COIN-OR::LEMON - Graph Library

source: lemon/lemon/min_mean_cycle.h @ 806:d66ff32624e2

Last change on this file since 806:d66ff32624e2 was 806:d66ff32624e2, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Simplify the interface of MinMeanCycle? (#179)
Remove init() and reset(), and move their content into findMinMean().

File size: 13.0 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_MIN_MEAN_CYCLE_H
20#define LEMON_MIN_MEAN_CYCLE_H
21
22/// \ingroup shortest_path
23///
24/// \file
25/// \brief Howard's algorithm for finding a minimum mean cycle.
26
27#include <vector>
28#include <lemon/core.h>
29#include <lemon/path.h>
30#include <lemon/tolerance.h>
31#include <lemon/connectivity.h>
32
33namespace lemon {
34
35  /// \addtogroup shortest_path
36  /// @{
37
38  /// \brief Implementation of Howard's algorithm for finding a minimum
39  /// mean cycle.
40  ///
41  /// \ref MinMeanCycle implements Howard's algorithm for finding a
42  /// directed cycle of minimum mean length (cost) in a digraph.
43  ///
44  /// \tparam GR The type of the digraph the algorithm runs on.
45  /// \tparam LEN The type of the length map. The default
46  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
47  ///
48  /// \warning \c LEN::Value must be convertible to \c double.
49#ifdef DOXYGEN
50  template <typename GR, typename LEN>
51#else
52  template < typename GR,
53             typename LEN = typename GR::template ArcMap<int> >
54#endif
55  class MinMeanCycle
56  {
57  public:
58 
59    /// The type of the digraph the algorithm runs on
60    typedef GR Digraph;
61    /// The type of the length map
62    typedef LEN LengthMap;
63    /// The type of the arc lengths
64    typedef typename LengthMap::Value Value;
65    /// The type of the paths
66    typedef lemon::Path<Digraph> Path;
67
68  private:
69
70    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
71 
72    // The digraph the algorithm runs on
73    const Digraph &_gr;
74    // The length of the arcs
75    const LengthMap &_length;
76
77    // The total length of the found cycle
78    Value _cycle_length;
79    // The number of arcs on the found cycle
80    int _cycle_size;
81    // The found cycle
82    Path *_cycle_path;
83
84    bool _local_path;
85    bool _cycle_found;
86    Node _cycle_node;
87
88    typename Digraph::template NodeMap<bool> _reached;
89    typename Digraph::template NodeMap<double> _dist;
90    typename Digraph::template NodeMap<Arc> _policy;
91
92    typename Digraph::template NodeMap<int> _comp;
93    int _comp_num;
94
95    std::vector<Node> _nodes;
96    std::vector<Arc> _arcs;
97    Tolerance<double> _tol;
98
99  public:
100
101    /// \brief Constructor.
102    ///
103    /// The constructor of the class.
104    ///
105    /// \param digraph The digraph the algorithm runs on.
106    /// \param length The lengths (costs) of the arcs.
107    MinMeanCycle( const Digraph &digraph,
108                  const LengthMap &length ) :
109      _gr(digraph), _length(length), _cycle_length(0), _cycle_size(-1),
110      _cycle_path(NULL), _local_path(false), _reached(digraph),
111      _dist(digraph), _policy(digraph), _comp(digraph)
112    {}
113
114    /// Destructor.
115    ~MinMeanCycle() {
116      if (_local_path) delete _cycle_path;
117    }
118
119    /// \brief Set the path structure for storing the found cycle.
120    ///
121    /// This function sets an external path structure for storing the
122    /// found cycle.
123    ///
124    /// If you don't call this function before calling \ref run() or
125    /// \ref findMinMean(), it will allocate a local \ref Path "path"
126    /// structure. The destuctor deallocates this automatically
127    /// allocated object, of course.
128    ///
129    /// \note The algorithm calls only the \ref lemon::Path::addBack()
130    /// "addBack()" function of the given path structure.
131    ///
132    /// \return <tt>(*this)</tt>
133    ///
134    /// \sa cycle()
135    MinMeanCycle& cyclePath(Path &path) {
136      if (_local_path) {
137        delete _cycle_path;
138        _local_path = false;
139      }
140      _cycle_path = &path;
141      return *this;
142    }
143
144    /// \name Execution control
145    /// The simplest way to execute the algorithm is to call the \ref run()
146    /// function.\n
147    /// If you only need the minimum mean length, you may call
148    /// \ref findMinMean().
149
150    /// @{
151
152    /// \brief Run the algorithm.
153    ///
154    /// This function runs the algorithm.
155    /// It can be called more than once (e.g. if the underlying digraph
156    /// and/or the arc lengths have been modified).
