COIN-OR::LEMON - Graph Library

source: lemon/lemon/hartmann_orlin.h @ 815:0a42883c8221

Last change on this file since 815:0a42883c8221 was 815:0a42883c8221, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Separate group for the min mean cycle classes (#179)

File size: 18.5 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_HARTMANN_ORLIN_H
20#define LEMON_HARTMANN_ORLIN_H
21
22/// \ingroup min_mean_cycle
23///
24/// \file
25/// \brief Hartmann-Orlin'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 HartmannOrlin algorithm.
37  ///
38  /// Default traits class of HartmannOrlin algorithm.
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::Rea_data "Rea_data" 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 HartmannOrlinDefaultTraits
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 HartmannOrlinDefaultTraits<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 the Hartmann-Orlin algorithm for finding
97  /// a minimum mean cycle.
98  ///
99  /// This class implements the Hartmann-Orlin algorithm for finding
100  /// a directed cycle of minimum mean length (cost) in a digraph.
101  /// It is an improved version of \ref Karp "Karp"'s original algorithm,
102  /// it applies an efficient early termination scheme.
103  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
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 = HartmannOrlinDefaultTraits<GR, LEN> >
114#endif
115  class HartmannOrlin
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 HartmannOrlinDefaultTraits "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 HartmannOrlinDefaultTraits "default traits class",
141    /// it is \ref lemon::Path "Path<Digraph>".
142    typedef typename TR::Path Path;
143
144    /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm
145    typedef TR Traits;
146
147  private:
148
149    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
150
151    // Data sturcture for path data
152    struct PathData
153    {
154      LargeValue dist;
155      Arc pred;
156      PathData(LargeValue d, Arc p = INVALID) :
157        dist(d), pred(p) {}
158    };
159
160    typedef typename Digraph::template NodeMap<std::vector<PathData> >
161      PathDataNodeMap;
162
163  private:
164
165    // The digraph the algorithm runs on
166    const Digraph &_gr;
167    // The length of the arcs
168    const LengthMap &_length;
169
170    // Data for storing the strongly connected components
171    int _comp_num;
172    typename Digraph::template NodeMap<int> _comp;
173    std::vector<std::vector<Node> > _comp_nodes;
174    std::vector<Node>* _nodes;
175    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
176
177    // Data for the found cycles
178    bool _curr_found, _best_found;
179    LargeValue _curr_length, _best_length;
180    int _curr_size, _best_size;
181    Node _curr_node, _best_node;
182    int _curr_level, _best_level;
183
184    Path *_cycle_path;
185    bool _local_path;
186
187    // Node map for storing path data
188    PathDataNodeMap _data;
189    // The processed nodes in the last round
190    std::vector<Node> _process;
191
192    Tolerance _tolerance;
193
194    // Infinite constant
195    const LargeValue INF;
196
197  public:
198
199    /// \name Named Template Parameters
200    /// @{
201
202    template <typename T>
203    struct SetLargeValueTraits : public Traits {
204      typedef T LargeValue;
205      typedef lemon::Tolerance<T> Tolerance;
206    };
207
208    /// \brief \ref named-templ-param "Named parameter" for setting
209    /// \c LargeValue type.
210    ///
211    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
212    /// type. It is used for internal computations in the algorithm.
213    template <typename T>
214    struct SetLargeValue
215      : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > {
216      typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create;
217    };
218
219    template <typename T>
220    struct SetPathTraits : public Traits {
221      typedef T Path;
222    };
223
224    /// \brief \ref named-templ-param "Named parameter" for setting
225    /// \c %Path type.
226    ///
227    /// \ref named-templ-param "Named parameter" for setting the \c %Path
228    /// type of the found cycles.
229    /// It must conform to the \ref lemon::concepts::Path "Path" concept
230    /// and it must have an \c addFront() function.
231    template <typename T>
232    struct SetPath
233      : public HartmannOrlin<GR, LEN, SetPathTraits<T> > {
234      typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create;
235    };
236
237    /// @}
238
239  public:
240
241    /// \brief Constructor.
242    ///
243    /// The constructor of the class.
244    ///
245    /// \param digraph The digraph the algorithm runs on.
246    /// \param length The lengths (costs) of the arcs.
247    HartmannOrlin( const Digraph &digraph,
248                   const LengthMap &length ) :
249      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
250      _best_found(false), _best_length(0), _best_size(1),
251      _cycle_path(NULL), _local_path(false), _data(digraph),
252      INF(std::numeric_limits<LargeValue>::has_infinity ?
253          std::numeric_limits<LargeValue>::infinity() :
254          std::numeric_limits<LargeValue>::max())
255    {}
256
257    /// Destructor.
258    ~HartmannOrlin() {
259      if (_local_path) delete _cycle_path;
260    }
261
262    /// \brief Set the path structure for storing the found cycle.
263    ///
264    /// This function sets an external path structure for storing the
265    /// found cycle.
