COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/min_mean_cycle.h

Last change on this file was 2620:8f41a3129746, checked in by Peter Kovacs, 11 years ago

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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_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 directed cycle.
26
27#include <vector>
28#include <lemon/graph_utils.h>
29#include <lemon/path.h>
30#include <lemon/tolerance.h>
31#include <lemon/topology.h>
32
33namespace lemon {
34
35  /// \addtogroup shortest_path
36  /// @{
37
38  /// \brief Implementation of Howard's algorithm for finding a minimum
39  /// mean directed cycle.
40  ///
41  /// \ref MinMeanCycle implements Howard's algorithm for finding a
42  /// minimum mean directed cycle.
43  ///
44  /// \tparam Graph The directed graph type the algorithm runs on.
45  /// \tparam LengthMap The type of the length (cost) map.
46  ///
47  /// \warning \c LengthMap::Value must be convertible to \c double.
48  ///
49  /// \author Peter Kovacs
50
51  template < typename Graph,
52             typename LengthMap = typename Graph::template EdgeMap<int> >
53  class MinMeanCycle
54  {
55    GRAPH_TYPEDEFS(typename Graph);
56
57    typedef typename LengthMap::Value Length;
58    typedef lemon::Path<Graph> Path;
59
60  private:
61
62    // The directed graph the algorithm runs on
63    const Graph &_graph;
64    // The length of the edges
65    const LengthMap &_length;
66
67    // The total length of the found cycle
68    Length _cycle_length;
69    // The number of edges on the found cycle
70    int _cycle_size;
71    // The found cycle
72    Path *_cycle_path;
73
74    bool _local_path;
75    bool _cycle_found;
76    Node _cycle_node;
77
78    typename Graph::template NodeMap<bool> _reached;
79    typename Graph::template NodeMap<double> _dist;
80    typename Graph::template NodeMap<Edge> _policy;
81
82    typename Graph::template NodeMap<int> _component;
83    int _component_num;
84
85    std::vector<Node> _nodes;
86    std::vector<Edge> _edges;
87    Tolerance<double> _tolerance;
88
89  public:
90
91    /// \brief The constructor of the class.
92    ///
93    /// The constructor of the class.
94    ///
95    /// \param graph The directed graph the algorithm runs on.
96    /// \param length The length (cost) of the edges.
97    MinMeanCycle( const Graph &graph,
98                  const LengthMap &length ) :
99      _graph(graph), _length(length), _cycle_length(0), _cycle_size(-1),
100      _cycle_path(NULL), _local_path(false), _reached(graph),
101      _dist(graph), _policy(graph), _component(graph)
102    {}
103
104    /// The destructor of the class.
105    ~MinMeanCycle() {
106      if (_local_path) delete _cycle_path;
107    }
108
109    /// \brief Sets the \ref Path "path" structure for storing the found
110    /// cycle.
111    ///
112    /// Sets an external \ref Path "path" structure for storing the
113    /// found cycle.
114    ///
115    /// If you don't call this function before calling \ref run() or
116    /// \ref init(), it will allocate a local \ref Path "path"
117    /// structure.
118    /// The destuctor deallocates this automatically allocated map,
119    /// of course.
120    ///
121    /// \note The algorithm calls only the \ref lemon::Path::addBack()
122    /// "addBack()" function of the given \ref Path "path" structure.
123    ///
124    /// \return <tt>(*this)</tt>
125    ///
126    /// \sa cycle()
127    MinMeanCycle& cyclePath(Path &path) {
128      if (_local_path) {
129        delete _cycle_path;
130        _local_path = false;
131      }
132      _cycle_path = &path;
133      return *this;
134    }
135
136    /// \name Execution control
137    /// The simplest way to execute the algorithm is to call the run()
138    /// function.
139    /// \n
140    /// If you only need the minimum mean value, you may call init()
141    /// and findMinMean().
142    /// \n
143    /// If you would like to run the algorithm again (e.g. the
144    /// underlaying graph and/or the edge costs were modified), you may
145    /// not create a new instance of the class, rather call reset(),
146    /// findMinMean(), and findCycle() instead.
147
148    /// @{
149
150    /// \brief Runs the algorithm.
151    ///
152    /// Runs the algorithm.
153    ///
154    /// \return Returns \c true if a directed cycle exists in the graph.
155    ///
156    /// \note Apart from the return value, <tt>mmc.run()</tt> is just a
157    /// shortcut of the following code.
158    /// \code
159    ///   mmc.init();
160    ///   mmc.findMinMean();
161    ///   mmc.findCycle();
162    /// \endcode
163    bool run() {
164      init();
165      return findMinMean() && findCycle();
166    }
167
168    /// \brief Initializes the internal data structures.
169    ///
170    /// Initializes the internal data structures.
