COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/karp.h @ 814:0643a9c2c3ae

Last change on this file since 814:0643a9c2c3ae was 772:f964a00b9068, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Small fix in the doc (#179)

File size: 16.9 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#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 = KarpDefaultTraits<GR, LEN> >
113#endif
114  class Karp
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 KarpDefaultTraits "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 KarpDefaultTraits "default traits class",
140    /// it is \ref lemon::Path "Path<Digraph>".
141    typedef typename TR::Path Path;
142
143    /// The \ref KarpDefaultTraits "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;
155      PathData(LargeValue d, Arc p = INVALID) :
156        dist(d), pred(p) {}
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 cycle
177    LargeValue _cycle_length;
178    int _cycle_size;
179    Node _cycle_node;
180
181    Path *_cycle_path;
182    bool _local_path;
183
184    // Node map for storing path data
185    PathDataNodeMap _data;
186    // The processed nodes in the last round
187    std::vector<Node> _process;
188
189    Tolerance _tolerance;
190   
191    // Infinite constant
192    const LargeValue INF;
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 Karp<GR, LEN, SetLargeValueTraits<T> > {
213      typedef Karp<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 Karp<GR, LEN, SetPathTraits<T> > {
231      typedef Karp<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    Karp( const Digraph &digraph,
245          const LengthMap &length ) :
246      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
247      _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
248      _cycle_path(NULL), _local_path(false), _data(digraph),
249      INF(std::numeric_limits<LargeValue>::has_infinity ?
250          std::numeric_limits<LargeValue>::infinity() :
251          std::numeric_limits<LargeValue>::max())
252    {}
253
254    /// Destructor.
255    ~Karp() {
256      if (_local_path) delete _cycle_path;
257    }
258
259    /// \brief Set the path structure for storing the found cycle.
260    ///
261    /// This function sets an external path structure for storing the
262    /// found cycle.
263    ///
264    /// If you don't call this function before calling \ref run() or
265    /// \ref findMinMean(), it will allocate a local \ref Path "path"
266    /// structure. The destuctor deallocates this automatically
267    /// allocated object, of course.
268    ///
269    /// \note The algorithm calls only the \ref lemon::Path::addFront()
270    /// "addFront()" function of the given path structure.
271    ///
272    /// \return <tt>(*this)</tt>
273    Karp& cycle(Path &path) {
274      if (_local_path) {
275        delete _cycle_path;
276        _local_path = false;
277      }
278      _cycle_path = &path;
279      return *this;
280    }
281
282    /// \brief Set the tolerance used by the algorithm.
283    ///
284    /// This function sets the tolerance object used by the algorithm.
285    ///
286    /// \return <tt>(*this)</tt>
287    Karp& tolerance(const Tolerance& tolerance) {
288      _tolerance = tolerance;
289      return *this;
290    }
291
292    /// \brief Return a const reference to the tolerance.
293    ///
294    /// This function returns a const reference to the tolerance object
295    /// used by the algorithm.
296    const Tolerance& tolerance() const {
297      return _tolerance;
298    }
299
300    /// \name Execution control
301    /// The simplest way to execute the algorithm is to call the \ref run()
302    /// function.\n
303    /// If you only need the minimum mean length, you may call
304    /// \ref findMinMean().
305
306    /// @{
307
308    /// \brief Run the algorithm.
309    ///
310    /// This function runs the algorithm.
311    /// It can be called more than once (e.g. if the underlying digraph
312    /// and/or the arc lengths have been modified).
313    ///
314    /// \return \c true if a directed cycle exists in the digraph.
315    ///
316    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
317    /// \code
318    ///   return mmc.findMinMean() && mmc.findCycle();
319    /// \endcode
320    bool run() {
321      return findMinMean() && findCycle();
322    }
323
324    /// \brief Find the minimum cycle mean.
325    ///
326    /// This function finds the minimum mean length of the directed
327    /// cycles in the digraph.
328    ///
329    /// \return \c true if a directed cycle exists in the digraph.
330    bool findMinMean() {
331      // Initialization and find strongly connected components
332      init();
333      findComponents();
334     
335      // Find the minimum cycle mean in the components
336      for (int comp = 0; comp < _comp_num; ++comp) {
337        if (!initComponent(comp)) continue;
338        processRounds();
339        updateMinMean();
340      }
341      return (_cycle_node != INVALID);
342    }
343
344    /// \brief Find a minimum mean directed cycle.
345    ///
346    /// This function finds a directed cycle of minimum mean length
347    /// in the digraph using the data computed by findMinMean().
348    ///
349    /// \return \c true if a directed cycle exists in the digraph.
350    ///
351    /// \pre \ref findMinMean() must be called before using this function.
352    bool findCycle() {
353      if (_cycle_node == INVALID) return false;
354      IntNodeMap reached(_gr, -1);
355      int r = _data[_cycle_node].size();
356      Node u = _cycle_node;
357      while (reached[u] < 0) {
358        reached[u] = --r;
359        u = _gr.source(_data[u][r].pred);
360      }
361      r = reached[u];
362      Arc e = _data[u][r].pred;
363      _cycle_path->addFront(e);
364      _cycle_length = _length[e];
365      _cycle_size = 1;
366      Node v;
367      while ((v = _gr.source(e)) != u) {
368        e = _data[v][--r].pred;
369        _cycle_path->addFront(e);
370        _cycle_length += _length[e];
371        ++_cycle_size;
372      }
373      return true;
374    }
375
376    /// @}
377
378    /// \name Query Functions
379    /// The results of the algorithm can be obtained using these
380    /// functions.\n
381    /// The algorithm should be executed before using them.
382
383    /// @{
384
385    /// \brief Return the total length of the found cycle.
386    ///
387    /// This function returns the total length of the found cycle.
