COIN-OR::LEMON - Graph Library

source: lemon/lemon/hartmann_orlin.h @ 814:11c946fa8d13

Last change on this file since 814:11c946fa8d13 was 814:11c946fa8d13, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Simplify comparisons in min mean cycle classes (#179)
using extreme INF values instead of bool flags.

File size: 18.5 KB
RevLine 
[813]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 shortest_path
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 shortest_path
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  ///
104  /// \tparam GR The type of the digraph the algorithm runs on.
105  /// \tparam LEN The type of the length map. The default
106  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
107#ifdef DOXYGEN
108  template <typename GR, typename LEN, typename TR>
109#else
110  template < typename GR,
111             typename LEN = typename GR::template ArcMap<int>,
112             typename TR = HartmannOrlinDefaultTraits<GR, LEN> >
113#endif
114  class HartmannOrlin
115  {
116  public:
117
118    /// The type of the digraph
119    typedef typename TR::Digraph Digraph;
120    /// The type of the length map
121    typedef typename TR::LengthMap LengthMap;
122    /// The type of the arc lengths
123    typedef typename TR::Value Value;
124
125    /// \brief The large value type
126    ///
127    /// The large value type used for internal computations.
128    /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
129    /// it is \c long \c long if the \c Value type is integer,
130    /// otherwise it is \c double.
131    typedef typename TR::LargeValue LargeValue;
132
133    /// The tolerance type
134    typedef typename TR::Tolerance Tolerance;
135
136    /// \brief The path type of the found cycles
137    ///
138    /// The path type of the found cycles.
139    /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
140    /// it is \ref lemon::Path "Path<Digraph>".
141    typedef typename TR::Path Path;
142
143    /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm
144    typedef TR Traits;
145
146  private:
147
148    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
149
150    // Data sturcture for path data
151    struct PathData
152    {
153      LargeValue dist;
154      Arc pred;
[814]155      PathData(LargeValue d, Arc p = INVALID) :
156        dist(d), pred(p) {}
[813]157    };
158
159    typedef typename Digraph::template NodeMap<std::vector<PathData> >
160      PathDataNodeMap;
161
162  private:
163
164    // The digraph the algorithm runs on
165    const Digraph &_gr;
166    // The length of the arcs
167    const LengthMap &_length;
168
169    // Data for storing the strongly connected components
170    int _comp_num;
171    typename Digraph::template NodeMap<int> _comp;
172    std::vector<std::vector<Node> > _comp_nodes;
173    std::vector<Node>* _nodes;
174    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
175
176    // Data for the found cycles
177    bool _curr_found, _best_found;
178    LargeValue _curr_length, _best_length;
179    int _curr_size, _best_size;
180    Node _curr_node, _best_node;
181    int _curr_level, _best_level;
182
183    Path *_cycle_path;
184    bool _local_path;
185
186    // Node map for storing path data
187    PathDataNodeMap _data;
188    // The processed nodes in the last round
189    std::vector<Node> _process;
190
191    Tolerance _tolerance;
192
[814]193    // Infinite constant
194    const LargeValue INF;
195
[813]196  public:
197
198    /// \name Named Template Parameters
199    /// @{
200
201    template <typename T>
202    struct SetLargeValueTraits : public Traits {
203      typedef T LargeValue;
204      typedef lemon::Tolerance<T> Tolerance;
205    };
206
207    /// \brief \ref named-templ-param "Named parameter" for setting
208    /// \c LargeValue type.
209    ///
210    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
211    /// type. It is used for internal computations in the algorithm.
212    template <typename T>
213    struct SetLargeValue
214      : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > {
215      typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create;
216    };
217
218    template <typename T>
219    struct SetPathTraits : public Traits {
220      typedef T Path;
221    };
222
223    /// \brief \ref named-templ-param "Named parameter" for setting
224    /// \c %Path type.
225    ///
226    /// \ref named-templ-param "Named parameter" for setting the \c %Path
227    /// type of the found cycles.
