COIN-OR::LEMON - Graph Library

source: lemon/lemon/karp.h @ 812:3b544a9c92db

Last change on this file since 812:3b544a9c92db was 812:3b544a9c92db, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Add Karp algorithm class (#179)
based on the MinMeanCycle? implementation in SVN -r3436.
The interface is reworked to be the same as Howard's interface.

File size: 16.2 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 shortest_path
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 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 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 shortest_path
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  ///
102  /// \tparam GR The type of the digraph the algorithm runs on.
103  /// \tparam LEN The type of the length map. The default
104  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
105#ifdef DOXYGEN
106  template <typename GR, typename LEN, typename TR>
107#else
108  template < typename GR,
109             typename LEN = typename GR::template ArcMap<int>,
110             typename TR = KarpDefaultTraits<GR, LEN> >
111#endif
112  class Karp
113  {
114  public:
115
116    /// The type of the digraph
117    typedef typename TR::Digraph Digraph;
118    /// The type of the length map
119    typedef typename TR::LengthMap LengthMap;
120    /// The type of the arc lengths
121    typedef typename TR::Value Value;
122
123    /// \brief The large value type
124    ///
125    /// The large value type used for internal computations.
126    /// Using the \ref KarpDefaultTraits "default traits class",
127    /// it is \c long \c long if the \c Value type is integer,
128    /// otherwise it is \c double.
129    typedef typename TR::LargeValue LargeValue;
130
131    /// The tolerance type
132    typedef typename TR::Tolerance Tolerance;
133
134    /// \brief The path type of the found cycles
135    ///
136    /// The path type of the found cycles.
137    /// Using the \ref KarpDefaultTraits "default traits class",
138    /// it is \ref lemon::Path "Path<Digraph>".
139    typedef typename TR::Path Path;
140
141    /// The \ref KarpDefaultTraits "traits class" of the algorithm
142    typedef TR Traits;
143
144  private:
145
146    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
147
148    // Data sturcture for path data
149    struct PathData
150    {
151      bool found;
152      LargeValue dist;
153      Arc pred;
154      PathData(bool f = false, LargeValue d = 0, Arc p = INVALID) :
155        found(f), dist(d), pred(p) {}
156    };
157
158    typedef typename Digraph::template NodeMap<std::vector<PathData> >
159      PathDataNodeMap;
160
161  private:
162
163    // The digraph the algorithm runs on
164    const Digraph &_gr;
165    // The length of the arcs
166    const LengthMap &_length;
167
168    // Data for storing the strongly connected components
169    int _comp_num;
170    typename Digraph::template NodeMap<int> _comp;
171    std::vector<std::vector<Node> > _comp_nodes;
172    std::vector<Node>* _nodes;
173    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
174
175    // Data for the found cycle
176    LargeValue _cycle_length;
177    int _cycle_size;
178    Node _cycle_node;
179
180    Path *_cycle_path;
181    bool _local_path;
182
183    // Node map for storing path data
184    PathDataNodeMap _data;
185    // The processed nodes in the last round
186    std::vector<Node> _process;
187
188    Tolerance _tolerance;
189
190  public:
191
192    /// \name Named Template Parameters
193    /// @{
194
195    template <typename T>
196    struct SetLargeValueTraits : public Traits {
197      typedef T LargeValue;
198      typedef lemon::Tolerance<T> Tolerance;
199    };
200
201    /// \brief \ref named-templ-param "Named parameter" for setting
202    /// \c LargeValue type.
203    ///
204    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
205    /// type. It is used for internal computations in the algorithm.
206    template <typename T>
207    struct SetLargeValue
208      : public Karp<GR, LEN, SetLargeValueTraits<T> > {
209      typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create;
210    };
211
212    template <typename T>
213    struct SetPathTraits : public Traits {
214      typedef T Path;
215    };
216
217    /// \brief \ref named-templ-param "Named parameter" for setting
218    /// \c %Path type.
219    ///
220    /// \ref named-templ-param "Named parameter" for setting the \c %Path
221    /// type of the found cycles.
222    /// It must conform to the \ref lemon::concepts::Path "Path" concept
223    /// and it must have an \c addFront() function.
224    template <typename T>
225    struct SetPath
226      : public Karp<GR, LEN, SetPathTraits<T> > {
227      typedef Karp<GR, LEN, SetPathTraits<T> > Create;
228    };
229
230    /// @}
231
232  public:
233
234    /// \brief Constructor.
235    ///
236    /// The constructor of the class.
237    ///
238    /// \param digraph The digraph the algorithm runs on.
239    /// \param length The lengths (costs) of the arcs.
240    Karp( const Digraph &digraph,
241          const LengthMap &length ) :
242      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
243      _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
244      _cycle_path(NULL), _local_path(false), _data(digraph)
245    {}
246
247    /// Destructor.
