# source:lemon/lemon/suurballe.h@357:2f64c4a692a8

Last change on this file since 357:2f64c4a692a8 was 357:2f64c4a692a8, checked in by Alpar Juttner <alpar@…>, 15 years ago

Port Suurballe algorithm from svn -r3512

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
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
34  /// @{
35
36  /// \brief Implementation of an algorithm for finding arc-disjoint
37  /// paths between two nodes 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 directed
42  /// digraph.
43  ///
44  /// In fact, this implementation is the specialization of the
45  /// \ref CapacityScaling "successive shortest path" algorithm.
46  ///
47  /// \tparam Digraph The directed digraph type the algorithm runs on.
48  /// \tparam LengthMap The type of the length (cost) map.
49  ///
50  /// \warning Length values should be \e non-negative \e integers.
51  ///
52  /// \note For finding node-disjoint paths this algorithm can be used
54  ///
55  /// \author Attila Bernath and Peter Kovacs
56
57  template < typename Digraph,
58             typename LengthMap = typename Digraph::template ArcMap<int> >
59  class Suurballe
60  {
61    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
62
63    typedef typename LengthMap::Value Length;
64    typedef ConstMap<Arc, int> ConstArcMap;
65    typedef typename Digraph::template NodeMap<Arc> PredMap;
66
67  public:
68
69    /// The type of the flow map.
70    typedef typename Digraph::template ArcMap<int> FlowMap;
71    /// The type of the potential map.
72    typedef typename Digraph::template NodeMap<Length> PotentialMap;
73    /// The type of the path structures.
74    typedef SimplePath<Digraph> Path;
75
76  private:
77
78    /// \brief Special implementation of the \ref Dijkstra algorithm
79    /// for finding shortest paths in the residual network.
80    ///
81    /// \ref ResidualDijkstra is a special implementation of the
82    /// \ref Dijkstra algorithm for finding shortest paths in the
83    /// residual network of the digraph with respect to the reduced arc
84    /// lengths and modifying the node potentials according to the
85    /// distance of the nodes.
86    class ResidualDijkstra
87    {
88      typedef typename Digraph::template NodeMap<int> HeapCrossRef;
89      typedef BinHeap<Length, HeapCrossRef> Heap;
90
91    private:
92
93      // The directed digraph the algorithm runs on
94      const Digraph &_graph;
95
96      // The main maps
97      const FlowMap &_flow;
98      const LengthMap &_length;
99      PotentialMap &_potential;
100
101      // The distance map
102      PotentialMap _dist;
103      // The pred arc map
104      PredMap &_pred;
105      // The processed (i.e. permanently labeled) nodes
106      std::vector<Node> _proc_nodes;
107
108      Node _s;
109      Node _t;
110
111    public:
112
113      /// Constructor.
114      ResidualDijkstra( const Digraph &digraph,
115                        const FlowMap &flow,
116                        const LengthMap &length,
117                        PotentialMap &potential,
118                        PredMap &pred,
119                        Node s, Node t ) :
120        _graph(digraph), _flow(flow), _length(length), _potential(potential),
121        _dist(digraph), _pred(pred), _s(s), _t(t) {}
122
123      /// \brief Runs the algorithm. Returns \c true if a path is found
124      /// from the source node to the target node.
125      bool run() {
126        HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
127        Heap heap(heap_cross_ref);
128        heap.push(_s, 0);
129        _pred[_s] = INVALID;
130        _proc_nodes.clear();
131
132        // Processing nodes
133        while (!heap.empty() && heap.top() != _t) {
134          Node u = heap.top(), v;
135          Length d = heap.prio() + _potential[u], nd;
136          _dist[u] = heap.prio();
137          heap.pop();
138          _proc_nodes.push_back(u);
139
140          // Traversing outgoing arcs
141          for (OutArcIt e(_graph, u); e != INVALID; ++e) {
142            if (_flow[e] == 0) {
143              v = _graph.target(e);
144              switch(heap.state(v)) {
145              case Heap::PRE_HEAP:
146                heap.push(v, d + _length[e] - _potential[v]);
147                _pred[v] = e;
148                break;
149              case Heap::IN_HEAP:
150                nd = d + _length[e] - _potential[v];
151                if (nd < heap[v]) {
152                  heap.decrease(v, nd);
153                  _pred[v] = e;
154                }
155                break;
156              case Heap::POST_HEAP:
157                break;
158              }
159            }
160          }
161
162          // Traversing incoming arcs
163          for (InArcIt e(_graph, u); e != INVALID; ++e) {
164            if (_flow[e] == 1) {
165              v = _graph.source(e);
166              switch(heap.state(v)) {
167              case Heap::PRE_HEAP:
168                heap.push(v, d - _length[e] - _potential[v]);
169                _pred[v] = e;
170                break;
171              case Heap::IN_HEAP:
172                nd = d - _length[e] - _potential[v];
