COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/suurballe.h @ 346:7f26c4b32651

Last change on this file since 346:7f26c4b32651 was 346:7f26c4b32651, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Minor doc improvements related to Suurballe (#47)

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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_SUURBALLE_H
20#define LEMON_SUURBALLE_H
21
22///\ingroup shortest_path
23///\file
24///\brief An algorithm for finding arc-disjoint paths between two
25/// nodes having minimum total length.
26
27#include <vector>
28#include <lemon/bin_heap.h>
29#include <lemon/path.h>
30
31namespace lemon {
32
33  /// \addtogroup shortest_path
34  /// @{
35
36  /// \brief Algorithm for finding arc-disjoint paths between two nodes
37  /// having minimum total length.
38  ///
39  /// \ref lemon::Suurballe "Suurballe" implements an algorithm for
40  /// finding arc-disjoint paths having minimum total length (cost)
41  /// from a given source node to a given target node in a digraph.
42  ///
43  /// In fact, this implementation is the specialization of the
44  /// \ref CapacityScaling "successive shortest path" algorithm.
45  ///
46  /// \tparam Digraph The digraph type the algorithm runs on.
47  /// The default value is \c ListDigraph.
48  /// \tparam LengthMap The type of the length (cost) map.
49  /// The default value is <tt>Digraph::ArcMap<int></tt>.
50  ///
51  /// \warning Length values should be \e non-negative \e integers.
52  ///
53  /// \note For finding node-disjoint paths this algorithm can be used
54  /// with \ref SplitDigraphAdaptor.
55#ifdef DOXYGEN
56  template <typename Digraph, typename LengthMap>
57#else
58  template < typename Digraph = ListDigraph,
59             typename LengthMap = typename Digraph::template ArcMap<int> >
60#endif
61  class Suurballe
62  {
63    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
64
65    typedef typename LengthMap::Value Length;
66    typedef ConstMap<Arc, int> ConstArcMap;
67    typedef typename Digraph::template NodeMap<Arc> PredMap;
68
69  public:
70
71    /// The type of the flow map.
72    typedef typename Digraph::template ArcMap<int> FlowMap;
73    /// The type of the potential map.
74    typedef typename Digraph::template NodeMap<Length> PotentialMap;
75    /// The type of the path structures.
76    typedef SimplePath<Digraph> Path;
77
78  private:
79 
80    /// \brief Special implementation of the Dijkstra algorithm
81    /// for finding shortest paths in the residual network.
82    ///
83    /// \ref ResidualDijkstra is a special implementation of the
84    /// \ref Dijkstra algorithm for finding shortest paths in the
85    /// residual network of the digraph with respect to the reduced arc
86    /// lengths and modifying the node potentials according to the
87    /// distance of the nodes.
88    class ResidualDijkstra
89    {
90      typedef typename Digraph::template NodeMap<int> HeapCrossRef;
91      typedef BinHeap<Length, HeapCrossRef> Heap;
92
93    private:
94
95      // The digraph the algorithm runs on
96      const Digraph &_graph;
97
98      // The main maps
99      const FlowMap &_flow;
100      const LengthMap &_length;
101      PotentialMap &_potential;
102
103      // The distance map
104      PotentialMap _dist;
105      // The pred arc map
106      PredMap &_pred;
107      // The processed (i.e. permanently labeled) nodes
108      std::vector<Node> _proc_nodes;
109     
110      Node _s;
111      Node _t;
112
113    public:
114
115      /// Constructor.
116      ResidualDijkstra( const Digraph &digraph,
117                        const FlowMap &flow,
118                        const LengthMap &length,
119                        PotentialMap &potential,
120                        PredMap &pred,
121                        Node s, Node t ) :
122        _graph(digraph), _flow(flow), _length(length), _potential(potential),
123        _dist(digraph), _pred(pred), _s(s), _t(t) {}
124
125      /// \brief Run the algorithm. It returns \c true if a path is found
126      /// from the source node to the target node.