248    ~Karp() {
249      if (_local_path) delete _cycle_path;
250    }
251
252    /// \brief Set the path structure for storing the found cycle.
253    ///
254    /// This function sets an external path structure for storing the
255    /// found cycle.
256    ///
257    /// If you don't call this function before calling \ref run() or
258    /// \ref findMinMean(), it will allocate a local \ref Path "path"
259    /// structure. The destuctor deallocates this automatically
260    /// allocated object, of course.
261    ///
262    /// \note The algorithm calls only the \ref lemon::Path::addFront()
263    /// "addFront()" function of the given path structure.
264    ///
265    /// \return <tt>(*this)</tt>
266    Karp& cycle(Path &path) {
267      if (_local_path) {
268        delete _cycle_path;
269        _local_path = false;
270      }
271      _cycle_path = &path;
272      return *this;
273    }
274
275    /// \name Execution control
276    /// The simplest way to execute the algorithm is to call the \ref run()
277    /// function.\n
278    /// If you only need the minimum mean length, you may call
279    /// \ref findMinMean().
280
281    /// @{
282
283    /// \brief Run the algorithm.
284    ///
285    /// This function runs the algorithm.
286    /// It can be called more than once (e.g. if the underlying digraph
287    /// and/or the arc lengths have been modified).
288    ///
289    /// \return \c true if a directed cycle exists in the digraph.
290    ///
291    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
292    /// \code
293    ///   return mmc.findMinMean() && mmc.findCycle();
294    /// \endcode
295    bool run() {
296      return findMinMean() && findCycle();
297    }
298
299    /// \brief Find the minimum cycle mean.
300    ///
301    /// This function finds the minimum mean length of the directed
302    /// cycles in the digraph.
303    ///
304    /// \return \c true if a directed cycle exists in the digraph.
305    bool findMinMean() {
306      // Initialization and find strongly connected components
307      init();
308      findComponents();
309     
310      // Find the minimum cycle mean in the components
311      for (int comp = 0; comp < _comp_num; ++comp) {
312        if (!initComponent(comp)) continue;
313        processRounds();
314        updateMinMean();
315      }
316      return (_cycle_node != INVALID);
317    }
318
319    /// \brief Find a minimum mean directed cycle.
320    ///
321    /// This function finds a directed cycle of minimum mean length
322    /// in the digraph using the data computed by findMinMean().
323    ///
324    /// \return \c true if a directed cycle exists in the digraph.
325    ///
326    /// \pre \ref findMinMean() must be called before using this function.
327    bool findCycle() {
328      if (_cycle_node == INVALID) return false;
329      IntNodeMap reached(_gr, -1);
330      int r = _data[_cycle_node].size();
331      Node u = _cycle_node;
332      while (reached[u] < 0) {
333        reached[u] = --r;
334        u = _gr.source(_data[u][r].pred);
335      }
336      r = reached[u];
337      Arc e = _data[u][r].pred;
338      _cycle_path->addFront(e);
339      _cycle_length = _length[e];
340      _cycle_size = 1;
341      Node v;
342      while ((v = _gr.source(e)) != u) {
343        e = _data[v][--r].pred;
344        _cycle_path->addFront(e);
345        _cycle_length += _length[e];
346        ++_cycle_size;
347      }
348      return true;
349    }
350
351    /// @}
352
353    /// \name Query Functions
354    /// The results of the algorithm can be obtained using these
355    /// functions.\n
356    /// The algorithm should be executed before using them.
357
358    /// @{
359
360    /// \brief Return the total length of the found cycle.
361    ///
362    /// This function returns the total length of the found cycle.
363    ///
364    /// \pre \ref run() or \ref findMinMean() must be called before
365    /// using this function.
366    LargeValue cycleLength() const {
367      return _cycle_length;
368    }
369
370    /// \brief Return the number of arcs on the found cycle.
371    ///
372    /// This function returns the number of arcs on the found cycle.
373    ///
374    /// \pre \ref run() or \ref findMinMean() must be called before
375    /// using this function.
376    int cycleArcNum() const {
377      return _cycle_size;
378    }
379
380    /// \brief Return the mean length of the found cycle.
381    ///
382    /// This function returns the mean length of the found cycle.
383    ///
384    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
385    /// following code.
386    /// \code
387    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
388    /// \endcode
389    ///
390    /// \pre \ref run() or \ref findMinMean() must be called before
391    /// using this function.
392    double cycleMean() const {
393      return static_cast<double>(_cycle_length) / _cycle_size;
394    }
395
396    /// \brief Return the found cycle.
397    ///
398    /// This function returns a const reference to the path structure
399    /// storing the found cycle.
400    ///
401    /// \pre \ref run() or \ref findCycle() must be called before using
402    /// this function.