173                if (nd < heap[v]) {
174                  heap.decrease(v, nd);
175                  _pred[v] = e;
176                }
177                break;
178              case Heap::POST_HEAP:
179                break;
180              }
181            }
182          }
183        }
184        if (heap.empty()) return false;
185
186        // Updating potentials of processed nodes
187        Length t_dist = heap.prio();
188        for (int i = 0; i < int(_proc_nodes.size()); ++i)
189          _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
190        return true;
191      }
192
193    }; //class ResidualDijkstra
194
195  private:
196
197    // The directed digraph the algorithm runs on
198    const Digraph &_graph;
199    // The length map
200    const LengthMap &_length;
201
202    // Arc map of the current flow
203    FlowMap *_flow;
204    bool _local_flow;
205    // Node map of the current potentials
206    PotentialMap *_potential;
207    bool _local_potential;
208
209    // The source node
210    Node _source;
211    // The target node
212    Node _target;
213
214    // Container to store the found paths
215    std::vector< SimplePath<Digraph> > paths;
216    int _path_num;
217
218    // The pred arc map
219    PredMap _pred;
220    // Implementation of the Dijkstra algorithm for finding augmenting
221    // shortest paths in the residual network
222    ResidualDijkstra *_dijkstra;
223
224  public:
225
226    /// \brief Constructor.
227    ///
228    /// Constructor.
229    ///
230    /// \param digraph The directed digraph the algorithm runs on.
231    /// \param length The length (cost) values of the arcs.
232    /// \param s The source node.
233    /// \param t The target node.
234    Suurballe( const Digraph &digraph,
235               const LengthMap &length,
236               Node s, Node t ) :
237      _graph(digraph), _length(length), _flow(0), _local_flow(false),
238      _potential(0), _local_potential(false), _source(s), _target(t),
239      _pred(digraph) {}
240
241    /// Destructor.
242    ~Suurballe() {
243      if (_local_flow) delete _flow;
244      if (_local_potential) delete _potential;
245      delete _dijkstra;
246    }
247
248    /// \brief Sets the flow map.
249    ///
250    /// Sets the flow map.
251    ///
252    /// The found flow contains only 0 and 1 values. It is the union of
253    /// the found arc-disjoint paths.
254    ///
255    /// \return \c (*this)
256    Suurballe& flowMap(FlowMap &map) {
257      if (_local_flow) {
258        delete _flow;
259        _local_flow = false;
260      }
261      _flow = &map;
262      return *this;
263    }
264
265    /// \brief Sets the potential map.
266    ///
267    /// Sets the potential map.
268    ///
269    /// The potentials provide the dual solution of the underlying
270    /// minimum cost flow problem.
271    ///
272    /// \return \c (*this)
273    Suurballe& potentialMap(PotentialMap &map) {
274      if (_local_potential) {
275        delete _potential;
276        _local_potential = false;
277      }
278      _potential = &map;
279      return *this;
280    }
281
282    /// \name Execution control
283    /// The simplest way to execute the algorithm is to call the run()
284    /// function.
285    /// \n
286    /// If you only need the flow that is the union of the found
287    /// arc-disjoint paths, you may call init() and findFlow().
288
289    /// @{
290
291    /// \brief Runs the algorithm.
292    ///
293    /// Runs the algorithm.
294    ///
295    /// \param k The number of paths to be found.
296    ///
297    /// \return \c k if there are at least \c k arc-disjoint paths
298    /// from \c s to \c t. Otherwise it returns the number of
299    /// arc-disjoint paths found.
300    ///
301    /// \note Apart from the return value, <tt>s.run(k)</tt> is just a
302    /// shortcut of the following code.
303    /// \code
304    ///   s.init();
305    ///   s.findFlow(k);
306    ///   s.findPaths();
307    /// \endcode
308    int run(int k = 2) {
309      init();
310      findFlow(k);
311      findPaths();
312      return _path_num;
313    }
314
315    /// \brief Initializes the algorithm.
316    ///
317    /// Initializes the algorithm.
318    void init() {
319      // Initializing maps
320      if (!_flow) {
321        _flow = new FlowMap(_graph);
322        _local_flow = true;
323      }
324      if (!_potential) {
325        _potential = new PotentialMap(_graph);
326        _local_potential = true;
327      }
328      for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
329      for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
330
331      _dijkstra = new ResidualDijkstra( _graph, *_flow, _length,
332                                        *_potential, _pred,
333                                        _source, _target );
334    }
335
336    /// \brief Executes the successive shortest path algorithm to find
337    /// an optimal flow.
338    ///
339    /// Executes the successive shortest path algorithm to find a
340    /// minimum cost flow, which is the union of \c k or less
341    /// arc-disjoint paths.