157    ///
158    /// \return \c true if a directed cycle exists in the digraph.
159    ///
160    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
161    /// \code
162    ///   return mmc.findMinMean() && mmc.findCycle();
163    /// \endcode
164    bool run() {
165      return findMinMean() && findCycle();
166    }
167
168    /// \brief Find the minimum cycle mean.
169    ///
170    /// This function finds the minimum mean length of the directed
171    /// cycles in the digraph.
172    ///
173    /// \return \c true if a directed cycle exists in the digraph.
174    bool findMinMean() {
175      // Initialize
176      _tol.epsilon(1e-6);
177      if (!_cycle_path) {
178        _local_path = true;
179        _cycle_path = new Path;
180      }
181      _cycle_path->clear();
182      _cycle_found = false;
183
184      // Find the minimum cycle mean in the components
185      _comp_num = stronglyConnectedComponents(_gr, _comp);
186      for (int comp = 0; comp < _comp_num; ++comp) {
187        if (!initCurrentComponent(comp)) continue;
188        while (true) {
189          if (!findPolicyCycles()) break;
190          contractPolicyGraph(comp);
191          if (!computeNodeDistances()) break;
192        }
193      }
194      return _cycle_found;
195    }
196
197    /// \brief Find a minimum mean directed cycle.
198    ///
199    /// This function finds a directed cycle of minimum mean length
200    /// in the digraph using the data computed by findMinMean().
201    ///
202    /// \return \c true if a directed cycle exists in the digraph.
203    ///
204    /// \pre \ref findMinMean() must be called before using this function.
205    bool findCycle() {
206      if (!_cycle_found) return false;
207      _cycle_path->addBack(_policy[_cycle_node]);
208      for ( Node v = _cycle_node;
209            (v = _gr.target(_policy[v])) != _cycle_node; ) {
210        _cycle_path->addBack(_policy[v]);
211      }
212      return true;
213    }
214
215    /// @}
216
217    /// \name Query Functions
218    /// The results of the algorithm can be obtained using these
219    /// functions.\n
220    /// The algorithm should be executed before using them.
221
222    /// @{
223
224    /// \brief Return the total length of the found cycle.
225    ///
226    /// This function returns the total length of the found cycle.
227    ///
228    /// \pre \ref run() or \ref findCycle() must be called before
229    /// using this function.
230    Value cycleLength() const {
231      return _cycle_length;
232    }
233
234    /// \brief Return the number of arcs on the found cycle.
235    ///
236    /// This function returns the number of arcs on the found cycle.
237    ///
238    /// \pre \ref run() or \ref findCycle() must be called before
239    /// using this function.
240    int cycleArcNum() const {
241      return _cycle_size;
242    }
243
244    /// \brief Return the mean length of the found cycle.
245    ///
246    /// This function returns the mean length of the found cycle.
247    ///
248    /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the
249    /// following code.
250    /// \code
251    ///   return double(mmc.cycleLength()) / mmc.cycleArcNum();
252    /// \endcode
253    ///
254    /// \pre \ref run() or \ref findMinMean() must be called before
255    /// using this function.
256    double cycleMean() const {
257      return double(_cycle_length) / _cycle_size;
258    }
259
260    /// \brief Return the found cycle.
261    ///
262    /// This function returns a const reference to the path structure
263    /// storing the found cycle.
264    ///
265    /// \pre \ref run() or \ref findCycle() must be called before using
266    /// this function.
267    ///
268    /// \sa cyclePath()
269    const Path& cycle() const {
270      return *_cycle_path;
271    }
272
273    ///@}
274
275  private:
276
277    // Initialize the internal data structures for the current strongly
278    // connected component and create the policy graph.
279    // The policy graph can be represented by the _policy map because
280    // the out-degree of every node is 1.
281    bool initCurrentComponent(int comp) {
282      // Find the nodes of the current component
283      _nodes.clear();
284      for (NodeIt n(_gr); n != INVALID; ++n) {
285        if (_comp[n] == comp) _nodes.push_back(n);
286      }
287      if (_nodes.size() <= 1) return false;
288      // Find the arcs of the current component
289      _arcs.clear();
290      for (ArcIt e(_gr); e != INVALID; ++e) {
291        if ( _comp[_gr.source(e)] == comp &&
292             _comp[_gr.target(e)] == comp )
293          _arcs.push_back(e);
294      }
295      // Initialize _reached, _dist, _policy maps
296      for (int i = 0; i < int(_nodes.size()); ++i) {
297        _reached[_nodes[i]] = false;
298        _policy[_nodes[i]] = INVALID;
299      }
300      Node u; Arc e;
301      for (int j = 0; j < int(_arcs.size()); ++j) {
302        e = _arcs[j];
303        u = _gr.source(e);
304        if (!_reached[u] || _length[e] < _dist[u]) {
305          _dist[u] = _length[e];
306          _policy[u] = e;
307          _reached[u] = true;
308        }
309      }
310      return true;
311    }
312
313    // Find all cycles in the policy graph.