171    ///
172    /// \sa reset()
173    void init() {
174      _tolerance.epsilon(1e-6);
175      if (!_cycle_path) {
176        _local_path = true;
177        _cycle_path = new Path;
178      }
179      _cycle_found = false;
180      _component_num = stronglyConnectedComponents(_graph, _component);
181    }
182
183    /// \brief Resets the internal data structures.
184    ///
185    /// Resets the internal data structures so that \ref findMinMean()
186    /// and \ref findCycle() can be called again (e.g. when the
187    /// underlaying graph has been modified).
188    ///
189    /// \sa init()
190    void reset() {
191      if (_cycle_path) _cycle_path->clear();
192      _cycle_found = false;
193      _component_num = stronglyConnectedComponents(_graph, _component);
194    }
195
196    /// \brief Finds the minimum cycle mean length in the graph.
197    ///
198    /// Computes all the required data and finds the minimum cycle mean
199    /// length in the graph.
200    ///
201    /// \return Returns \c true if a directed cycle exists in the graph.
202    ///
203    /// \pre \ref init() must be called before using this function.
204    bool findMinMean() {
205      // Finding the minimum mean cycle in the components
206      for (int comp = 0; comp < _component_num; ++comp) {
207        if (!initCurrentComponent(comp)) continue;
208        while (true) {
209          if (!findPolicyCycles()) break;
210          contractPolicyGraph(comp);
211          if (!computeNodeDistances(comp)) break;
212        }
213      }
214      return _cycle_found;
215    }
216
217    /// \brief Finds a critical (minimum mean) directed cycle.
218    ///
219    /// Finds a critical (minimum mean) directed cycle using the data
220    /// computed in the \ref findMinMean() function.
221    ///
222    /// \return Returns \c true if a directed cycle exists in the graph.
223    ///
224    /// \pre \ref init() and \ref findMinMean() must be called before
225    /// using this function.
226    bool findCycle() {
227      if (!_cycle_found) return false;
228      _cycle_path->addBack(_policy[_cycle_node]);
229      for ( Node v = _cycle_node;
230            (v = _graph.target(_policy[v])) != _cycle_node; ) {
231        _cycle_path->addBack(_policy[v]);
232      }
233      return true;
234    }
235
236    /// @}
237
238    /// \name Query Functions
239    /// The result of the algorithm can be obtained using these
240    /// functions.
241    /// \n The algorithm should be executed before using them.
242
243    /// @{
244
245    /// \brief Returns the total length of the found cycle.
246    ///
247    /// Returns the total length of the found cycle.
248    ///
249    /// \pre \ref run() or \ref findMinMean() must be called before
250    /// using this function.
251    Length cycleLength() const {
252      return _cycle_length;
253    }
254
255    /// \brief Returns the number of edges on the found cycle.
256    ///
257    /// Returns the number of edges on the found cycle.
258    ///
259    /// \pre \ref run() or \ref findMinMean() must be called before
260    /// using this function.
261    int cycleEdgeNum() const {
262      return _cycle_size;
263    }
264
265    /// \brief Returns the mean length of the found cycle.
266    ///
267    /// Returns the mean length of the found cycle.
268    ///
269    /// \pre \ref run() or \ref findMinMean() must be called before
270    /// using this function.
271    ///
272    /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the
273    /// following code.
274    /// \code
275    ///   return double(mmc.cycleLength()) / mmc.cycleEdgeNum();
276    /// \endcode
277    double cycleMean() const {
278      return double(_cycle_length) / _cycle_size;
279    }
280
281    /// \brief Returns a const reference to the \ref Path "path"
282    /// structure storing the found cycle.
283    ///
284    /// Returns a const reference to the \ref Path "path"
285    /// structure storing the found cycle.
286    ///
287    /// \pre \ref run() or \ref findCycle() must be called before using
288    /// this function.
289    ///
290    /// \sa cyclePath()
291    const Path& cycle() const {
292      return *_cycle_path;
293    }
294
295    ///@}
296
297  private:
298
299    // Initializes the internal data structures for the current strongly
300    // connected component and creating the policy graph.
301    // The policy graph can be represented by the _policy map because
302    // the out degree of every node is 1.
303    bool initCurrentComponent(int comp) {
304      // Finding the nodes of the current component
305      _nodes.clear();
306      for (NodeIt n(_graph); n != INVALID; ++n) {
307        if (_component[n] == comp) _nodes.push_back(n);
308      }
309      if (_nodes.size() <= 1) return false;
310      // Finding the edges of the current component
311      _edges.clear();
312      for (EdgeIt e(_graph); e != INVALID; ++e) {
313        if ( _component[_graph.source(e)] == comp &&
314             _component[_graph.target(e)] == comp )
315          _edges.push_back(e);
316      }
317      // Initializing _reached, _dist, _policy maps
318      for (int i = 0; i < int(_nodes.size()); ++i) {
319        _reached[_nodes[i]] = false;
320        _policy[_nodes[i]] = INVALID;
321      }
322      Node u; Edge e;
323      for (int j = 0; j < int(_edges.size()); ++j) {
324        e = _edges[j];
325        u = _graph.source(e);
326        if (!_reached[u] || _length[e] < _dist[u]) {
327          _dist[u] = _length[e];
328          _policy[u] = e;
329          _reached[u] = true;
330        }
331      }
332      return true;
333    }
334
335    // Finds all cycles in the policy graph.