228    /// It must conform to the \ref lemon::concepts::Path "Path" concept
229    /// and it must have an \c addFront() function.
230    template <typename T>
231    struct SetPath
232      : public HartmannOrlin<GR, LEN, SetPathTraits<T> > {
233      typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create;
234    };
235
236    /// @}
237
238  public:
239
240    /// \brief Constructor.
241    ///
242    /// The constructor of the class.
243    ///
244    /// \param digraph The digraph the algorithm runs on.
245    /// \param length The lengths (costs) of the arcs.
246    HartmannOrlin( const Digraph &digraph,
247                   const LengthMap &length ) :
248      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
249      _best_found(false), _best_length(0), _best_size(1),
[814]250      _cycle_path(NULL), _local_path(false), _data(digraph),
251      INF(std::numeric_limits<LargeValue>::has_infinity ?
252          std::numeric_limits<LargeValue>::infinity() :
253          std::numeric_limits<LargeValue>::max())
[813]254    {}
255
256    /// Destructor.
257    ~HartmannOrlin() {
258      if (_local_path) delete _cycle_path;
259    }
260
261    /// \brief Set the path structure for storing the found cycle.
262    ///
263    /// This function sets an external path structure for storing the
264    /// found cycle.
265    ///
266    /// If you don't call this function before calling \ref run() or
267    /// \ref findMinMean(), it will allocate a local \ref Path "path"
268    /// structure. The destuctor deallocates this automatically
269    /// allocated object, of course.
270    ///
271    /// \note The algorithm calls only the \ref lemon::Path::addFront()
272    /// "addFront()" function of the given path structure.
273    ///
274    /// \return <tt>(*this)</tt>
275    HartmannOrlin& cycle(Path &path) {
276      if (_local_path) {
277        delete _cycle_path;
278        _local_path = false;
279      }
280      _cycle_path = &path;
281      return *this;
282    }
283
284    /// \name Execution control
285    /// The simplest way to execute the algorithm is to call the \ref run()
286    /// function.\n
287    /// If you only need the minimum mean length, you may call
288    /// \ref findMinMean().
289
290    /// @{
291
292    /// \brief Run the algorithm.
293    ///
294    /// This function runs the algorithm.
295    /// It can be called more than once (e.g. if the underlying digraph
296    /// and/or the arc lengths have been modified).
297    ///
298    /// \return \c true if a directed cycle exists in the digraph.
299    ///
300    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
301    /// \code
302    ///   return mmc.findMinMean() && mmc.findCycle();
303    /// \endcode
304    bool run() {
305      return findMinMean() && findCycle();
306    }
307
308    /// \brief Find the minimum cycle mean.
309    ///
310    /// This function finds the minimum mean length of the directed
311    /// cycles in the digraph.
312    ///
313    /// \return \c true if a directed cycle exists in the digraph.
314    bool findMinMean() {
315      // Initialization and find strongly connected components
316      init();
317      findComponents();
318     
319      // Find the minimum cycle mean in the components
320      for (int comp = 0; comp < _comp_num; ++comp) {
321        if (!initComponent(comp)) continue;
322        processRounds();
323       
324        // Update the best cycle (global minimum mean cycle)
325        if ( _curr_found && (!_best_found ||
326             _curr_length * _best_size < _best_length * _curr_size) ) {
327          _best_found = true;
328          _best_length = _curr_length;
329          _best_size = _curr_size;
330          _best_node = _curr_node;
331          _best_level = _curr_level;
332        }
333      }
334      return _best_found;
335    }
336
337    /// \brief Find a minimum mean directed cycle.
338    ///
339    /// This function finds a directed cycle of minimum mean length
340    /// in the digraph using the data computed by findMinMean().
341    ///
342    /// \return \c true if a directed cycle exists in the digraph.
343    ///
344    /// \pre \ref findMinMean() must be called before using this function.
