COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/hartmann_orlin.h @ 795:921d5bf41ac2

Last change on this file since 795:921d5bf41ac2 was 795:921d5bf41ac2, checked in by Balazs Dezso <deba@…>, 10 years ago

Fix in HartmannOrlin? algorithm (#333)

File size: 19.1 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 addFront() 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  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
102  /// It is an improved version of \ref Karp "Karp"'s original algorithm,
103  /// it applies an efficient early termination scheme.
104  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
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#ifdef DOXYGEN
110  template <typename GR, typename LEN, typename TR>
111#else
112  template < typename GR,
113             typename LEN = typename GR::template ArcMap<int>,
114             typename TR = HartmannOrlinDefaultTraits<GR, LEN> >
115#endif
116  class HartmannOrlin
117  {
118  public:
119
120    /// The type of the digraph
121    typedef typename TR::Digraph Digraph;
122    /// The type of the length map
123    typedef typename TR::LengthMap LengthMap;
124    /// The type of the arc lengths
125    typedef typename TR::Value Value;
126
127    /// \brief The large value type
128    ///
129    /// The large value type used for internal computations.
130    /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
131    /// it is \c long \c long if the \c Value type is integer,
132    /// otherwise it is \c double.
133    typedef typename TR::LargeValue LargeValue;
134
135    /// The tolerance type
136    typedef typename TR::Tolerance Tolerance;
137
138    /// \brief The path type of the found cycles
139    ///
140    /// The path type of the found cycles.
141    /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
142    /// it is \ref lemon::Path "Path<Digraph>".
143    typedef typename TR::Path Path;
144
145    /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm
146    typedef TR Traits;
147
148  private:
149
150    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
151
152    // Data sturcture for path data
153    struct PathData
154    {
155      LargeValue dist;
156      Arc pred;
157      PathData(LargeValue d, Arc p = INVALID) :
158        dist(d), pred(p) {}
159    };
160
161    typedef typename Digraph::template NodeMap<std::vector<PathData> >
162      PathDataNodeMap;
163
164  private:
165
166    // The digraph the algorithm runs on
167    const Digraph &_gr;
168    // The length of the arcs
169    const LengthMap &_length;
170
171    // Data for storing the strongly connected components
172    int _comp_num;
173    typename Digraph::template NodeMap<int> _comp;
174    std::vector<std::vector<Node> > _comp_nodes;
175    std::vector<Node>* _nodes;
176    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
177
178    // Data for the found cycles
179    bool _curr_found, _best_found;
180    LargeValue _curr_length, _best_length;
181    int _curr_size, _best_size;
182    Node _curr_node, _best_node;
183    int _curr_level, _best_level;
184
185    Path *_cycle_path;
186    bool _local_path;
187
188    // Node map for storing path data
189    PathDataNodeMap _data;
190    // The processed nodes in the last round
191    std::vector<Node> _process;
192
193    Tolerance _tolerance;
194
195    // Infinite constant
196    const LargeValue INF;
197
198  public:
199
200    /// \name Named Template Parameters
201    /// @{
202
203    template <typename T>
204    struct SetLargeValueTraits : public Traits {
205      typedef T LargeValue;
206      typedef lemon::Tolerance<T> Tolerance;
207    };
208
209    /// \brief \ref named-templ-param "Named parameter" for setting
210    /// \c LargeValue type.
211    ///
212    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
213    /// type. It is used for internal computations in the algorithm.
214    template <typename T>
215    struct SetLargeValue
216      : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > {
217      typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create;
218    };
219
220    template <typename T>
221    struct SetPathTraits : public Traits {
222      typedef T Path;
223    };
224
225    /// \brief \ref named-templ-param "Named parameter" for setting
226    /// \c %Path type.
227    ///
228    /// \ref named-templ-param "Named parameter" for setting the \c %Path
229    /// type of the found cycles.
230    /// It must conform to the \ref lemon::concepts::Path "Path" concept
231    /// and it must have an \c addFront() function.
232    template <typename T>
233    struct SetPath
234      : public HartmannOrlin<GR, LEN, SetPathTraits<T> > {
235      typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create;
236    };
237
238    /// @}
239
240  public:
241
242    /// \brief Constructor.
