COIN-OR::LEMON - Graph Library

source: lemon/lemon/hartmann_orlin.h @ 891:75e6020b19b1

Last change on this file since 891:75e6020b19b1 was 891:75e6020b19b1, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Add doc for the traits class parameters (#315)

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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_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  /// \tparam TR The traits class that defines various types used by the
110  /// algorithm. By default, it is \ref HartmannOrlinDefaultTraits
111  /// "HartmannOrlinDefaultTraits<GR, LEN>".
112  /// In most cases, this parameter should not be set directly,
113  /// consider to use the named template parameters instead.
114#ifdef DOXYGEN
115  template <typename GR, typename LEN, typename TR>
116#else
117  template < typename GR,
118             typename LEN = typename GR::template ArcMap<int>,
119             typename TR = HartmannOrlinDefaultTraits<GR, LEN> >
120#endif
121  class HartmannOrlin
122  {
123  public:
124
125    /// The type of the digraph
126    typedef typename TR::Digraph Digraph;
127    /// The type of the length map
128    typedef typename TR::LengthMap LengthMap;
129    /// The type of the arc lengths
130    typedef typename TR::Value Value;
131
132    /// \brief The large value type
133    ///
134    /// The large value type used for internal computations.
135    /// By default, it is \c long \c long if the \c Value type is integer,
136    /// otherwise it is \c double.
137    typedef typename TR::LargeValue LargeValue;
138
139    /// The tolerance type
140    typedef typename TR::Tolerance Tolerance;
141
142    /// \brief The path type of the found cycles
143    ///
144    /// The path type of the found cycles.
145    /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
146    /// it is \ref lemon::Path "Path<Digraph>".
147    typedef typename TR::Path Path;
148
149    /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm
150    typedef TR Traits;
151
152  private:
153
154    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
155
156    // Data sturcture for path data
157    struct PathData
158    {
159      LargeValue dist;
160      Arc pred;
161      PathData(LargeValue d, Arc p = INVALID) :
162        dist(d), pred(p) {}
163    };
164
165    typedef typename Digraph::template NodeMap<std::vector<PathData> >
166      PathDataNodeMap;
167
168  private:
169
170    // The digraph the algorithm runs on
171    const Digraph &_gr;
172    // The length of the arcs
173    const LengthMap &_length;
174
175    // Data for storing the strongly connected components
176    int _comp_num;
177    typename Digraph::template NodeMap<int> _comp;
178    std::vector<std::vector<Node> > _comp_nodes;
179    std::vector<Node>* _nodes;
180    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
181
182    // Data for the found cycles
183    bool _curr_found, _best_found;
184    LargeValue _curr_length, _best_length;
185    int _curr_size, _best_size;
186    Node _curr_node, _best_node;
187    int _curr_level, _best_level;
188
189    Path *_cycle_path;
190    bool _local_path;
191
192    // Node map for storing path data
193    PathDataNodeMap _data;
194    // The processed nodes in the last round
195    std::vector<Node> _process;
196
197    Tolerance _tolerance;
198
199    // Infinite constant
200    const LargeValue INF;
201
202  public:
203
204    /// \name Named Template Parameters
205    /// @{
206
207    template <typename T>
208    struct SetLargeValueTraits : public Traits {
209      typedef T LargeValue;
210      typedef lemon::Tolerance<T> Tolerance;
211    };
212
213    /// \brief \ref named-templ-param "Named parameter" for setting
214    /// \c LargeValue type.
215    ///
216    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
217    /// type. It is used for internal computations in the algorithm.
218    template <typename T>
219    struct SetLargeValue
220      : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > {
221      typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create;
222    };
223
224    template <typename T>
225    struct SetPathTraits : public Traits {
226      typedef T Path;
227    };
228
229    /// \brief \ref named-templ-param "Named parameter" for setting
230    /// \c %Path type.
231    ///
232    /// \ref named-templ-param "Named parameter" for setting the \c %Path
233    /// type of the found cycles.
234    /// It must conform to the \ref lemon::concepts::Path "Path" concept
235    /// and it must have an \c addFront() function.