345    bool findCycle() {
346      if (!_best_found) return false;
347      IntNodeMap reached(_gr, -1);
348      int r = _best_level + 1;
349      Node u = _best_node;
350      while (reached[u] < 0) {
351        reached[u] = --r;
352        u = _gr.source(_data[u][r].pred);
353      }
354      r = reached[u];
355      Arc e = _data[u][r].pred;
356      _cycle_path->addFront(e);
357      _best_length = _length[e];
358      _best_size = 1;
359      Node v;
360      while ((v = _gr.source(e)) != u) {
361        e = _data[v][--r].pred;
362        _cycle_path->addFront(e);
363        _best_length += _length[e];
364        ++_best_size;
365      }
366      return true;
367    }
368
369    /// @}
370
371    /// \name Query Functions
372    /// The results of the algorithm can be obtained using these
373    /// functions.\n
374    /// The algorithm should be executed before using them.
375
376    /// @{
377
378    /// \brief Return the total length of the found cycle.
379    ///
380    /// This function returns the total length of the found cycle.
381    ///
382    /// \pre \ref run() or \ref findMinMean() must be called before
383    /// using this function.
384    LargeValue cycleLength() const {
385      return _best_length;
386    }
387
388    /// \brief Return the number of arcs on the found cycle.
389    ///
390    /// This function returns the number of arcs on the found cycle.
391    ///
392    /// \pre \ref run() or \ref findMinMean() must be called before
393    /// using this function.
394    int cycleArcNum() const {
395      return _best_size;
396    }
397
398    /// \brief Return the mean length of the found cycle.
399    ///
400    /// This function returns the mean length of the found cycle.
401    ///
402    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
403    /// following code.
404    /// \code
405    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
406    /// \endcode
407    ///
408    /// \pre \ref run() or \ref findMinMean() must be called before
409    /// using this function.
410    double cycleMean() const {
411      return static_cast<double>(_best_length) / _best_size;
412    }
413
414    /// \brief Return the found cycle.
415    ///
416    /// This function returns a const reference to the path structure
417    /// storing the found cycle.
418    ///
419    /// \pre \ref run() or \ref findCycle() must be called before using
420    /// this function.
421    const Path& cycle() const {
422      return *_cycle_path;
423    }
424
425    ///@}
426
427  private:
428
429    // Initialization
430    void init() {
431      if (!_cycle_path) {
432        _local_path = true;
433        _cycle_path = new Path;
434      }
435      _cycle_path->clear();
436      _best_found = false;
437      _best_length = 0;
438      _best_size = 1;
439      _cycle_path->clear();
440      for (NodeIt u(_gr); u != INVALID; ++u)
441        _data[u].clear();
442    }
443
444    // Find strongly connected components and initialize _comp_nodes
445    // and _out_arcs
446    void findComponents() {
447      _comp_num = stronglyConnectedComponents(_gr, _comp);
448      _comp_nodes.resize(_comp_num);
449      if (_comp_num == 1) {
450        _comp_nodes[0].clear();
451        for (NodeIt n(_gr); n != INVALID; ++n) {
452          _comp_nodes[0].push_back(n);
453          _out_arcs[n].clear();
454          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
455            _out_arcs[n].push_back(a);
456          }
457        }
458      } else {
459        for (int i = 0; i < _comp_num; ++i)
460          _comp_nodes[i].clear();
461        for (NodeIt n(_gr); n != INVALID; ++n) {
462          int k = _comp[n];
463          _comp_nodes[k].push_back(n);
464          _out_arcs[n].clear();
465          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
466            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
467          }
468        }
469      }
470    }
471
472    // Initialize path data for the current component
473    bool initComponent(int comp) {
474      _nodes = &(_comp_nodes[comp]);
475      int n = _nodes->size();
476      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
477        return false;
478      }     
479      for (int i = 0; i < n; ++i) {
[814]480        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
[813]481      }
482      return true;
483    }
484
485    // Process all rounds of computing path data for the current component.
486    // _data[v][k] is the length of a shortest directed walk from the root
487    // node to node v containing exactly k arcs.