243    ///
244    /// The constructor of the class.
245    ///
246    /// \param digraph The digraph the algorithm runs on.
247    /// \param length The lengths (costs) of the arcs.
248    HartmannOrlin( const Digraph &digraph,
249                   const LengthMap &length ) :
250      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
251      _best_found(false), _best_length(0), _best_size(1),
252      _cycle_path(NULL), _local_path(false), _data(digraph),
253      INF(std::numeric_limits<LargeValue>::has_infinity ?
254          std::numeric_limits<LargeValue>::infinity() :
255          std::numeric_limits<LargeValue>::max())
256    {}
257
258    /// Destructor.
259    ~HartmannOrlin() {
260      if (_local_path) delete _cycle_path;
261    }
262
263    /// \brief Set the path structure for storing the found cycle.
264    ///
265    /// This function sets an external path structure for storing the
266    /// found cycle.
267    ///
268    /// If you don't call this function before calling \ref run() or
269    /// \ref findMinMean(), it will allocate a local \ref Path "path"
270    /// structure. The destuctor deallocates this automatically
271    /// allocated object, of course.
272    ///
273    /// \note The algorithm calls only the \ref lemon::Path::addFront()
274    /// "addFront()" function of the given path structure.
275    ///
276    /// \return <tt>(*this)</tt>
277    HartmannOrlin& cycle(Path &path) {
278      if (_local_path) {
279        delete _cycle_path;
280        _local_path = false;
281      }
282      _cycle_path = &path;
283      return *this;
284    }
285
286    /// \brief Set the tolerance used by the algorithm.
287    ///
288    /// This function sets the tolerance object used by the algorithm.
289    ///
290    /// \return <tt>(*this)</tt>
291    HartmannOrlin& tolerance(const Tolerance& tolerance) {
292      _tolerance = tolerance;
293      return *this;
294    }
295
296    /// \brief Return a const reference to the tolerance.
297    ///
298    /// This function returns a const reference to the tolerance object
299    /// used by the algorithm.
300    const Tolerance& tolerance() const {
301      return _tolerance;
302    }
303
304    /// \name Execution control
305    /// The simplest way to execute the algorithm is to call the \ref run()
306    /// function.\n
307    /// If you only need the minimum mean length, you may call
308    /// \ref findMinMean().
309
310    /// @{
311
312    /// \brief Run the algorithm.
313    ///
314    /// This function runs the algorithm.
315    /// It can be called more than once (e.g. if the underlying digraph
316    /// and/or the arc lengths have been modified).
317    ///
318    /// \return \c true if a directed cycle exists in the digraph.
319    ///
320    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
321    /// \code
322    ///   return mmc.findMinMean() && mmc.findCycle();
323    /// \endcode
324    bool run() {
325      return findMinMean() && findCycle();
326    }
327
328    /// \brief Find the minimum cycle mean.
329    ///
330    /// This function finds the minimum mean length of the directed
331    /// cycles in the digraph.
332    ///
333    /// \return \c true if a directed cycle exists in the digraph.
334    bool findMinMean() {
335      // Initialization and find strongly connected components
336      init();
337      findComponents();
338     
339      // Find the minimum cycle mean in the components
340      for (int comp = 0; comp < _comp_num; ++comp) {
341        if (!initComponent(comp)) continue;
342        processRounds();
343       
344        // Update the best cycle (global minimum mean cycle)
345        if ( _curr_found && (!_best_found ||
346             _curr_length * _best_size < _best_length * _curr_size) ) {
347          _best_found = true;
348          _best_length = _curr_length;
349          _best_size = _curr_size;
350          _best_node = _curr_node;
351          _best_level = _curr_level;
352        }
353      }
354      return _best_found;
355    }
356
357    /// \brief Find a minimum mean directed cycle.
358    ///
359    /// This function finds a directed cycle of minimum mean length
360    /// in the digraph using the data computed by findMinMean().
361    ///
362    /// \return \c true if a directed cycle exists in the digraph.
