COIN-OR::LEMON - Graph Library

source: lemon/lemon/hartmann_orlin.h @ 813:97744b6dabf8

Last change on this file since 813:97744b6dabf8 was 813:97744b6dabf8, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Add HartmannOrlin? algorithm class (#179)
This algorithm is an improved version of Karp's original method,
it applies an efficient early termination scheme.
The interface is the same as Karp's and Howard's interface.

File size: 18.4 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 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      bool found;
154      LargeValue dist;
155      Arc pred;
156      PathData(bool f = false, LargeValue d = 0, Arc p = INVALID) :
157        found(f), 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  public:
195
196    /// \name Named Template Parameters
197    /// @{
198
199    template <typename T>
200    struct SetLargeValueTraits : public Traits {
201      typedef T LargeValue;
202      typedef lemon::Tolerance<T> Tolerance;
203    };
204
205    /// \brief \ref named-templ-param "Named parameter" for setting
206    /// \c LargeValue type.
207    ///
208    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
209    /// type. It is used for internal computations in the algorithm.
210    template <typename T>
211    struct SetLargeValue
212      : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > {
213      typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create;
214    };
215
216    template <typename T>
217    struct SetPathTraits : public Traits {
218      typedef T Path;
219    };
220
221    /// \brief \ref named-templ-param "Named parameter" for setting
222    /// \c %Path type.
223    ///
224    /// \ref named-templ-param "Named parameter" for setting the \c %Path
225    /// type of the found cycles.
226    /// It must conform to the \ref lemon::concepts::Path "Path" concept
227    /// and it must have an \c addFront() function.
228    template <typename T>
229    struct SetPath
230      : public HartmannOrlin<GR, LEN, SetPathTraits<T> > {
231      typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create;
232    };
233
234    /// @}
235
236  public:
237
238    /// \brief Constructor.
239    ///
240    /// The constructor of the class.
241    ///
242    /// \param digraph The digraph the algorithm runs on.
243    /// \param length The lengths (costs) of the arcs.
244    HartmannOrlin( const Digraph &digraph,
245                   const LengthMap &length ) :
246      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
247      _best_found(false), _best_length(0), _best_size(1),
248      _cycle_path(NULL), _local_path(false), _data(digraph)
249    {}
250
251    /// Destructor.
252    ~HartmannOrlin() {
253      if (_local_path) delete _cycle_path;
254    }
255
256    /// \brief Set the path structure for storing the found cycle.
257    ///
258    /// This function sets an external path structure for storing the
259    /// found cycle.
260    ///
261    /// If you don't call this function before calling \ref run() or
262    /// \ref findMinMean(), it will allocate a local \ref Path "path"
263    /// structure. The destuctor deallocates this automatically
264    /// allocated object, of course.
265    ///
266    /// \note The algorithm calls only the \ref lemon::Path::addFront()
267    /// "addFront()" function of the given path structure.
268    ///
269    /// \return <tt>(*this)</tt>
270    HartmannOrlin& cycle(Path &path) {
271      if (_local_path) {
272        delete _cycle_path;
273        _local_path = false;
274      }
275      _cycle_path = &path;
276      return *this;
277    }
278
279    /// \name Execution control
280    /// The simplest way to execute the algorithm is to call the \ref run()
281    /// function.\n
282    /// If you only need the minimum mean length, you may call
283    /// \ref findMinMean().
284
285    /// @{
286
287    /// \brief Run the algorithm.
288    ///
289    /// This function runs the algorithm.
290    /// It can be called more than once (e.g. if the underlying digraph
291    /// and/or the arc lengths have been modified).
292    ///
293    /// \return \c true if a directed cycle exists in the digraph.
294    ///
295    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
296    /// \code
297    ///   return mmc.findMinMean() && mmc.findCycle();
298    /// \endcode
299    bool run() {
300      return findMinMean() && findCycle();
301    }
302
303    /// \brief Find the minimum cycle mean.
304    ///
305    /// This function finds the minimum mean length of the directed
306    /// cycles in the digraph.
307    ///
308    /// \return \c true if a directed cycle exists in the digraph.
309    bool findMinMean() {
310      // Initialization and find strongly connected components
311      init();
312      findComponents();
313     
314      // Find the minimum cycle mean in the components
315      for (int comp = 0; comp < _comp_num; ++comp) {
316        if (!initComponent(comp)) continue;
317        processRounds();
318       
319        // Update the best cycle (global minimum mean cycle)
320        if ( _curr_found && (!_best_found ||
321             _curr_length * _best_size < _best_length * _curr_size) ) {
322          _best_found = true;
323          _best_length = _curr_length;
324          _best_size = _curr_size;
325          _best_node = _curr_node;
326          _best_level = _curr_level;
327        }
328      }
329      return _best_found;
330    }
331
332    /// \brief Find a minimum mean directed cycle.