236    template <typename T>
237    struct SetPath
238      : public HartmannOrlin<GR, LEN, SetPathTraits<T> > {
239      typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create;
240    };
241
242    /// @}
243
244  public:
245
246    /// \brief Constructor.
247    ///
248    /// The constructor of the class.
249    ///
250    /// \param digraph The digraph the algorithm runs on.
251    /// \param length The lengths (costs) of the arcs.
252    HartmannOrlin( const Digraph &digraph,
253                   const LengthMap &length ) :
254      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
255      _best_found(false), _best_length(0), _best_size(1),
256      _cycle_path(NULL), _local_path(false), _data(digraph),
257      INF(std::numeric_limits<LargeValue>::has_infinity ?
258          std::numeric_limits<LargeValue>::infinity() :
259          std::numeric_limits<LargeValue>::max())
260    {}
261
262    /// Destructor.
263    ~HartmannOrlin() {
264      if (_local_path) delete _cycle_path;
265    }
266
267    /// \brief Set the path structure for storing the found cycle.
268    ///
269    /// This function sets an external path structure for storing the
270    /// found cycle.
271    ///
272    /// If you don't call this function before calling \ref run() or
273    /// \ref findMinMean(), it will allocate a local \ref Path "path"
274    /// structure. The destuctor deallocates this automatically
275    /// allocated object, of course.
276    ///
277    /// \note The algorithm calls only the \ref lemon::Path::addFront()
278    /// "addFront()" function of the given path structure.
279    ///
280    /// \return <tt>(*this)</tt>
281    HartmannOrlin& cycle(Path &path) {
282      if (_local_path) {
283        delete _cycle_path;
284        _local_path = false;
285      }
286      _cycle_path = &path;
287      return *this;
288    }
289
290    /// \brief Set the tolerance used by the algorithm.
291    ///
292    /// This function sets the tolerance object used by the algorithm.
293    ///
294    /// \return <tt>(*this)</tt>
295    HartmannOrlin& tolerance(const Tolerance& tolerance) {
296      _tolerance = tolerance;
297      return *this;
298    }
299
300    /// \brief Return a const reference to the tolerance.
301    ///
302    /// This function returns a const reference to the tolerance object
303    /// used by the algorithm.
304    const Tolerance& tolerance() const {
305      return _tolerance;
306    }
307
308    /// \name Execution control
309    /// The simplest way to execute the algorithm is to call the \ref run()
310    /// function.\n
311    /// If you only need the minimum mean length, you may call
312    /// \ref findMinMean().
313
314    /// @{
315
316    /// \brief Run the algorithm.
317    ///
318    /// This function runs the algorithm.
319    /// It can be called more than once (e.g. if the underlying digraph
320    /// and/or the arc lengths have been modified).
321    ///
322    /// \return \c true if a directed cycle exists in the digraph.
323    ///
324    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
325    /// \code
326    ///   return mmc.findMinMean() && mmc.findCycle();
327    /// \endcode
328    bool run() {
329      return findMinMean() && findCycle();
330    }
331
332    /// \brief Find the minimum cycle mean.
333    ///
334    /// This function finds the minimum mean length of the directed
335    /// cycles in the digraph.
336    ///
337    /// \return \c true if a directed cycle exists in the digraph.
338    bool findMinMean() {
339      // Initialization and find strongly connected components
340      init();
341      findComponents();
342     
343      // Find the minimum cycle mean in the components
344      for (int comp = 0; comp < _comp_num; ++comp) {
345        if (!initComponent(comp)) continue;
346        processRounds();
347       
348        // Update the best cycle (global minimum mean cycle)
349        if ( _curr_found && (!_best_found ||
350             _curr_length * _best_size < _best_length * _curr_size) ) {
351          _best_found = true;
352          _best_length = _curr_length;
353          _best_size = _curr_size;
354          _best_node = _curr_node;
355          _best_level = _curr_level;
356        }
357      }
358      return _best_found;
359    }
360
361    /// \brief Find a minimum mean directed cycle.
362    ///
363    /// This function finds a directed cycle of minimum mean length
364    /// in the digraph using the data computed by findMinMean().
365    ///
366    /// \return \c true if a directed cycle exists in the digraph.
