COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/karp.h @ 841:aa8c9008b3de

Last change on this file since 841:aa8c9008b3de was 841:aa8c9008b3de, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Better return type for cycleLength() functions (#179)
in the min mean cycle algorithms.

The original Value type is used instead of the LargeValue? type,
which is introduced for internal computations.

File size: 17.1 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_KARP_H
20#define LEMON_KARP_H
21
22/// \ingroup min_mean_cycle
23///
24/// \file
25/// \brief Karp'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 Karp algorithm.
37  ///
38  /// Default traits class of Karp 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::ReadMap "ReadMap" 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 KarpDefaultTraits
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 KarpDefaultTraits<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 Karp's algorithm for finding a minimum
97  /// mean cycle.
98  ///
99  /// This class implements Karp's algorithm for finding a directed
100  /// cycle of minimum mean length (cost) in a digraph
101  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
102  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
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  /// \tparam TR The traits class that defines various types used by the
108  /// algorithm. By default, it is \ref KarpDefaultTraits
109  /// "KarpDefaultTraits<GR, LEN>".
110  /// In most cases, this parameter should not be set directly,
111  /// consider to use the named template parameters instead.
112#ifdef DOXYGEN
113  template <typename GR, typename LEN, typename TR>
114#else
115  template < typename GR,
116             typename LEN = typename GR::template ArcMap<int>,
117             typename TR = KarpDefaultTraits<GR, LEN> >
118#endif
119  class Karp
120  {
121  public:
122
123    /// The type of the digraph
124    typedef typename TR::Digraph Digraph;
125    /// The type of the length map
126    typedef typename TR::LengthMap LengthMap;
127    /// The type of the arc lengths
128    typedef typename TR::Value Value;
129
130    /// \brief The large value type
131    ///
132    /// The large value type used for internal computations.
133    /// By default, it is \c long \c long if the \c Value type is integer,
134    /// otherwise it is \c double.
135    typedef typename TR::LargeValue LargeValue;
136
137    /// The tolerance type
138    typedef typename TR::Tolerance Tolerance;
139
140    /// \brief The path type of the found cycles
141    ///
142    /// The path type of the found cycles.
143    /// Using the \ref KarpDefaultTraits "default traits class",
144    /// it is \ref lemon::Path "Path<Digraph>".
145    typedef typename TR::Path Path;
146
147    /// The \ref KarpDefaultTraits "traits class" of the algorithm
148    typedef TR Traits;
149
150  private:
151
152    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
153
154    // Data sturcture for path data
155    struct PathData
156    {
157      LargeValue dist;
158      Arc pred;
159      PathData(LargeValue d, Arc p = INVALID) :
160        dist(d), pred(p) {}
161    };
162
163    typedef typename Digraph::template NodeMap<std::vector<PathData> >
164      PathDataNodeMap;
165
166  private:
167
168    // The digraph the algorithm runs on
169    const Digraph &_gr;
170    // The length of the arcs
171    const LengthMap &_length;
172
173    // Data for storing the strongly connected components
174    int _comp_num;
175    typename Digraph::template NodeMap<int> _comp;
176    std::vector<std::vector<Node> > _comp_nodes;
177    std::vector<Node>* _nodes;
178    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
179
180    // Data for the found cycle
181    LargeValue _cycle_length;
182    int _cycle_size;
183    Node _cycle_node;
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 Karp<GR, LEN, SetLargeValueTraits<T> > {
217      typedef Karp<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 Karp<GR, LEN, SetPathTraits<T> > {
235      typedef Karp<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    Karp( const Digraph &digraph,
249          const LengthMap &length ) :
250      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
251      _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
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    ~Karp() {
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    Karp& 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    Karp& 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        updateMinMean();
344      }
345      return (_cycle_node != INVALID);
346    }
347
348    /// \brief Find a minimum mean directed cycle.
349    ///
350    /// This function finds a directed cycle of minimum mean length
351    /// in the digraph using the data computed by findMinMean().
352    ///
353    /// \return \c true if a directed cycle exists in the digraph.
354    ///
355    /// \pre \ref findMinMean() must be called before using this function.
356    bool findCycle() {
357      if (_cycle_node == INVALID) return false;
358      IntNodeMap reached(_gr, -1);
359      int r = _data[_cycle_node].size();
360      Node u = _cycle_node;
361      while (reached[u] < 0) {
362        reached[u] = --r;
363        u = _gr.source(_data[u][r].pred);
364      }
365      r = reached[u];
366      Arc e = _data[u][r].pred;
367      _cycle_path->addFront(e);
368      _cycle_length = _length[e];
369      _cycle_size = 1;
370      Node v;
371      while ((v = _gr.source(e)) != u) {
372        e = _data[v][--r].pred;
373        _cycle_path->addFront(e);
374        _cycle_length += _length[e];
375        ++_cycle_size;
376      }