363    ///
364    /// \pre \ref findMinMean() must be called before using this function.
365    bool findCycle() {
366      if (!_best_found) return false;
367      IntNodeMap reached(_gr, -1);
368      int r = _best_level + 1;
369      Node u = _best_node;
370      while (reached[u] < 0) {
371        reached[u] = --r;
372        u = _gr.source(_data[u][r].pred);
373      }
374      r = reached[u];
375      Arc e = _data[u][r].pred;
376      _cycle_path->addFront(e);
377      _best_length = _length[e];
378      _best_size = 1;
379      Node v;
380      while ((v = _gr.source(e)) != u) {
381        e = _data[v][--r].pred;
382        _cycle_path->addFront(e);
383        _best_length += _length[e];
384        ++_best_size;
385      }
386      return true;
387    }
388
389    /// @}
390
391    /// \name Query Functions
392    /// The results of the algorithm can be obtained using these
393    /// functions.\n
394    /// The algorithm should be executed before using them.
395
396    /// @{
397
398    /// \brief Return the total length of the found cycle.
399    ///
400    /// This function returns the total length of the found cycle.
401    ///
402    /// \pre \ref run() or \ref findMinMean() must be called before
403    /// using this function.
404    LargeValue cycleLength() const {
405      return _best_length;
406    }
407
408    /// \brief Return the number of arcs on the found cycle.
409    ///
410    /// This function returns the number of arcs on the found cycle.
411    ///
412    /// \pre \ref run() or \ref findMinMean() must be called before
413    /// using this function.
414    int cycleArcNum() const {
415      return _best_size;
416    }
417
418    /// \brief Return the mean length of the found cycle.
419    ///
420    /// This function returns the mean length of the found cycle.
421    ///
422    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
423    /// following code.
424    /// \code
425    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
426    /// \endcode
427    ///
428    /// \pre \ref run() or \ref findMinMean() must be called before
429    /// using this function.
430    double cycleMean() const {
431      return static_cast<double>(_best_length) / _best_size;
432    }
433
434    /// \brief Return the found cycle.
435    ///
436    /// This function returns a const reference to the path structure
437    /// storing the found cycle.
438    ///
439    /// \pre \ref run() or \ref findCycle() must be called before using
440    /// this function.
441    const Path& cycle() const {
442      return *_cycle_path;
443    }
444
445    ///@}
446
447  private:
448
449    // Initialization
450    void init() {
451      if (!_cycle_path) {
452        _local_path = true;
453        _cycle_path = new Path;
454      }
455      _cycle_path->clear();
456      _best_found = false;
457      _best_length = 0;
458      _best_size = 1;
459      _cycle_path->clear();
460      for (NodeIt u(_gr); u != INVALID; ++u)
461        _data[u].clear();
462    }
463
464    // Find strongly connected components and initialize _comp_nodes
465    // and _out_arcs
466    void findComponents() {
467      _comp_num = stronglyConnectedComponents(_gr, _comp);
468      _comp_nodes.resize(_comp_num);
469      if (_comp_num == 1) {
470        _comp_nodes[0].clear();
471        for (NodeIt n(_gr); n != INVALID; ++n) {
472          _comp_nodes[0].push_back(n);
473          _out_arcs[n].clear();
474          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
475            _out_arcs[n].push_back(a);
476          }
477        }
478      } else {
479        for (int i = 0; i < _comp_num; ++i)
480          _comp_nodes[i].clear();
481        for (NodeIt n(_gr); n != INVALID; ++n) {
482          int k = _comp[n];
483          _comp_nodes[k].push_back(n);
484          _out_arcs[n].clear();
485          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
486            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
487          }
488        }
489      }
490    }
491
492    // Initialize path data for the current component
493    bool initComponent(int comp) {
494      _nodes = &(_comp_nodes[comp]);
495      int n = _nodes->size();
496      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
497        return false;
498      }     
499      for (int i = 0; i < n; ++i) {
500        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
501      }
502      return true;
503    }
504
505    // Process all rounds of computing path data for the current component.
506    // _data[v][k] is the length of a shortest directed walk from the root
507    // node to node v containing exactly k arcs.
