COIN-OR::LEMON - Graph Library

source: lemon/lemon/howard.h @ 811:1fac515a59c1

Last change on this file since 811:1fac515a59c1 was 811:1fac515a59c1, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Rename MinMeanCycle? to Howard (#179)

File size: 16.9 KB
RevLine 
[805]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
[811]19#ifndef LEMON_HOWARD_H
20#define LEMON_HOWARD_H
[805]21
22/// \ingroup shortest_path
23///
24/// \file
25/// \brief Howard's algorithm for finding a minimum mean cycle.
26
27#include <vector>
[810]28#include <limits>
[805]29#include <lemon/core.h>
30#include <lemon/path.h>
31#include <lemon/tolerance.h>
32#include <lemon/connectivity.h>
33
34namespace lemon {
35
[811]36  /// \brief Default traits class of Howard class.
[808]37  ///
[811]38  /// Default traits class of Howard class.
[808]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
[811]48  struct HowardDefaultTraits
[808]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>
[811]78  struct HowardDefaultTraits<GR, LEN, true>
[808]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
[805]93  /// \addtogroup shortest_path
94  /// @{
95
96  /// \brief Implementation of Howard's algorithm for finding a minimum
97  /// mean cycle.
98  ///
[811]99  /// This class implements Howard's policy iteration algorithm for finding
100  /// a directed cycle of minimum mean length (cost) in a digraph.
[805]101  ///
102  /// \tparam GR The type of the digraph the algorithm runs on.
103  /// \tparam LEN The type of the length map. The default
104  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
105#ifdef DOXYGEN
[808]106  template <typename GR, typename LEN, typename TR>
[805]107#else
108  template < typename GR,
[808]109             typename LEN = typename GR::template ArcMap<int>,
[811]110             typename TR = HowardDefaultTraits<GR, LEN> >
[805]111#endif
[811]112  class Howard
[805]113  {
114  public:
115 
[808]116    /// The type of the digraph
117    typedef typename TR::Digraph Digraph;
[805]118    /// The type of the length map
[808]119    typedef typename TR::LengthMap LengthMap;
[805]120    /// The type of the arc lengths
[808]121    typedef typename TR::Value Value;
122
123    /// \brief The large value type
124    ///
125    /// The large value type used for internal computations.
[811]126    /// Using the \ref HowardDefaultTraits "default traits class",
[808]127    /// it is \c long \c long if the \c Value type is integer,
128    /// otherwise it is \c double.
129    typedef typename TR::LargeValue LargeValue;
130
131    /// The tolerance type
132    typedef typename TR::Tolerance Tolerance;
133
134    /// \brief The path type of the found cycles
135    ///
136    /// The path type of the found cycles.
[811]137    /// Using the \ref HowardDefaultTraits "default traits class",
[808]138    /// it is \ref lemon::Path "Path<Digraph>".
139    typedef typename TR::Path Path;
140
[811]141    /// The \ref HowardDefaultTraits "traits class" of the algorithm
[808]142    typedef TR Traits;
[805]143
144  private:
145
146    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
147 
148    // The digraph the algorithm runs on
149    const Digraph &_gr;
150    // The length of the arcs
151    const LengthMap &_length;
152
[807]153    // Data for the found cycles
154    bool _curr_found, _best_found;
[808]155    LargeValue _curr_length, _best_length;
[807]156    int _curr_size, _best_size;
157    Node _curr_node, _best_node;
158
[805]159    Path *_cycle_path;
[807]160    bool _local_path;
[805]161
[807]162    // Internal data used by the algorithm
163    typename Digraph::template NodeMap<Arc> _policy;
164    typename Digraph::template NodeMap<bool> _reached;
165    typename Digraph::template NodeMap<int> _level;
[808]166    typename Digraph::template NodeMap<LargeValue> _dist;
[805]167
[807]168    // Data for storing the strongly connected components
169    int _comp_num;
[805]170    typename Digraph::template NodeMap<int> _comp;
[807]171    std::vector<std::vector<Node> > _comp_nodes;
172    std::vector<Node>* _nodes;
173    typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
174   
175    // Queue used for BFS search
176    std::vector<Node> _queue;
177    int _qfront, _qback;
[808]178
179    Tolerance _tolerance;
180 
181  public:
182 
183    /// \name Named Template Parameters
184    /// @{
185
186    template <typename T>
187    struct SetLargeValueTraits : public Traits {
188      typedef T LargeValue;
189      typedef lemon::Tolerance<T> Tolerance;
190    };
191
192    /// \brief \ref named-templ-param "Named parameter" for setting
193    /// \c LargeValue type.