266    ///
267    /// If you don't call this function before calling \ref run() or
268    /// \ref findMinMean(), it will allocate a local \ref Path "path"
269    /// structure. The destuctor deallocates this automatically
270    /// allocated object, of course.
271    ///
272    /// \note The algorithm calls only the \ref lemon::Path::addFront()
273    /// "addFront()" function of the given path structure.
274    ///
275    /// \return <tt>(*this)</tt>
276    HartmannOrlin& cycle(Path &path) {
277      if (_local_path) {
278        delete _cycle_path;
279        _local_path = false;
280      }
281      _cycle_path = &path;
282      return *this;
283    }
284
285    /// \name Execution control
286    /// The simplest way to execute the algorithm is to call the \ref run()
287    /// function.\n
288    /// If you only need the minimum mean length, you may call
289    /// \ref findMinMean().
290
291    /// @{
292
293    /// \brief Run the algorithm.
294    ///
295    /// This function runs the algorithm.
296    /// It can be called more than once (e.g. if the underlying digraph
297    /// and/or the arc lengths have been modified).
298    ///
299    /// \return \c true if a directed cycle exists in the digraph.
300    ///
301    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
302    /// \code
303    ///   return mmc.findMinMean() && mmc.findCycle();
304    /// \endcode
305    bool run() {
306      return findMinMean() && findCycle();
307    }
308
309    /// \brief Find the minimum cycle mean.
310    ///
311    /// This function finds the minimum mean length of the directed
312    /// cycles in the digraph.
313    ///
314    /// \return \c true if a directed cycle exists in the digraph.
315    bool findMinMean() {
316      // Initialization and find strongly connected components
317      init();
318      findComponents();
319     
320      // Find the minimum cycle mean in the components
321      for (int comp = 0; comp < _comp_num; ++comp) {
322        if (!initComponent(comp)) continue;
323        processRounds();
324       
325        // Update the best cycle (global minimum mean cycle)
326        if ( _curr_found && (!_best_found ||
327             _curr_length * _best_size < _best_length * _curr_size) ) {
328          _best_found = true;
329          _best_length = _curr_length;
330          _best_size = _curr_size;
331          _best_node = _curr_node;
332          _best_level = _curr_level;
333        }
334      }
335      return _best_found;
336    }
337
338    /// \brief Find a minimum mean directed cycle.
339    ///
340    /// This function finds a directed cycle of minimum mean length
341    /// in the digraph using the data computed by findMinMean().
342    ///
343    /// \return \c true if a directed cycle exists in the digraph.
344    ///
345    /// \pre \ref findMinMean() must be called before using this function.
346    bool findCycle() {
347      if (!_best_found) return false;
348      IntNodeMap reached(_gr, -1);
349      int r = _best_level + 1;
350      Node u = _best_node;
351      while (reached[u] < 0) {
352        reached[u] = --r;
353        u = _gr.source(_data[u][r].pred);
354      }
355      r = reached[u];
356      Arc e = _data[u][r].pred;
357      _cycle_path->addFront(e);
358      _best_length = _length[e];
359      _best_size = 1;
360      Node v;
361      while ((v = _gr.source(e)) != u) {
362        e = _data[v][--r].pred;
363        _cycle_path->addFront(e);
364        _best_length += _length[e];
365        ++_best_size;
366      }
367      return true;
368    }
369
370    /// @}
371
372    /// \name Query Functions
373    /// The results of the algorithm can be obtained using these
374    /// functions.\n
375    /// The algorithm should be executed before using them.
376
377    /// @{
378
379    /// \brief Return the total length of the found cycle.
380    ///
381    /// This function returns the total length of the found cycle.
382    ///
383    /// \pre \ref run() or \ref findMinMean() must be called before
384    /// using this function.
385    LargeValue cycleLength() const {
386      return _best_length;
387    }
388
389    /// \brief Return the number of arcs on the found cycle.
390    ///
391    /// This function returns the number of arcs on the found cycle.
392    ///
393    /// \pre \ref run() or \ref findMinMean() must be called before
394    /// using this function.
395    int cycleArcNum() const {
396      return _best_size;
397    }
398
399    /// \brief Return the mean length of the found cycle.
400    ///
401    /// This function returns the mean length of the found cycle.
402    ///
403    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
404    /// following code.
405    /// \code
406    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
407    /// \endcode
408    ///
409    /// \pre \ref run() or \ref findMinMean() must be called before
410    /// using this function.
411    double cycleMean() const {
412      return static_cast<double>(_best_length) / _best_size;
413    }
414
415    /// \brief Return the found cycle.
416    ///
417    /// This function returns a const reference to the path structure
418    /// storing the found cycle.
419    ///
420    /// \pre \ref run() or \ref findCycle() must be called before using
421    /// this function.