508    void processRounds() {
509      Node start = (*_nodes)[0];
510      _data[start][0] = PathData(0);
511      _process.clear();
512      _process.push_back(start);
513
514      int k, n = _nodes->size();
515      int next_check = 4;
516      bool terminate = false;
517      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
518        processNextBuildRound(k);
519        if (k == next_check || k == n) {
520          terminate = checkTermination(k);
521          next_check = next_check * 3 / 2;
522        }
523      }
524      for ( ; k <= n && !terminate; ++k) {
525        processNextFullRound(k);
526        if (k == next_check || k == n) {
527          terminate = checkTermination(k);
528          next_check = next_check * 3 / 2;
529        }
530      }
531    }
532
533    // Process one round and rebuild _process
534    void processNextBuildRound(int k) {
535      std::vector<Node> next;
536      Node u, v;
537      Arc e;
538      LargeValue d;
539      for (int i = 0; i < int(_process.size()); ++i) {
540        u = _process[i];
541        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
542          e = _out_arcs[u][j];
543          v = _gr.target(e);
544          d = _data[u][k-1].dist + _length[e];
545          if (_tolerance.less(d, _data[v][k].dist)) {
546            if (_data[v][k].dist == INF) next.push_back(v);
547            _data[v][k] = PathData(d, e);
548          }
549        }
550      }
551      _process.swap(next);
552    }
553
554    // Process one round using _nodes instead of _process
555    void processNextFullRound(int k) {
556      Node u, v;
557      Arc e;
558      LargeValue d;
559      for (int i = 0; i < int(_nodes->size()); ++i) {
560        u = (*_nodes)[i];
561        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
562          e = _out_arcs[u][j];
563          v = _gr.target(e);
564          d = _data[u][k-1].dist + _length[e];
565          if (_tolerance.less(d, _data[v][k].dist)) {
566            _data[v][k] = PathData(d, e);
567          }
568        }
569      }
570    }
571   
572    // Check early termination
573    bool checkTermination(int k) {
574      typedef std::pair<int, int> Pair;
575      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
576      typename GR::template NodeMap<LargeValue> pi(_gr);
577      int n = _nodes->size();
578      LargeValue length;
579      int size;
580      Node u;
581     
582      // Search for cycles that are already found
583      _curr_found = false;
584      for (int i = 0; i < n; ++i) {
585        u = (*_nodes)[i];
586        if (_data[u][k].dist == INF) continue;
587        for (int j = k; j >= 0; --j) {
588          if (level[u].first == i && level[u].second > 0) {
589            // A cycle is found
590            length = _data[u][level[u].second].dist - _data[u][j].dist;
591            size = level[u].second - j;
592            if (!_curr_found || length * _curr_size < _curr_length * size) {
593              _curr_length = length;
594              _curr_size = size;
595              _curr_node = u;
596              _curr_level = level[u].second;
597              _curr_found = true;
598            }
599          }
600          level[u] = Pair(i, j);
601          if (j != 0) {
602            u = _gr.source(_data[u][j].pred);
603          }
604        }
605      }
606
607      // If at least one cycle is found, check the optimality condition
608      LargeValue d;
609      if (_curr_found && k < n) {
610        // Find node potentials
611        for (int i = 0; i < n; ++i) {
612          u = (*_nodes)[i];
613          pi[u] = INF;
614          for (int j = 0; j <= k; ++j) {
615            if (_data[u][j].dist < INF) {
616              d = _data[u][j].dist * _curr_size - j * _curr_length;
617              if (_tolerance.less(d, pi[u])) pi[u] = d;
618            }
619          }
620        }
621
622        // Check the optimality condition for all arcs
623        bool done = true;
624        for (ArcIt a(_gr); a != INVALID; ++a) {
625          if (_tolerance.less(_length[a] * _curr_size - _curr_length,
626                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
627            done = false;
628            break;
629          }
630        }
631        return done;
632      }
633      return (k == n);
634    }
635
636  }; //class HartmannOrlin
637
638  ///@}
639
640} //namespace lemon
641
642#endif //LEMON_HARTMANN_ORLIN_H
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