333    ///
334    /// This function finds a directed cycle of minimum mean length
335    /// in the digraph using the data computed by findMinMean().
336    ///
337    /// \return \c true if a directed cycle exists in the digraph.
338    ///
339    /// \pre \ref findMinMean() must be called before using this function.
340    bool findCycle() {
341      if (!_best_found) return false;
342      IntNodeMap reached(_gr, -1);
343      int r = _best_level + 1;
344      Node u = _best_node;
345      while (reached[u] < 0) {
346        reached[u] = --r;
347        u = _gr.source(_data[u][r].pred);
348      }
349      r = reached[u];
350      Arc e = _data[u][r].pred;
351      _cycle_path->addFront(e);
352      _best_length = _length[e];
353      _best_size = 1;
354      Node v;
355      while ((v = _gr.source(e)) != u) {
356        e = _data[v][--r].pred;
357        _cycle_path->addFront(e);
358        _best_length += _length[e];
359        ++_best_size;
360      }
361      return true;
362    }
363
364    /// @}
365
366    /// \name Query Functions
367    /// The results of the algorithm can be obtained using these
368    /// functions.\n
369    /// The algorithm should be executed before using them.
370
371    /// @{
372
373    /// \brief Return the total length of the found cycle.
374    ///
375    /// This function returns the total length of the found cycle.
376    ///
377    /// \pre \ref run() or \ref findMinMean() must be called before
378    /// using this function.
379    LargeValue cycleLength() const {
380      return _best_length;
381    }
382
383    /// \brief Return the number of arcs on the found cycle.
384    ///
385    /// This function returns the number of arcs on the found cycle.
386    ///
387    /// \pre \ref run() or \ref findMinMean() must be called before
388    /// using this function.
389    int cycleArcNum() const {
390      return _best_size;
391    }
392
393    /// \brief Return the mean length of the found cycle.
394    ///
395    /// This function returns the mean length of the found cycle.
396    ///
397    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
398    /// following code.
399    /// \code
400    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
401    /// \endcode
402    ///
403    /// \pre \ref run() or \ref findMinMean() must be called before
404    /// using this function.
405    double cycleMean() const {
406      return static_cast<double>(_best_length) / _best_size;
407    }
408
409    /// \brief Return the found cycle.
410    ///
411    /// This function returns a const reference to the path structure
412    /// storing the found cycle.
413    ///
414    /// \pre \ref run() or \ref findCycle() must be called before using
415    /// this function.
416    const Path& cycle() const {
417      return *_cycle_path;
418    }
419
420    ///@}
421
422  private:
423
424    // Initialization
425    void init() {
426      if (!_cycle_path) {
427        _local_path = true;
428        _cycle_path = new Path;
429      }
430      _cycle_path->clear();
431      _best_found = false;
432      _best_length = 0;
433      _best_size = 1;
434      _cycle_path->clear();
435      for (NodeIt u(_gr); u != INVALID; ++u)
436        _data[u].clear();
437    }
438
439    // Find strongly connected components and initialize _comp_nodes
440    // and _out_arcs
441    void findComponents() {
442      _comp_num = stronglyConnectedComponents(_gr, _comp);
443      _comp_nodes.resize(_comp_num);
444      if (_comp_num == 1) {
445        _comp_nodes[0].clear();
446        for (NodeIt n(_gr); n != INVALID; ++n) {
447          _comp_nodes[0].push_back(n);
448          _out_arcs[n].clear();
449          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
450            _out_arcs[n].push_back(a);
451          }
452        }
453      } else {
454        for (int i = 0; i < _comp_num; ++i)
455          _comp_nodes[i].clear();
456        for (NodeIt n(_gr); n != INVALID; ++n) {
457          int k = _comp[n];
458          _comp_nodes[k].push_back(n);
459          _out_arcs[n].clear();
460          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
461            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
462          }
463        }
464      }
465    }
466
467    // Initialize path data for the current component
468    bool initComponent(int comp) {
469      _nodes = &(_comp_nodes[comp]);
470      int n = _nodes->size();
471      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
472        return false;
473      }     
474      for (int i = 0; i < n; ++i) {
475        _data[(*_nodes)[i]].resize(n + 1);
476      }
477      return true;
478    }
479
480    // Process all rounds of computing path data for the current component.