314    // Set _cycle_found to true if a cycle is found and set
315    // _cycle_length, _cycle_size, _cycle_node to represent the minimum
316    // mean cycle in the policy graph.
317    bool findPolicyCycles() {
318      typename Digraph::template NodeMap<int> level(_gr, -1);
319      bool curr_cycle_found = false;
320      Value clength;
321      int csize;
322      int path_cnt = 0;
323      Node u, v;
324      // Searching for cycles
325      for (int i = 0; i < int(_nodes.size()); ++i) {
326        if (level[_nodes[i]] < 0) {
327          u = _nodes[i];
328          level[u] = path_cnt;
329          while (level[u = _gr.target(_policy[u])] < 0)
330            level[u] = path_cnt;
331          if (level[u] == path_cnt) {
332            // A cycle is found
333            curr_cycle_found = true;
334            clength = _length[_policy[u]];
335            csize = 1;
336            for (v = u; (v = _gr.target(_policy[v])) != u; ) {
337              clength += _length[_policy[v]];
338              ++csize;
339            }
340            if ( !_cycle_found ||
341                 clength * _cycle_size < _cycle_length * csize ) {
342              _cycle_found = true;
343              _cycle_length = clength;
344              _cycle_size = csize;
345              _cycle_node = u;
346            }
347          }
348          ++path_cnt;
349        }
350      }
351      return curr_cycle_found;
352    }
353
354    // Contract the policy graph to be connected by cutting all cycles
355    // except for the main cycle (i.e. the minimum mean cycle).
356    void contractPolicyGraph(int comp) {
357      // Find the component of the main cycle using reverse BFS search
358      typename Digraph::template NodeMap<int> found(_gr, false);
359      std::deque<Node> queue;
360      queue.push_back(_cycle_node);
361      found[_cycle_node] = true;
362      Node u, v;
363      while (!queue.empty()) {
364        v = queue.front(); queue.pop_front();
365        for (InArcIt e(_gr, v); e != INVALID; ++e) {
366          u = _gr.source(e);
367          if (_policy[u] == e && !found[u]) {
368            found[u] = true;
369            queue.push_back(u);
370          }
371        }
372      }
373      // Connect all other nodes to this component using reverse BFS search
374      queue.clear();
375      for (int i = 0; i < int(_nodes.size()); ++i)
376        if (found[_nodes[i]]) queue.push_back(_nodes[i]);
377      int found_cnt = queue.size();
378      while (found_cnt < int(_nodes.size())) {
379        v = queue.front(); queue.pop_front();
380        for (InArcIt e(_gr, v); e != INVALID; ++e) {
381          u = _gr.source(e);
382          if (_comp[u] == comp && !found[u]) {
383            found[u] = true;
384            ++found_cnt;
385            _policy[u] = e;
386            queue.push_back(u);
387          }
388        }
389      }
390    }
391
392    // Compute node distances in the policy graph and update the
393    // policy graph if the node distances can be improved.
394    bool computeNodeDistances() {
395      // Compute node distances using reverse BFS search
396      double cycle_mean = double(_cycle_length) / _cycle_size;
397      typename Digraph::template NodeMap<int> found(_gr, false);
398      std::deque<Node> queue;
399      queue.push_back(_cycle_node);
400      found[_cycle_node] = true;
401      _dist[_cycle_node] = 0;
402      Node u, v;
403      while (!queue.empty()) {
404        v = queue.front(); queue.pop_front();
405        for (InArcIt e(_gr, v); e != INVALID; ++e) {
406          u = _gr.source(e);
407          if (_policy[u] == e && !found[u]) {
408            found[u] = true;
409            _dist[u] = _dist[v] + _length[e] - cycle_mean;
410            queue.push_back(u);
411          }
412        }
413      }
414      // Improving node distances
415      bool improved = false;
416      for (int j = 0; j < int(_arcs.size()); ++j) {
417        Arc e = _arcs[j];
418        u = _gr.source(e); v = _gr.target(e);
419        double delta = _dist[v] + _length[e] - cycle_mean;
420        if (_tol.less(delta, _dist[u])) {
421          improved = true;
422          _dist[u] = delta;
423          _policy[u] = e;
424        }
425      }
426      return improved;
427    }
428
429  }; //class MinMeanCycle
430
431  ///@}
432
433} //namespace lemon
434
435#endif //LEMON_MIN_MEAN_CYCLE_H
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