367    ///
368    /// \pre \ref findMinMean() must be called before using this function.
369    bool findCycle() {
370      if (!_best_found) return false;
371      IntNodeMap reached(_gr, -1);
372      int r = _best_level + 1;
373      Node u = _best_node;
374      while (reached[u] < 0) {
375        reached[u] = --r;
376        u = _gr.source(_data[u][r].pred);
377      }
378      r = reached[u];
379      Arc e = _data[u][r].pred;
380      _cycle_path->addFront(e);
381      _best_length = _length[e];
382      _best_size = 1;
383      Node v;
384      while ((v = _gr.source(e)) != u) {
385        e = _data[v][--r].pred;
386        _cycle_path->addFront(e);
387        _best_length += _length[e];
388        ++_best_size;
389      }
390      return true;
391    }
392
393    /// @}
394
395    /// \name Query Functions
396    /// The results of the algorithm can be obtained using these
397    /// functions.\n
398    /// The algorithm should be executed before using them.
399
400    /// @{
401
402    /// \brief Return the total length of the found cycle.
403    ///
404    /// This function returns the total length of the found cycle.
405    ///
406    /// \pre \ref run() or \ref findMinMean() must be called before
407    /// using this function.
408    LargeValue cycleLength() const {
409      return _best_length;
410    }
411
412    /// \brief Return the number of arcs on the found cycle.
413    ///
414    /// This function returns the number of arcs on the found cycle.
415    ///
416    /// \pre \ref run() or \ref findMinMean() must be called before
417    /// using this function.
418    int cycleArcNum() const {
419      return _best_size;
420    }
421
422    /// \brief Return the mean length of the found cycle.
423    ///
424    /// This function returns the mean length of the found cycle.
425    ///
426    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
427    /// following code.
428    /// \code
429    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
430    /// \endcode
431    ///
432    /// \pre \ref run() or \ref findMinMean() must be called before
433    /// using this function.
434    double cycleMean() const {
435      return static_cast<double>(_best_length) / _best_size;
436    }
437
438    /// \brief Return the found cycle.
439    ///
440    /// This function returns a const reference to the path structure
441    /// storing the found cycle.
442    ///
443    /// \pre \ref run() or \ref findCycle() must be called before using
444    /// this function.
445    const Path& cycle() const {
446      return *_cycle_path;
447    }
448
449    ///@}
450
451  private:
452
453    // Initialization
454    void init() {
455      if (!_cycle_path) {
456        _local_path = true;
457        _cycle_path = new Path;
458      }
459      _cycle_path->clear();
460      _best_found = false;
461      _best_length = 0;
462      _best_size = 1;
463      _cycle_path->clear();
464      for (NodeIt u(_gr); u != INVALID; ++u)
465        _data[u].clear();
466    }
467
468    // Find strongly connected components and initialize _comp_nodes
469    // and _out_arcs
470    void findComponents() {
471      _comp_num = stronglyConnectedComponents(_gr, _comp);
472      _comp_nodes.resize(_comp_num);
473      if (_comp_num == 1) {
474        _comp_nodes[0].clear();
475        for (NodeIt n(_gr); n != INVALID; ++n) {
476          _comp_nodes[0].push_back(n);
477          _out_arcs[n].clear();
478          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
479            _out_arcs[n].push_back(a);
480          }
481        }
482      } else {
483        for (int i = 0; i < _comp_num; ++i)
484          _comp_nodes[i].clear();
485        for (NodeIt n(_gr); n != INVALID; ++n) {
486          int k = _comp[n];
487          _comp_nodes[k].push_back(n);
488          _out_arcs[n].clear();
489          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
490            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
491          }
492        }
493      }
494    }
495
496    // Initialize path data for the current component
497    bool initComponent(int comp) {
498      _nodes = &(_comp_nodes[comp]);
499      int n = _nodes->size();
500      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
501        return false;
502      }     
503      for (int i = 0; i < n; ++i) {
504        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
505      }
506      return true;
507    }
508
509    // Process all rounds of computing path data for the current component.
510    // _data[v][k] is the length of a shortest directed walk from the root
511    // node to node v containing exactly k arcs.