481    // _data[v][k] is the length of a shortest directed walk from the root
482    // node to node v containing exactly k arcs.
483    void processRounds() {
484      Node start = (*_nodes)[0];
485      _data[start][0] = PathData(true, 0);
486      _process.clear();
487      _process.push_back(start);
488
489      int k, n = _nodes->size();
490      int next_check = 4;
491      bool terminate = false;
492      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
493        processNextBuildRound(k);
494        if (k == next_check || k == n) {
495          terminate = checkTermination(k);
496          next_check = next_check * 3 / 2;
497        }
498      }
499      for ( ; k <= n && !terminate; ++k) {
500        processNextFullRound(k);
501        if (k == next_check || k == n) {
502          terminate = checkTermination(k);
503          next_check = next_check * 3 / 2;
504        }
505      }
506    }
507
508    // Process one round and rebuild _process
509    void processNextBuildRound(int k) {
510      std::vector<Node> next;
511      Node u, v;
512      Arc e;
513      LargeValue d;
514      for (int i = 0; i < int(_process.size()); ++i) {
515        u = _process[i];
516        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
517          e = _out_arcs[u][j];
518          v = _gr.target(e);
519          d = _data[u][k-1].dist + _length[e];
520          if (!_data[v][k].found) {
521            next.push_back(v);
522            _data[v][k] = PathData(true, _data[u][k-1].dist + _length[e], e);
523          }
524          else if (_tolerance.less(d, _data[v][k].dist)) {
525            _data[v][k] = PathData(true, d, e);
526          }
527        }
528      }
529      _process.swap(next);
530    }
531
532    // Process one round using _nodes instead of _process
533    void processNextFullRound(int k) {
534      Node u, v;
535      Arc e;
536      LargeValue d;
537      for (int i = 0; i < int(_nodes->size()); ++i) {
538        u = (*_nodes)[i];
539        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
540          e = _out_arcs[u][j];
541          v = _gr.target(e);
542          d = _data[u][k-1].dist + _length[e];
543          if (!_data[v][k].found || _tolerance.less(d, _data[v][k].dist)) {
544            _data[v][k] = PathData(true, d, e);
545          }
546        }
547      }
548    }
549   
550    // Check early termination
551    bool checkTermination(int k) {
552      typedef std::pair<int, int> Pair;
553      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
554      typename GR::template NodeMap<LargeValue> pi(_gr);
555      int n = _nodes->size();
556      LargeValue length;
557      int size;
558      Node u;
559     
560      // Search for cycles that are already found
561      _curr_found = false;
562      for (int i = 0; i < n; ++i) {
563        u = (*_nodes)[i];
564        if (!_data[u][k].found) continue;
565        for (int j = k; j >= 0; --j) {
566          if (level[u].first == i && level[u].second > 0) {
567            // A cycle is found
568            length = _data[u][level[u].second].dist - _data[u][j].dist;
569            size = level[u].second - j;
570            if (!_curr_found || length * _curr_size < _curr_length * size) {
571              _curr_length = length;
572              _curr_size = size;
573              _curr_node = u;
574              _curr_level = level[u].second;
575              _curr_found = true;
576            }
577          }
578          level[u] = Pair(i, j);
579          u = _gr.source(_data[u][j].pred);
580        }
581      }
582
583      // If at least one cycle is found, check the optimality condition
584      LargeValue d;
585      if (_curr_found && k < n) {
586        // Find node potentials
587        for (int i = 0; i < n; ++i) {
588          u = (*_nodes)[i];
589          pi[u] = std::numeric_limits<LargeValue>::max();
590          for (int j = 0; j <= k; ++j) {
591            d = _data[u][j].dist * _curr_size - j * _curr_length;
592            if (_data[u][j].found && _tolerance.less(d, pi[u])) {
593              pi[u] = d;
594            }
595          }
596        }
597
598        // Check the optimality condition for all arcs
599        bool done = true;
600        for (ArcIt a(_gr); a != INVALID; ++a) {
601          if (_tolerance.less(_length[a] * _curr_size - _curr_length,
602                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
603            done = false;
604            break;
605          }
606        }
607        return done;
608      }
609      return (k == n);
610    }
611
612  }; //class HartmannOrlin
613
614  ///@}
615
616} //namespace lemon
617
618#endif //LEMON_HARTMANN_ORLIN_H
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