_length[e] < _dist[u]) {
492            _dist[u] = _length[e];
493            _policy[u] = e;
494          }
495        }
496      }
497      return true;
498    }
499
500    // Find the minimum mean cycle in the policy graph
501    void findPolicyCycle() {
502      for (int i = 0; i < int(_nodes->size()); ++i) {
503        _level[(*_nodes)[i]] = -1;
504      }
505      LargeValue clength;
506      int csize;
507      Node u, v;
508      _curr_found = false;
509      for (int i = 0; i < int(_nodes->size()); ++i) {
510        u = (*_nodes)[i];
511        if (_level[u] >= 0) continue;
512        for (; _level[u] < 0; u = _gr.target(_policy[u])) {
513          _level[u] = i;
514        }
515        if (_level[u] == i) {
516          // A cycle is found
517          clength = _length[_policy[u]];
518          csize = 1;
519          for (v = u; (v = _gr.target(_policy[v])) != u; ) {
520            clength += _length[_policy[v]];
521            ++csize;
522          }
523          if ( !_curr_found ||
524               (clength * _curr_size < _curr_length * csize) ) {
525            _curr_found = true;
526            _curr_length = clength;
527            _curr_size = csize;
528            _curr_node = u;
529          }
530        }
531      }
532    }
533
534    // Contract the policy graph and compute node distances
535    bool computeNodeDistances() {
536      // Find the component of the main cycle and compute node distances
537      // using reverse BFS
538      for (int i = 0; i < int(_nodes->size()); ++i) {
539        _reached[(*_nodes)[i]] = false;
540      }
541      _qfront = _qback = 0;
542      _queue[0] = _curr_node;
543      _reached[_curr_node] = true;
544      _dist[_curr_node] = 0;
545      Node u, v;
546      Arc e;
547      while (_qfront <= _qback) {
548        v = _queue[_qfront++];
549        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
550          e = _in_arcs[v][j];
551          u = _gr.source(e);
552          if (_policy[u] == e && !_reached[u]) {
553            _reached[u] = true;
554            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
555            _queue[++_qback] = u;
556          }
557        }
558      }
559
560      // Connect all other nodes to this component and compute node
561      // distances using reverse BFS
562      _qfront = 0;
563      while (_qback < int(_nodes->size())-1) {
564        v = _queue[_qfront++];
565        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
566          e = _in_arcs[v][j];
567          u = _gr.source(e);
568          if (!_reached[u]) {
569            _reached[u] = true;
570            _policy[u] = e;
571            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
572            _queue[++_qback] = u;
573          }
574        }
575      }
576
577      // Improve node distances
578      bool improved = false;
579      for (int i = 0; i < int(_nodes->size()); ++i) {
580        v = (*_nodes)[i];
581        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
582          e = _in_arcs[v][j];
583          u = _gr.source(e);
584          LargeValue delta = _dist[v] + _length[e] * _curr_size - _curr_length;
585          if (_tolerance.less(delta, _dist[u])) {
586            _dist[u] = delta;
587            _policy[u] = e;
588            improved = true;
589          }
590        }
591      }
592      return improved;
593    }
594
595  }; //class Howard
596
597  ///@}
598
599} //namespace lemon
600
601#endif //LEMON_HOWARD_H
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