127      bool run() {
128        HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
129        Heap heap(heap_cross_ref);
130        heap.push(_s, 0);
131        _pred[_s] = INVALID;
132        _proc_nodes.clear();
133
134        // Process nodes
135        while (!heap.empty() && heap.top() != _t) {
136          Node u = heap.top(), v;
137          Length d = heap.prio() + _potential[u], nd;
138          _dist[u] = heap.prio();
139          heap.pop();
140          _proc_nodes.push_back(u);
141
142          // Traverse outgoing arcs
143          for (OutArcIt e(_graph, u); e != INVALID; ++e) {
144            if (_flow[e] == 0) {
145              v = _graph.target(e);
146              switch(heap.state(v)) {
147              case Heap::PRE_HEAP:
148                heap.push(v, d + _length[e] - _potential[v]);
149                _pred[v] = e;
150                break;
151              case Heap::IN_HEAP:
152                nd = d + _length[e] - _potential[v];
153                if (nd < heap[v]) {
154                  heap.decrease(v, nd);
155                  _pred[v] = e;
156                }
157                break;
158              case Heap::POST_HEAP:
159                break;
160              }
161            }
162          }
163
164          // Traverse incoming arcs
165          for (InArcIt e(_graph, u); e != INVALID; ++e) {
166            if (_flow[e] == 1) {
167              v = _graph.source(e);
168              switch(heap.state(v)) {
169              case Heap::PRE_HEAP:
170                heap.push(v, d - _length[e] - _potential[v]);
171                _pred[v] = e;
172                break;
173              case Heap::IN_HEAP:
174                nd = d - _length[e] - _potential[v];
175                if (nd < heap[v]) {
176                  heap.decrease(v, nd);
177                  _pred[v] = e;
178                }
179                break;
180              case Heap::POST_HEAP:
181                break;
182              }
183            }
184          }
185        }
186        if (heap.empty()) return false;
187
188        // Update potentials of processed nodes
189        Length t_dist = heap.prio();
190        for (int i = 0; i < int(_proc_nodes.size()); ++i)
191          _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
192        return true;
193      }
194
195    }; //class ResidualDijkstra
196
197  private:
198
199    // The digraph the algorithm runs on
200    const Digraph &_graph;
201    // The length map
202    const LengthMap &_length;
203   
204    // Arc map of the current flow
205    FlowMap *_flow;
206    bool _local_flow;
207    // Node map of the current potentials
208    PotentialMap *_potential;
209    bool _local_potential;
210
211    // The source node
212    Node _source;
213    // The target node
214    Node _target;
215
216    // Container to store the found paths
217    std::vector< SimplePath<Digraph> > paths;
218    int _path_num;
219
220    // The pred arc map
221    PredMap _pred;
222    // Implementation of the Dijkstra algorithm for finding augmenting
223    // shortest paths in the residual network
224    ResidualDijkstra *_dijkstra;
225
226  public:
227
228    /// \brief Constructor.
229    ///
230    /// Constructor.
231    ///
232    /// \param digraph The digraph the algorithm runs on.
233    /// \param length The length (cost) values of the arcs.
234    /// \param s The source node.
235    /// \param t The target node.
236    Suurballe( const Digraph &digraph,
237               const LengthMap &length,
238               Node s, Node t ) :
239      _graph(digraph), _length(length), _flow(0), _local_flow(false),
240      _potential(0), _local_potential(false), _source(s), _target(t),
241      _pred(digraph) {}
242
243    /// Destructor.
244    ~Suurballe() {
245      if (_local_flow) delete _flow;
246      if (_local_potential) delete _potential;
247      delete _dijkstra;
248    }
249
250    /// \brief Set the flow map.
251    ///
252    /// This function sets the flow map.
253    ///
254    /// The found flow contains only 0 and 1 values. It is the union of
255    /// the found arc-disjoint paths.
256    ///
257    /// \return \c (*this)
258    Suurballe& flowMap(FlowMap &map) {
259      if (_local_flow) {
260        delete _flow;
261        _local_flow = false;
262      }
263      _flow = &map;
264      return *this;
265    }
266
267    /// \brief Set the potential map.
268    ///
269    /// This function sets the potential map.
270    ///
271    /// The potentials provide the dual solution of the underlying
272    /// minimum cost flow problem.
273    ///
274    /// \return \c (*this)
275    Suurballe& potentialMap(PotentialMap &map) {
276      if (_local_potential) {
277        delete _potential;
278        _local_potential = false;
279      }
280      _potential = &map;
281      return *this;
282    }
283
284    /// \name Execution control
285    /// The simplest way to execute the algorithm is to call the run()
286    /// function.
287    /// \n
288    /// If you only need the flow that is the union of the found
289    /// arc-disjoint paths, you may call init() and findFlow().
290
291    /// @{
292
293    /// \brief Run the algorithm.
294    ///
295    /// This function runs the algorithm.
296    ///
297    /// \param k The number of paths to be found.
298    ///
299    /// \return \c k if there are at least \c k arc-disjoint paths from
300    /// \c s to \c t in the digraph. Otherwise it returns the number of
301    /// arc-disjoint paths found.
302    ///
303    /// \note Apart from the return value, <tt>s.run(k)</tt> is just a
304    /// shortcut of the following code.
305    /// \code
306    ///   s.init();
307    ///   s.findFlow(k);
308    ///   s.findPaths();
309    /// \endcode
310    int run(int k = 2) {
311      init();
312      findFlow(k);
313      findPaths();
314      return _path_num;
315    }
316
317    /// \brief Initialize the algorithm.
318    ///
319    /// This function initializes the algorithm.
320    void init() {
321      // Initialize maps
322      if (!_flow) {
323        _flow = new FlowMap(_graph);
324        _local_flow = true;
325      }
326      if (!_potential) {
327        _potential = new PotentialMap(_graph);
328        _local_potential = true;
329      }
330      for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
331      for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
332
333      _dijkstra = new ResidualDijkstra( _graph, *_flow, _length,
334                                        *_potential, _pred,
335                                        _source, _target );
336    }
337
338    /// \brief Execute the successive shortest path algorithm to find
339    /// an optimal flow.