403    const Path& cycle() const {
404      return *_cycle_path;
405    }
406
407    ///@}
408
409  private:
410
411    // Initialization
412    void init() {
413      if (!_cycle_path) {
414        _local_path = true;
415        _cycle_path = new Path;
416      }
417      _cycle_path->clear();
418      _cycle_length = 0;
419      _cycle_size = 1;
420      _cycle_node = INVALID;
421      for (NodeIt u(_gr); u != INVALID; ++u)
422        _data[u].clear();
423    }
424
425    // Find strongly connected components and initialize _comp_nodes
426    // and _out_arcs
427    void findComponents() {
428      _comp_num = stronglyConnectedComponents(_gr, _comp);
429      _comp_nodes.resize(_comp_num);
430      if (_comp_num == 1) {
431        _comp_nodes[0].clear();
432        for (NodeIt n(_gr); n != INVALID; ++n) {
433          _comp_nodes[0].push_back(n);
434          _out_arcs[n].clear();
435          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
436            _out_arcs[n].push_back(a);
437          }
438        }
439      } else {
440        for (int i = 0; i < _comp_num; ++i)
441          _comp_nodes[i].clear();
442        for (NodeIt n(_gr); n != INVALID; ++n) {
443          int k = _comp[n];
444          _comp_nodes[k].push_back(n);
445          _out_arcs[n].clear();
446          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
447            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
448          }
449        }
450      }
451    }
452
453    // Initialize path data for the current component
454    bool initComponent(int comp) {
455      _nodes = &(_comp_nodes[comp]);
456      int n = _nodes->size();
457      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
458        return false;
459      }     
460      for (int i = 0; i < n; ++i) {
461        _data[(*_nodes)[i]].resize(n + 1);
462      }
463      return true;
464    }
465
466    // Process all rounds of computing path data for the current component.
467    // _data[v][k] is the length of a shortest directed walk from the root
468    // node to node v containing exactly k arcs.
469    void processRounds() {
470      Node start = (*_nodes)[0];
471      _data[start][0] = PathData(true, 0);
472      _process.clear();
473      _process.push_back(start);
474
475      int k, n = _nodes->size();
476      for (k = 1; k <= n && int(_process.size()) < n; ++k) {
477        processNextBuildRound(k);
478      }
479      for ( ; k <= n; ++k) {
480        processNextFullRound(k);
481      }
482    }
483
484    // Process one round and rebuild _process
485    void processNextBuildRound(int k) {
486      std::vector<Node> next;
487      Node u, v;
488      Arc e;
489      LargeValue d;
490      for (int i = 0; i < int(_process.size()); ++i) {
491        u = _process[i];
492        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
493          e = _out_arcs[u][j];
494          v = _gr.target(e);
495          d = _data[u][k-1].dist + _length[e];
496          if (!_data[v][k].found) {
497            next.push_back(v);
498            _data[v][k] = PathData(true, _data[u][k-1].dist + _length[e], e);
499          }
500          else if (_tolerance.less(d, _data[v][k].dist)) {
501            _data[v][k] = PathData(true, d, e);
502          }
503        }
504      }
505      _process.swap(next);
506    }
507
508    // Process one round using _nodes instead of _process
509    void processNextFullRound(int k) {
510      Node u, v;
511      Arc e;
512      LargeValue d;
513      for (int i = 0; i < int(_nodes->size()); ++i) {
514        u = (*_nodes)[i];
515        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
516          e = _out_arcs[u][j];
517          v = _gr.target(e);
518          d = _data[u][k-1].dist + _length[e];
519          if (!_data[v][k].found || _tolerance.less(d, _data[v][k].dist)) {
520            _data[v][k] = PathData(true, d, e);
521          }
522        }
523      }
524    }
525
526    // Update the minimum cycle mean
527    void updateMinMean() {
528      int n = _nodes->size();
529      for (int i = 0; i < n; ++i) {
530        Node u = (*_nodes)[i];
531        if (!_data[u][n].found) continue;
532        LargeValue length, max_length = 0;
533        int size, max_size = 1;
534        bool found_curr = false;
535        for (int k = 0; k < n; ++k) {
536          if (!_data[u][k].found) continue;
537          length = _data[u][n].dist - _data[u][k].dist;
538          size = n - k;
539          if (!found_curr || length * max_size > max_length * size) {
540            found_curr = true;
541            max_length = length;
542            max_size = size;
543          }
544        }
545        if ( found_curr && (_cycle_node == INVALID ||
546             max_length * _cycle_size < _cycle_length * max_size) ) {
547          _cycle_length = max_length;
548          _cycle_size = max_size;
549          _cycle_node = u;
550        }
551      }
552    }
553
554  }; //class Karp
555
556  ///@}
557
558} //namespace lemon
559
560#endif //LEMON_KARP_H
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