342    ///
343    /// \return \c k if there are at least \c k arc-disjoint paths
344    /// from \c s to \c t. Otherwise it returns the number of
345    /// arc-disjoint paths found.
346    ///
347    /// \pre \ref init() must be called before using this function.
348    int findFlow(int k = 2) {
349      // Finding shortest paths
350      _path_num = 0;
351      while (_path_num < k) {
352        // Running Dijkstra
353        if (!_dijkstra->run()) break;
354        ++_path_num;
355
356        // Setting the flow along the found shortest path
357        Node u = _target;
358        Arc e;
359        while ((e = _pred[u]) != INVALID) {
360          if (u == _graph.target(e)) {
361            (*_flow)[e] = 1;
362            u = _graph.source(e);
363          } else {
364            (*_flow)[e] = 0;
365            u = _graph.target(e);
366          }
367        }
368      }
369      return _path_num;
370    }
371
372    /// \brief Computes the paths from the flow.
373    ///
374    /// Computes the paths from the flow.
375    ///
376    /// \pre \ref init() and \ref findFlow() must be called before using
377    /// this function.
378    void findPaths() {
379      // Creating the residual flow map (the union of the paths not
380      // found so far)
381      FlowMap res_flow(_graph);
382      for(ArcIt a(_graph);a!=INVALID;++a) res_flow[a]=(*_flow)[a];
383
384      paths.clear();
385      paths.resize(_path_num);
386      for (int i = 0; i < _path_num; ++i) {
387        Node n = _source;
388        while (n != _target) {
389          OutArcIt e(_graph, n);
390          for ( ; res_flow[e] == 0; ++e) ;
391          n = _graph.target(e);
393          res_flow[e] = 0;
394        }
395      }
396    }
397
398    /// @}
399
400    /// \name Query Functions
401    /// The result of the algorithm can be obtained using these
402    /// functions.
403    /// \n The algorithm should be executed before using them.
404
405    /// @{
406
407    /// \brief Returns a const reference to the arc map storing the
408    /// found flow.
409    ///
410    /// Returns a const reference to the arc map storing the flow that
411    /// is the union of the found arc-disjoint paths.
412    ///
413    /// \pre \ref run() or findFlow() must be called before using this
414    /// function.
415    const FlowMap& flowMap() const {
416      return *_flow;
417    }
418
419    /// \brief Returns a const reference to the node map storing the
420    /// found potentials (the dual solution).
421    ///
422    /// Returns a const reference to the node map storing the found
423    /// potentials that provide the dual solution of the underlying
424    /// minimum cost flow problem.
425    ///
426    /// \pre \ref run() or findFlow() must be called before using this
427    /// function.
428    const PotentialMap& potentialMap() const {
429      return *_potential;
430    }
431
432    /// \brief Returns the flow on the given arc.
433    ///
434    /// Returns the flow on the given arc.
435    /// It is \c 1 if the arc is involved in one of the found paths,
436    /// otherwise it is \c 0.
437    ///
438    /// \pre \ref run() or findFlow() must be called before using this
439    /// function.
440    int flow(const Arc& arc) const {
441      return (*_flow)[arc];
442    }
443
444    /// \brief Returns the potential of the given node.
445    ///
446    /// Returns the potential of the given node.
447    ///
448    /// \pre \ref run() or findFlow() must be called before using this
449    /// function.
450    Length potential(const Node& node) const {
451      return (*_potential)[node];
452    }
453
454    /// \brief Returns the total length (cost) of the found paths (flow).
455    ///
456    /// Returns the total length (cost) of the found paths (flow).
457    /// The complexity of the function is \f$O(e) \f$.
458    ///
459    /// \pre \ref run() or findFlow() must be called before using this
460    /// function.
461    Length totalLength() const {
462      Length c = 0;
463      for (ArcIt e(_graph); e != INVALID; ++e)
464        c += (*_flow)[e] * _length[e];
465      return c;
466    }
467
468    /// \brief Returns the number of the found paths.
469    ///
470    /// Returns the number of the found paths.
471    ///
472    /// \pre \ref run() or findFlow() must be called before using this
473    /// function.
474    int pathNum() const {
475      return _path_num;
476    }
477
478    /// \brief Returns a const reference to the specified path.
479    ///
480    /// Returns a const reference to the specified path.
481    ///
482    /// \param i The function returns the \c i-th path.
483    /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
484    ///
485    /// \pre \ref run() or findPaths() must be called before using this
486    /// function.
487    Path path(int i) const {
488      return paths[i];
489    }
490
491    /// @}
492
493  }; //class Suurballe
494
495  ///@}
496
497} //namespace lemon
498
499#endif //LEMON_SUURBALLE_H
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