488    void processRounds() {
489      Node start = (*_nodes)[0];
[814]490      _data[start][0] = PathData(0);
[813]491      _process.clear();
492      _process.push_back(start);
493
494      int k, n = _nodes->size();
495      int next_check = 4;
496      bool terminate = false;
497      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
498        processNextBuildRound(k);
499        if (k == next_check || k == n) {
500          terminate = checkTermination(k);
501          next_check = next_check * 3 / 2;
502        }
503      }
504      for ( ; k <= n && !terminate; ++k) {
505        processNextFullRound(k);
506        if (k == next_check || k == n) {
507          terminate = checkTermination(k);
508          next_check = next_check * 3 / 2;
509        }
510      }
511    }
512
513    // Process one round and rebuild _process
514    void processNextBuildRound(int k) {
515      std::vector<Node> next;
516      Node u, v;
517      Arc e;
518      LargeValue d;
519      for (int i = 0; i < int(_process.size()); ++i) {
520        u = _process[i];
521        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
522          e = _out_arcs[u][j];
523          v = _gr.target(e);
524          d = _data[u][k-1].dist + _length[e];
[814]525          if (_tolerance.less(d, _data[v][k].dist)) {
526            if (_data[v][k].dist == INF) next.push_back(v);
527            _data[v][k] = PathData(d, e);
[813]528          }
529        }
530      }
531      _process.swap(next);
532    }
533
534    // Process one round using _nodes instead of _process
535    void processNextFullRound(int k) {
536      Node u, v;
537      Arc e;
538      LargeValue d;
539      for (int i = 0; i < int(_nodes->size()); ++i) {
540        u = (*_nodes)[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];
[814]545          if (_tolerance.less(d, _data[v][k].dist)) {
546            _data[v][k] = PathData(d, e);
[813]547          }
548        }
549      }
550    }
551   
552    // Check early termination
553    bool checkTermination(int k) {
554      typedef std::pair<int, int> Pair;
555      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
556      typename GR::template NodeMap<LargeValue> pi(_gr);
557      int n = _nodes->size();
558      LargeValue length;
559      int size;
560      Node u;
561     
562      // Search for cycles that are already found
563      _curr_found = false;
564      for (int i = 0; i < n; ++i) {
565        u = (*_nodes)[i];
[814]566        if (_data[u][k].dist == INF) continue;
[813]567        for (int j = k; j >= 0; --j) {
568          if (level[u].first == i && level[u].second > 0) {
569            // A cycle is found
570            length = _data[u][level[u].second].dist - _data[u][j].dist;
571            size = level[u].second - j;
572            if (!_curr_found || length * _curr_size < _curr_length * size) {
573              _curr_length = length;
574              _curr_size = size;
575              _curr_node = u;
576              _curr_level = level[u].second;
577              _curr_found = true;
578            }
579          }
580          level[u] = Pair(i, j);
581          u = _gr.source(_data[u][j].pred);
582        }
583      }
584
585      // If at least one cycle is found, check the optimality condition
586      LargeValue d;
587      if (_curr_found && k < n) {
588        // Find node potentials
589        for (int i = 0; i < n; ++i) {
590          u = (*_nodes)[i];
[814]591          pi[u] = INF;
[813]592          for (int j = 0; j <= k; ++j) {
[814]593            if (_data[u][j].dist < INF) {
594              d = _data[u][j].dist * _curr_size - j * _curr_length;
595              if (_tolerance.less(d, pi[u])) pi[u] = d;
[813]596            }
597          }
598        }
599
600        // Check the optimality condition for all arcs
601        bool done = true;
602        for (ArcIt a(_gr); a != INVALID; ++a) {
603          if (_tolerance.less(_length[a] * _curr_size - _curr_length,
604                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
605            done = false;
606            break;
607          }
608        }
609        return done;
610      }
611      return (k == n);
612    }
613
614  }; //class HartmannOrlin
615
616  ///@}
617
618} //namespace lemon
619
620#endif //LEMON_HARTMANN_ORLIN_H
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