340    ///
341    /// This function executes the successive shortest path algorithm to
342    /// find a minimum cost flow, which is the union of \c k or less
343    /// arc-disjoint paths.
344    ///
345    /// \return \c k if there are at least \c k arc-disjoint paths from
346    /// \c s to \c t in the digraph. Otherwise it returns the number of
347    /// arc-disjoint paths found.
348    ///
349    /// \pre \ref init() must be called before using this function.
350    int findFlow(int k = 2) {
351      // Find shortest paths
352      _path_num = 0;
353      while (_path_num < k) {
354        // Run Dijkstra
355        if (!_dijkstra->run()) break;
356        ++_path_num;
357
358        // Set the flow along the found shortest path
359        Node u = _target;
360        Arc e;
361        while ((e = _pred[u]) != INVALID) {
362          if (u == _graph.target(e)) {
363            (*_flow)[e] = 1;
364            u = _graph.source(e);
365          } else {
366            (*_flow)[e] = 0;
367            u = _graph.target(e);
368          }
369        }
370      }
371      return _path_num;
372    }
373   
374    /// \brief Compute the paths from the flow.
375    ///
376    /// This function computes the paths from the flow.
377    ///
378    /// \pre \ref init() and \ref findFlow() must be called before using
379    /// this function.
380    void findPaths() {
381      // Create the residual flow map (the union of the paths not found
382      // so far)
383      FlowMap res_flow(_graph);
384      for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
385
386      paths.clear();
387      paths.resize(_path_num);
388      for (int i = 0; i < _path_num; ++i) {
389        Node n = _source;
390        while (n != _target) {
391          OutArcIt e(_graph, n);
392          for ( ; res_flow[e] == 0; ++e) ;
393          n = _graph.target(e);
394          paths[i].addBack(e);
395          res_flow[e] = 0;
396        }
397      }
398    }
399
400    /// @}
401
402    /// \name Query Functions
403    /// The results of the algorithm can be obtained using these
404    /// functions.
405    /// \n The algorithm should be executed before using them.
406
407    /// @{
408
409    /// \brief Return a const reference to the arc map storing the
410    /// found flow.
411    ///
412    /// This function returns a const reference to the arc map storing
413    /// the flow that is the union of the found arc-disjoint paths.
414    ///
415    /// \pre \ref run() or \ref findFlow() must be called before using
416    /// this function.
417    const FlowMap& flowMap() const {
418      return *_flow;
419    }
420
421    /// \brief Return a const reference to the node map storing the
422    /// found potentials (the dual solution).
423    ///
424    /// This function returns a const reference to the node map storing
425    /// the found potentials that provide the dual solution of the
426    /// underlying minimum cost flow problem.
427    ///
428    /// \pre \ref run() or \ref findFlow() must be called before using
429    /// this function.
430    const PotentialMap& potentialMap() const {
431      return *_potential;
432    }
433
434    /// \brief Return the flow on the given arc.
435    ///
436    /// This function returns the flow on the given arc.
437    /// It is \c 1 if the arc is involved in one of the found paths,
438    /// otherwise it is \c 0.
439    ///
440    /// \pre \ref run() or \ref findFlow() must be called before using
441    /// this function.
442    int flow(const Arc& arc) const {
443      return (*_flow)[arc];
444    }
445
446    /// \brief Return the potential of the given node.
447    ///
448    /// This function returns the potential of the given node.
449    ///
450    /// \pre \ref run() or \ref findFlow() must be called before using
451    /// this function.
452    Length potential(const Node& node) const {
453      return (*_potential)[node];
454    }
455
456    /// \brief Return the total length (cost) of the found paths (flow).
457    ///
458    /// This function returns the total length (cost) of the found paths
459    /// (flow). The complexity of the function is \f$ O(e) \f$.
460    ///
461    /// \pre \ref run() or \ref findFlow() must be called before using
462    /// this function.
463    Length totalLength() const {
464      Length c = 0;
465      for (ArcIt e(_graph); e != INVALID; ++e)
466        c += (*_flow)[e] * _length[e];
467      return c;
468    }
469
470    /// \brief Return the number of the found paths.
471    ///
472    /// This function returns the number of the found paths.
473    ///
474    /// \pre \ref run() or \ref findFlow() must be called before using
475    /// this function.
476    int pathNum() const {
477      return _path_num;
478    }
479
480    /// \brief Return a const reference to the specified path.
481    ///
482    /// This function returns a const reference to the specified path.
483    ///
484    /// \param i The function returns the \c i-th path.
485    /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
486    ///
487    /// \pre \ref run() or \ref findPaths() must be called before using
488    /// this function.
489    Path path(int i) const {
490      return paths[i];
491    }
492
493    /// @}
494
495  }; //class Suurballe
496
497  ///@}
498
499} //namespace lemon
500
501#endif //LEMON_SUURBALLE_H
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