194    ///
195    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
196    /// type. It is used for internal computations in the algorithm.
197    template <typename T>
198    struct SetLargeValue
[811]199      : public Howard<GR, LEN, SetLargeValueTraits<T> > {
200      typedef Howard<GR, LEN, SetLargeValueTraits<T> > Create;
[808]201    };
202
203    template <typename T>
204    struct SetPathTraits : public Traits {
205      typedef T Path;
206    };
207
208    /// \brief \ref named-templ-param "Named parameter" for setting
209    /// \c %Path type.
210    ///
211    /// \ref named-templ-param "Named parameter" for setting the \c %Path
212    /// type of the found cycles.
213    /// It must conform to the \ref lemon::concepts::Path "Path" concept
214    /// and it must have an \c addBack() function.
215    template <typename T>
216    struct SetPath
[811]217      : public Howard<GR, LEN, SetPathTraits<T> > {
218      typedef Howard<GR, LEN, SetPathTraits<T> > Create;
[808]219    };
[807]220   
[808]221    /// @}
[805]222
223  public:
224
225    /// \brief Constructor.
226    ///
227    /// The constructor of the class.
228    ///
229    /// \param digraph The digraph the algorithm runs on.
230    /// \param length The lengths (costs) of the arcs.
[811]231    Howard( const Digraph &digraph,
232            const LengthMap &length ) :
[807]233      _gr(digraph), _length(length), _cycle_path(NULL), _local_path(false),
234      _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
235      _comp(digraph), _in_arcs(digraph)
[805]236    {}
237
238    /// Destructor.
[811]239    ~Howard() {
[805]240      if (_local_path) delete _cycle_path;
241    }
242
243    /// \brief Set the path structure for storing the found cycle.
244    ///
245    /// This function sets an external path structure for storing the
246    /// found cycle.
247    ///
248    /// If you don't call this function before calling \ref run() or
[806]249    /// \ref findMinMean(), it will allocate a local \ref Path "path"
[805]250    /// structure. The destuctor deallocates this automatically
251    /// allocated object, of course.
252    ///
253    /// \note The algorithm calls only the \ref lemon::Path::addBack()
254    /// "addBack()" function of the given path structure.
255    ///
256    /// \return <tt>(*this)</tt>
[811]257    Howard& cycle(Path &path) {
[805]258      if (_local_path) {
259        delete _cycle_path;
260        _local_path = false;
261      }
262      _cycle_path = &path;
263      return *this;
264    }
265
266    /// \name Execution control
267    /// The simplest way to execute the algorithm is to call the \ref run()
268    /// function.\n
[806]269    /// If you only need the minimum mean length, you may call
270    /// \ref findMinMean().
[805]271
272    /// @{
273
274    /// \brief Run the algorithm.
275    ///
276    /// This function runs the algorithm.
[806]277    /// It can be called more than once (e.g. if the underlying digraph
278    /// and/or the arc lengths have been modified).
[805]279    ///
280    /// \return \c true if a directed cycle exists in the digraph.
281    ///
[806]282    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
[805]283    /// \code
[806]284    ///   return mmc.findMinMean() && mmc.findCycle();
[805]285    /// \endcode
286    bool run() {
287      return findMinMean() && findCycle();
288    }
289
[806]290    /// \brief Find the minimum cycle mean.
[805]291    ///
[806]292    /// This function finds the minimum mean length of the directed
293    /// cycles in the digraph.
[805]294    ///
[806]295    /// \return \c true if a directed cycle exists in the digraph.