336    // Sets _cycle_found to true if a cycle is found and sets
337    // _cycle_length, _cycle_size, _cycle_node to represent the minimum
338    // mean cycle in the policy graph.
339    bool findPolicyCycles() {
340      typename Graph::template NodeMap<int> level(_graph, -1);
341      bool curr_cycle_found = false;
342      Length clength;
343      int csize;
344      int path_cnt = 0;
345      Node u, v;
346      // Searching for cycles
347      for (int i = 0; i < int(_nodes.size()); ++i) {
348        if (level[_nodes[i]] < 0) {
349          u = _nodes[i];
350          level[u] = path_cnt;
351          while (level[u = _graph.target(_policy[u])] < 0)
352            level[u] = path_cnt;
353          if (level[u] == path_cnt) {
354            // A cycle is found
355            curr_cycle_found = true;
356            clength = _length[_policy[u]];
357            csize = 1;
358            for (v = u; (v = _graph.target(_policy[v])) != u; ) {
359              clength += _length[_policy[v]];
360              ++csize;
361            }
362            if ( !_cycle_found ||
363                 clength * _cycle_size < _cycle_length * csize ) {
364              _cycle_found = true;
365              _cycle_length = clength;
366              _cycle_size = csize;
367              _cycle_node = u;
368            }
369          }
370          ++path_cnt;
371        }
372      }
373      return curr_cycle_found;
374    }
375
376    // Contracts the policy graph to be connected by cutting all cycles
377    // except for the main cycle (i.e. the minimum mean cycle).
378    void contractPolicyGraph(int comp) {
379      // Finding the component of the main cycle using
380      // reverse BFS search
381      typename Graph::template NodeMap<int> found(_graph, false);
382      std::deque<Node> queue;
383      queue.push_back(_cycle_node);
384      found[_cycle_node] = true;
385      Node u, v;
386      while (!queue.empty()) {
387        v = queue.front(); queue.pop_front();
388        for (InEdgeIt e(_graph, v); e != INVALID; ++e) {
389          u = _graph.source(e);
390          if (_component[u] == comp && !found[u] && _policy[u] == e) {
391            found[u] = true;
392            queue.push_back(u);
393          }
394        }
395      }
396      // Connecting all other nodes to this component using
397      // reverse BFS search
398      queue.clear();
399      for (int i = 0; i < int(_nodes.size()); ++i)
400        if (found[_nodes[i]]) queue.push_back(_nodes[i]);
401      int found_cnt = queue.size();
402      while (found_cnt < int(_nodes.size()) && !queue.empty()) {
403        v = queue.front(); queue.pop_front();
404        for (InEdgeIt e(_graph, v); e != INVALID; ++e) {
405          u = _graph.source(e);
406          if (_component[u] == comp && !found[u]) {
407            found[u] = true;
408            ++found_cnt;
409            _policy[u] = e;
410            queue.push_back(u);
411          }
412        }
413      }
414    }
415
416    // Computes node distances in the policy graph and updates the
417    // policy graph if the node distances can be improved.
418    bool computeNodeDistances(int comp) {
419      // Computing node distances using reverse BFS search
420      double cycle_mean = double(_cycle_length) / _cycle_size;
421      typename Graph::template NodeMap<int> found(_graph, false);
422      std::deque<Node> queue;
423      queue.push_back(_cycle_node);
424      found[_cycle_node] = true;
425      _dist[_cycle_node] = 0;
426      Node u, v;
427      while (!queue.empty()) {
428        v = queue.front(); queue.pop_front();
429        for (InEdgeIt e(_graph, v); e != INVALID; ++e) {
430          u = _graph.source(e);
431          if (_component[u] == comp && !found[u] && _policy[u] == e) {
432            found[u] = true;
433            _dist[u] = _dist[v] + _length[e] - cycle_mean;
434            queue.push_back(u);
435          }
436        }
437      }
438      // Improving node distances
439      bool improved = false;
440      for (int j = 0; j < int(_edges.size()); ++j) {
441        Edge e = _edges[j];
442        u = _graph.source(e); v = _graph.target(e);
443        double delta = _dist[v] + _length[e] - cycle_mean;
444        if (_tolerance.less(delta, _dist[u])) {
445          improved = true;
446          _dist[u] = delta;
447          _policy[u] = e;
448        }
449      }
450      return improved;
451    }
452
453  }; //class MinMeanCycle
454
455  ///@}
456
457} //namespace lemon
458
459#endif //LEMON_MIN_MEAN_CYCLE_H
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