422    const Path& cycle() const {
423      return *_cycle_path;
424    }
425
426    ///@}
427
428  private:
429
430    // Initialization
431    void init() {
432      if (!_cycle_path) {
433        _local_path = true;
434        _cycle_path = new Path;
435      }
436      _cycle_path->clear();
437      _best_found = false;
438      _best_length = 0;
439      _best_size = 1;
440      _cycle_path->clear();
441      for (NodeIt u(_gr); u != INVALID; ++u)
442        _data[u].clear();
443    }
444
445    // Find strongly connected components and initialize _comp_nodes
446    // and _out_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          _out_arcs[n].clear();
455          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
456            _out_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          _out_arcs[n].clear();
466          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
467            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
468          }
469        }
470      }
471    }
472
473    // Initialize path data for the current component
474    bool initComponent(int comp) {
475      _nodes = &(_comp_nodes[comp]);
476      int n = _nodes->size();
477      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
478        return false;
479      }     
480      for (int i = 0; i < n; ++i) {
481        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
482      }
483      return true;
484    }
485
486    // Process all rounds of computing path data for the current component.
487    // _data[v][k] is the length of a shortest directed walk from the root
488    // node to node v containing exactly k arcs.
489    void processRounds() {
490      Node start = (*_nodes)[0];
491      _data[start][0] = PathData(0);
492      _process.clear();
493      _process.push_back(start);
494
495      int k, n = _nodes->size();
496      int next_check = 4;
497      bool terminate = false;
498      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
499        processNextBuildRound(k);
500        if (k == next_check || k == n) {
501          terminate = checkTermination(k);
502          next_check = next_check * 3 / 2;
503        }
504      }
505      for ( ; k <= n && !terminate; ++k) {
506        processNextFullRound(k);
507        if (k == next_check || k == n) {
508          terminate = checkTermination(k);
509          next_check = next_check * 3 / 2;
510        }
511      }
512    }
513
514    // Process one round and rebuild _process
515    void processNextBuildRound(int k) {
516      std::vector<Node> next;
517      Node u, v;
518      Arc e;
519      LargeValue d;
520      for (int i = 0; i < int(_process.size()); ++i) {
521        u = _process[i];
522        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
523          e = _out_arcs[u][j];
524          v = _gr.target(e);
525          d = _data[u][k-1].dist + _length[e];
526          if (_tolerance.less(d, _data[v][k].dist)) {
527            if (_data[v][k].dist == INF) next.push_back(v);
528            _data[v][k] = PathData(d, e);
529          }
530        }
531      }
532      _process.swap(next);
533    }
534
535    // Process one round using _nodes instead of _process
536    void processNextFullRound(int k) {
537      Node u, v;
538      Arc e;
539      LargeValue d;
540      for (int i = 0; i < int(_nodes->size()); ++i) {
541        u = (*_nodes)[i];
542        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
543          e = _out_arcs[u][j];
544          v = _gr.target(e);
545          d = _data[u][k-1].dist + _length[e];
546          if (_tolerance.less(d, _data[v][k].dist)) {
547            _data[v][k] = PathData(d, e);
548          }
549        }
550      }
551    }
552   
553    // Check early termination
554    bool checkTermination(int k) {
555      typedef std::pair<int, int> Pair;
556      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
557      typename GR::template NodeMap<LargeValue> pi(_gr);
558      int n = _nodes->size();
559      LargeValue length;
560      int size;
561      Node u;
562     
563      // Search for cycles that are already found
564      _curr_found = false;
565      for (int i = 0; i < n; ++i) {
566        u = (*_nodes)[i];
567        if (_data[u][k].dist == INF) continue;
568        for (int j = k; j >= 0; --j) {
569          if (level[u].first == i && level[u].second > 0) {
570            // A cycle is found
571            length = _data[u][level[u].second].dist - _data[u][j].dist;
572            size = level[u].second - j;
573            if (!_curr_found || length * _curr_size < _curr_length * size) {
574              _curr_length = length;
575              _curr_size = size;
576              _curr_node = u;
577              _curr_level = level[u].second;
578              _curr_found = true;
579            }
580          }
581          level[u] = Pair(i, j);
582          u = _gr.source(_data[u][j].pred);
583        }
584      }
585
586      // If at least one cycle is found, check the optimality condition
587      LargeValue d;
588      if (_curr_found && k < n) {
589        // Find node potentials
590        for (int i = 0; i < n; ++i) {
591          u = (*_nodes)[i];
592          pi[u] = INF;
593          for (int j = 0; j <= k; ++j) {
594            if (_data[u][j].dist < INF) {
595              d = _data[u][j].dist * _curr_size - j * _curr_length;
596              if (_tolerance.less(d, pi[u])) pi[u] = d;
597            }
598          }
599        }
600
601        // Check the optimality condition for all arcs
602        bool done = true;
603        for (ArcIt a(_gr); a != INVALID; ++a) {
604          if (_tolerance.less(_length[a] * _curr_size - _curr_length,
605                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
606            done = false;
607            break;
608          }
609        }
610        return done;
611      }
612      return (k == n);
613    }
614
615  }; //class HartmannOrlin
616
617  ///@}
618
619} //namespace lemon
620
621#endif //LEMON_HARTMANN_ORLIN_H
Note: See TracBrowser for help on using the repository browser.