512    void processRounds() {
513      Node start = (*_nodes)[0];
514      _data[start][0] = PathData(0);
515      _process.clear();
516      _process.push_back(start);
517
518      int k, n = _nodes->size();
519      int next_check = 4;
520      bool terminate = false;
521      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
522        processNextBuildRound(k);
523        if (k == next_check || k == n) {
524          terminate = checkTermination(k);
525          next_check = next_check * 3 / 2;
526        }
527      }
528      for ( ; k <= n && !terminate; ++k) {
529        processNextFullRound(k);
530        if (k == next_check || k == n) {
531          terminate = checkTermination(k);
532          next_check = next_check * 3 / 2;
533        }
534      }
535    }
536
537    // Process one round and rebuild _process
538    void processNextBuildRound(int k) {
539      std::vector<Node> next;
540      Node u, v;
541      Arc e;
542      LargeValue d;
543      for (int i = 0; i < int(_process.size()); ++i) {
544        u = _process[i];
545        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
546          e = _out_arcs[u][j];
547          v = _gr.target(e);
548          d = _data[u][k-1].dist + _length[e];
549          if (_tolerance.less(d, _data[v][k].dist)) {
550            if (_data[v][k].dist == INF) next.push_back(v);
551            _data[v][k] = PathData(d, e);
552          }
553        }
554      }
555      _process.swap(next);
556    }
557
558    // Process one round using _nodes instead of _process
559    void processNextFullRound(int k) {
560      Node u, v;
561      Arc e;
562      LargeValue d;
563      for (int i = 0; i < int(_nodes->size()); ++i) {
564        u = (*_nodes)[i];
565        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
566          e = _out_arcs[u][j];
567          v = _gr.target(e);
568          d = _data[u][k-1].dist + _length[e];
569          if (_tolerance.less(d, _data[v][k].dist)) {
570            _data[v][k] = PathData(d, e);
571          }
572        }
573      }
574    }
575   
576    // Check early termination
577    bool checkTermination(int k) {
578      typedef std::pair<int, int> Pair;
579      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
580      typename GR::template NodeMap<LargeValue> pi(_gr);
581      int n = _nodes->size();
582      LargeValue length;
583      int size;
584      Node u;
585     
586      // Search for cycles that are already found
587      _curr_found = false;
588      for (int i = 0; i < n; ++i) {
589        u = (*_nodes)[i];
590        if (_data[u][k].dist == INF) continue;
591        for (int j = k; j >= 0; --j) {
592          if (level[u].first == i && level[u].second > 0) {
593            // A cycle is found
594            length = _data[u][level[u].second].dist - _data[u][j].dist;
595            size = level[u].second - j;
596            if (!_curr_found || length * _curr_size < _curr_length * size) {
597              _curr_length = length;
598              _curr_size = size;
599              _curr_node = u;
600              _curr_level = level[u].second;
601              _curr_found = true;
602            }
603          }
604          level[u] = Pair(i, j);
605          if (j != 0) {
606            u = _gr.source(_data[u][j].pred);
607          }
608        }
609      }
610
611      // If at least one cycle is found, check the optimality condition
612      LargeValue d;
613      if (_curr_found && k < n) {
614        // Find node potentials
615        for (int i = 0; i < n; ++i) {
616          u = (*_nodes)[i];
617          pi[u] = INF;
618          for (int j = 0; j <= k; ++j) {
619            if (_data[u][j].dist < INF) {
620              d = _data[u][j].dist * _curr_size - j * _curr_length;
621              if (_tolerance.less(d, pi[u])) pi[u] = d;
622            }
623          }
624        }
625
626        // Check the optimality condition for all arcs
627        bool done = true;
628        for (ArcIt a(_gr); a != INVALID; ++a) {
629          if (_tolerance.less(_length[a] * _curr_size - _curr_length,
630                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
631            done = false;
632            break;
633          }
634        }
635        return done;
636      }
637      return (k == n);
638    }
639
640  }; //class HartmannOrlin
641
642  ///@}
643
644} //namespace lemon
645
646#endif //LEMON_HARTMANN_ORLIN_H
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