377      return true;
378    }
379
380    /// @}
381
382    /// \name Query Functions
383    /// The results of the algorithm can be obtained using these
384    /// functions.\n
385    /// The algorithm should be executed before using them.
386
387    /// @{
388
389    /// \brief Return the total length of the found cycle.
390    ///
391    /// This function returns the total length of the found cycle.
392    ///
393    /// \pre \ref run() or \ref findMinMean() must be called before
394    /// using this function.
395    Value cycleLength() const {
396      return static_cast<Value>(_cycle_length);
397    }
398
399    /// \brief Return the number of arcs on the found cycle.
400    ///
401    /// This function returns the number of arcs on the found cycle.
402    ///
403    /// \pre \ref run() or \ref findMinMean() must be called before
404    /// using this function.
405    int cycleArcNum() const {
406      return _cycle_size;
407    }
408
409    /// \brief Return the mean length of the found cycle.
410    ///
411    /// This function returns the mean length of the found cycle.
412    ///
413    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
414    /// following code.
415    /// \code
416    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
417    /// \endcode
418    ///
419    /// \pre \ref run() or \ref findMinMean() must be called before
420    /// using this function.
421    double cycleMean() const {
422      return static_cast<double>(_cycle_length) / _cycle_size;
423    }
424
425    /// \brief Return the found cycle.
426    ///
427    /// This function returns a const reference to the path structure
428    /// storing the found cycle.
429    ///
430    /// \pre \ref run() or \ref findCycle() must be called before using
431    /// this function.
432    const Path& cycle() const {
433      return *_cycle_path;
434    }
435
436    ///@}
437
438  private:
439
440    // Initialization
441    void init() {
442      if (!_cycle_path) {
443        _local_path = true;
444        _cycle_path = new Path;
445      }
446      _cycle_path->clear();
447      _cycle_length = 0;
448      _cycle_size = 1;
449      _cycle_node = INVALID;
450      for (NodeIt u(_gr); u != INVALID; ++u)
451        _data[u].clear();
452    }
453
454    // Find strongly connected components and initialize _comp_nodes
455    // and _out_arcs
456    void findComponents() {
457      _comp_num = stronglyConnectedComponents(_gr, _comp);
458      _comp_nodes.resize(_comp_num);
459      if (_comp_num == 1) {
460        _comp_nodes[0].clear();
461        for (NodeIt n(_gr); n != INVALID; ++n) {
462          _comp_nodes[0].push_back(n);
463          _out_arcs[n].clear();
464          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
465            _out_arcs[n].push_back(a);
466          }
467        }
468      } else {
469        for (int i = 0; i < _comp_num; ++i)
470          _comp_nodes[i].clear();
471        for (NodeIt n(_gr); n != INVALID; ++n) {
472          int k = _comp[n];
473          _comp_nodes[k].push_back(n);
474          _out_arcs[n].clear();
475          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
476            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
477          }
478        }
479      }
480    }
481
482    // Initialize path data for the current component
483    bool initComponent(int comp) {
484      _nodes = &(_comp_nodes[comp]);
485      int n = _nodes->size();
486      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
487        return false;
488      }     
489      for (int i = 0; i < n; ++i) {
490        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
491      }
492      return true;
493    }
494
495    // Process all rounds of computing path data for the current component.
496    // _data[v][k] is the length of a shortest directed walk from the root
497    // node to node v containing exactly k arcs.
498    void processRounds() {
499      Node start = (*_nodes)[0];
500      _data[start][0] = PathData(0);
501      _process.clear();
502      _process.push_back(start);
503
504      int k, n = _nodes->size();
505      for (k = 1; k <= n && int(_process.size()) < n; ++k) {
506        processNextBuildRound(k);
507      }
508      for ( ; k <= n; ++k) {
509        processNextFullRound(k);
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];
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);
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];
545          if (_tolerance.less(d, _data[v][k].dist)) {
546            _data[v][k] = PathData(d, e);
547          }
548        }
549      }
550    }
551
552    // Update the minimum cycle mean
553    void updateMinMean() {
554      int n = _nodes->size();
555      for (int i = 0; i < n; ++i) {
556        Node u = (*_nodes)[i];
557        if (_data[u][n].dist == INF) continue;
558        LargeValue length, max_length = 0;
559        int size, max_size = 1;
560        bool found_curr = false;
561        for (int k = 0; k < n; ++k) {
562          if (_data[u][k].dist == INF) continue;
563          length = _data[u][n].dist - _data[u][k].dist;
564          size = n - k;
565          if (!found_curr || length * max_size > max_length * size) {
566            found_curr = true;
567            max_length = length;
568            max_size = size;
569          }
570        }
571        if ( found_curr && (_cycle_node == INVALID ||
572             max_length * _cycle_size < _cycle_length * max_size) ) {
573          _cycle_length = max_length;
574          _cycle_size = max_size;
575          _cycle_node = u;
576        }
577      }
578    }
579
580  }; //class Karp
581
582  ///@}
583
584} //namespace lemon
585
586#endif //LEMON_KARP_H
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