296    bool findMinMean() {
[807]297      // Initialize and find strongly connected components
298      init();
299      findComponents();
300     
[806]301      // Find the minimum cycle mean in the components
[805]302      for (int comp = 0; comp < _comp_num; ++comp) {
[807]303        // Find the minimum mean cycle in the current component
304        if (!buildPolicyGraph(comp)) continue;
[805]305        while (true) {
[807]306          findPolicyCycle();
[805]307          if (!computeNodeDistances()) break;
308        }
[807]309        // Update the best cycle (global minimum mean cycle)
310        if ( !_best_found || (_curr_found &&
311             _curr_length * _best_size < _best_length * _curr_size) ) {
312          _best_found = true;
313          _best_length = _curr_length;
314          _best_size = _curr_size;
315          _best_node = _curr_node;
316        }
[805]317      }
[807]318      return _best_found;
[805]319    }
320
321    /// \brief Find a minimum mean directed cycle.
322    ///
323    /// This function finds a directed cycle of minimum mean length
324    /// in the digraph using the data computed by findMinMean().
325    ///
326    /// \return \c true if a directed cycle exists in the digraph.
327    ///
[806]328    /// \pre \ref findMinMean() must be called before using this function.
[805]329    bool findCycle() {
[807]330      if (!_best_found) return false;
331      _cycle_path->addBack(_policy[_best_node]);
332      for ( Node v = _best_node;
333            (v = _gr.target(_policy[v])) != _best_node; ) {
[805]334        _cycle_path->addBack(_policy[v]);
335      }
336      return true;
337    }
338
339    /// @}
340
341    /// \name Query Functions
[806]342    /// The results of the algorithm can be obtained using these
[805]343    /// functions.\n
344    /// The algorithm should be executed before using them.
345
346    /// @{
347
348    /// \brief Return the total length of the found cycle.
349    ///
350    /// This function returns the total length of the found cycle.
351    ///
[807]352    /// \pre \ref run() or \ref findMinMean() must be called before
[805]353    /// using this function.
[808]354    LargeValue cycleLength() const {
[807]355      return _best_length;
[805]356    }
357
358    /// \brief Return the number of arcs on the found cycle.
359    ///
360    /// This function returns the number of arcs on the found cycle.
361    ///
[807]362    /// \pre \ref run() or \ref findMinMean() must be called before
[805]363    /// using this function.
364    int cycleArcNum() const {
[807]365      return _best_size;
[805]366    }
367
368    /// \brief Return the mean length of the found cycle.
369    ///
370    /// This function returns the mean length of the found cycle.
371    ///
[807]372    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
[805]373    /// following code.
374    /// \code
[807]375    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
[805]376    /// \endcode
377    ///
378    /// \pre \ref run() or \ref findMinMean() must be called before
379    /// using this function.
380    double cycleMean() const {
[807]381      return static_cast<double>(_best_length) / _best_size;
[805]382    }
383
384    /// \brief Return the found cycle.
385    ///
386    /// This function returns a const reference to the path structure
387    /// storing the found cycle.
388    ///
389    /// \pre \ref run() or \ref findCycle() must be called before using
390    /// this function.
391    const Path& cycle() const {
392      return *_cycle_path;
393    }
394
395    ///@}
396
397  private:
398
[807]399    // Initialize
400    void init() {
401      if (!_cycle_path) {
402        _local_path = true;
403        _cycle_path = new Path;
[805]404      }
[807]405      _queue.resize(countNodes(_gr));
406      _best_found = false;
407      _best_length = 0;
408      _best_size = 1;
409      _cycle_path->clear();
410    }
411   
412    // Find strongly connected components and initialize _comp_nodes
413    // and _in_arcs
414    void findComponents() {
415      _comp_num = stronglyConnectedComponents(_gr, _comp);
416      _comp_nodes.resize(_comp_num);
417      if (_comp_num == 1) {
418        _comp_nodes[0].clear();
419        for (NodeIt n(_gr); n != INVALID; ++n) {
420          _comp_nodes[0].push_back(n);
421          _in_arcs[n].clear();
422          for (InArcIt a(_gr, n); a != INVALID; ++a) {
423            _in_arcs[n].push_back(a);
424          }
425        }
426      } else {
427        for (int i = 0; i < _comp_num; ++i)
428          _comp_nodes[i].clear();
429        for (NodeIt n(_gr); n != INVALID; ++n) {
430          int k = _comp[n];
431          _comp_nodes[k].push_back(n);