388    ///
389    /// \pre \ref run() or \ref findMinMean() must be called before
390    /// using this function.
391    LargeValue cycleLength() const {
392      return _cycle_length;
393    }
394
395    /// \brief Return the number of arcs on the found cycle.
396    ///
397    /// This function returns the number of arcs on the found cycle.
398    ///
399    /// \pre \ref run() or \ref findMinMean() must be called before
400    /// using this function.
401    int cycleArcNum() const {
402      return _cycle_size;
403    }
404
405    /// \brief Return the mean length of the found cycle.
406    ///
407    /// This function returns the mean length of the found cycle.
408    ///
409    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
410    /// following code.
411    /// \code
412    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
413    /// \endcode
414    ///
415    /// \pre \ref run() or \ref findMinMean() must be called before
416    /// using this function.
417    double cycleMean() const {
418      return static_cast<double>(_cycle_length) / _cycle_size;
419    }
420
421    /// \brief Return the found cycle.
422    ///
423    /// This function returns a const reference to the path structure
424    /// storing the found cycle.
425    ///
426    /// \pre \ref run() or \ref findCycle() must be called before using
427    /// this function.
428    const Path& cycle() const {
429      return *_cycle_path;
430    }
431
432    ///@}
433
434  private:
435
436    // Initialization
437    void init() {
438      if (!_cycle_path) {
439        _local_path = true;
440        _cycle_path = new Path;
441      }
442      _cycle_path->clear();
443      _cycle_length = 0;
444      _cycle_size = 1;
445      _cycle_node = INVALID;
446      for (NodeIt u(_gr); u != INVALID; ++u)
447        _data[u].clear();
448    }
449
450    // Find strongly connected components and initialize _comp_nodes
451    // and _out_arcs
452    void findComponents() {
453      _comp_num = stronglyConnectedComponents(_gr, _comp);
454      _comp_nodes.resize(_comp_num);
455      if (_comp_num == 1) {
456        _comp_nodes[0].clear();
457        for (NodeIt n(_gr); n != INVALID; ++n) {
458          _comp_nodes[0].push_back(n);
459          _out_arcs[n].clear();
460          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
461            _out_arcs[n].push_back(a);
462          }
463        }
464      } else {
465        for (int i = 0; i < _comp_num; ++i)
466          _comp_nodes[i].clear();
467        for (NodeIt n(_gr); n != INVALID; ++n) {
468          int k = _comp[n];
469          _comp_nodes[k].push_back(n);
470          _out_arcs[n].clear();
471          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
472            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
473          }
474        }
475      }
476    }
477
478    // Initialize path data for the current component
479    bool initComponent(int comp) {
480      _nodes = &(_comp_nodes[comp]);
481      int n = _nodes->size();
482      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
483        return false;
484      }     
485      for (int i = 0; i < n; ++i) {
486        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
487      }
488      return true;
489    }
490
491    // Process all rounds of computing path data for the current component.
492    // _data[v][k] is the length of a shortest directed walk from the root
493    // node to node v containing exactly k arcs.
494    void processRounds() {
495      Node start = (*_nodes)[0];
496      _data[start][0] = PathData(0);
497      _process.clear();
498      _process.push_back(start);
499
500      int k, n = _nodes->size();
501      for (k = 1; k <= n && int(_process.size()) < n; ++k) {
502        processNextBuildRound(k);
503      }
504      for ( ; k <= n; ++k) {
505        processNextFullRound(k);
506      }
507    }
508
509    // Process one round and rebuild _process
510    void processNextBuildRound(int k) {
511      std::vector<Node> next;
512      Node u, v;
513      Arc e;
514      LargeValue d;
515      for (int i = 0; i < int(_process.size()); ++i) {
516        u = _process[i];
517        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
518          e = _out_arcs[u][j];
519          v = _gr.target(e);
520          d = _data[u][k-1].dist + _length[e];
521          if (_tolerance.less(d, _data[v][k].dist)) {
522            if (_data[v][k].dist == INF) next.push_back(v);
523            _data[v][k] = PathData(d, e);
524          }
525        }
526      }
527      _process.swap(next);
528    }
529
530    // Process one round using _nodes instead of _process
531    void processNextFullRound(int k) {
532      Node u, v;
533      Arc e;
534      LargeValue d;
535      for (int i = 0; i < int(_nodes->size()); ++i) {
536        u = (*_nodes)[i];
537        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
538          e = _out_arcs[u][j];
539          v = _gr.target(e);
540          d = _data[u][k-1].dist + _length[e];
541          if (_tolerance.less(d, _data[v][k].dist)) {
542            _data[v][k] = PathData(d, e);
543          }
544        }
545      }
546    }
547
548    // Update the minimum cycle mean
549    void updateMinMean() {
550      int n = _nodes->size();
551      for (int i = 0; i < n; ++i) {
552        Node u = (*_nodes)[i];
553        if (_data[u][n].dist == INF) continue;
554        LargeValue length, max_length = 0;
555        int size, max_size = 1;
556        bool found_curr = false;
557        for (int k = 0; k < n; ++k) {
558          if (_data[u][k].dist == INF) continue;
559          length = _data[u][n].dist - _data[u][k].dist;
560          size = n - k;
561          if (!found_curr || length * max_size > max_length * size) {
562            found_curr = true;
563            max_length = length;
564            max_size = size;
565          }
566        }
567        if ( found_curr && (_cycle_node == INVALID ||
568             max_length * _cycle_size < _cycle_length * max_size) ) {
569          _cycle_length = max_length;
570          _cycle_size = max_size;
571          _cycle_node = u;
572        }
573      }
574    }
575
576  }; //class Karp
577
578  ///@}
579
580} //namespace lemon
581
582#endif //LEMON_KARP_H
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