432          _in_arcs[n].clear();
433          for (InArcIt a(_gr, n); a != INVALID; ++a) {
434            if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
435          }
436        }
[805]437      }
[807]438    }
439
440    // Build the policy graph in the given strongly connected component
441    // (the out-degree of every node is 1)
442    bool buildPolicyGraph(int comp) {
443      _nodes = &(_comp_nodes[comp]);
444      if (_nodes->size() < 1 ||
445          (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
446        return false;
[805]447      }
[807]448      for (int i = 0; i < int(_nodes->size()); ++i) {
[808]449        _dist[(*_nodes)[i]] = std::numeric_limits<LargeValue>::max();
[807]450      }
451      Node u, v;
452      Arc e;
453      for (int i = 0; i < int(_nodes->size()); ++i) {
454        v = (*_nodes)[i];
455        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
456          e = _in_arcs[v][j];
457          u = _gr.source(e);
458          if (_length[e] < _dist[u]) {
459            _dist[u] = _length[e];
460            _policy[u] = e;
461          }
[805]462        }
463      }
464      return true;
465    }
466
[807]467    // Find the minimum mean cycle in the policy graph
468    void findPolicyCycle() {
469      for (int i = 0; i < int(_nodes->size()); ++i) {
470        _level[(*_nodes)[i]] = -1;
471      }
[808]472      LargeValue clength;
[805]473      int csize;
474      Node u, v;
[807]475      _curr_found = false;
476      for (int i = 0; i < int(_nodes->size()); ++i) {
477        u = (*_nodes)[i];
478        if (_level[u] >= 0) continue;
479        for (; _level[u] < 0; u = _gr.target(_policy[u])) {
480          _level[u] = i;
481        }
482        if (_level[u] == i) {
483          // A cycle is found
484          clength = _length[_policy[u]];
485          csize = 1;
486          for (v = u; (v = _gr.target(_policy[v])) != u; ) {
487            clength += _length[_policy[v]];
488            ++csize;
[805]489          }
[807]490          if ( !_curr_found ||
491               (clength * _curr_size < _curr_length * csize) ) {
492            _curr_found = true;
493            _curr_length = clength;
494            _curr_size = csize;
495            _curr_node = u;
[805]496          }
497        }
498      }
499    }
500
[807]501    // Contract the policy graph and compute node distances
[805]502    bool computeNodeDistances() {
[807]503      // Find the component of the main cycle and compute node distances
504      // using reverse BFS
505      for (int i = 0; i < int(_nodes->size()); ++i) {
506        _reached[(*_nodes)[i]] = false;
507      }
508      _qfront = _qback = 0;
509      _queue[0] = _curr_node;
510      _reached[_curr_node] = true;
511      _dist[_curr_node] = 0;
[805]512      Node u, v;
[807]513      Arc e;
514      while (_qfront <= _qback) {
515        v = _queue[_qfront++];
516        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
517          e = _in_arcs[v][j];
[805]518          u = _gr.source(e);
[807]519          if (_policy[u] == e && !_reached[u]) {
520            _reached[u] = true;
[808]521            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
[807]522            _queue[++_qback] = u;
[805]523          }
524        }
525      }
[807]526
527      // Connect all other nodes to this component and compute node
528      // distances using reverse BFS
529      _qfront = 0;
530      while (_qback < int(_nodes->size())-1) {
531        v = _queue[_qfront++];
532        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
533          e = _in_arcs[v][j];
534          u = _gr.source(e);
535          if (!_reached[u]) {
536            _reached[u] = true;
537            _policy[u] = e;
[808]538            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
[807]539            _queue[++_qback] = u;
540          }
541        }
542      }
543
544      // Improve node distances
[805]545      bool improved = false;
[807]546      for (int i = 0; i < int(_nodes->size()); ++i) {
547        v = (*_nodes)[i];
548        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
549          e = _in_arcs[v][j];
550          u = _gr.source(e);
[808]551          LargeValue delta = _dist[v] + _length[e] * _curr_size - _curr_length;
552          if (_tolerance.less(delta, _dist[u])) {
[807]553            _dist[u] = delta;
554            _policy[u] = e;
555            improved = true;
556          }
[805]557        }
558      }
559      return improved;
560    }
561
[811]562  }; //class Howard
[805]563
564  ///@}
565
566} //namespace lemon
567
[811]568#endif //LEMON_HOWARD_H
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