# source:lemon/lemon/suurballe.h@924:c67e235c832f

Last change on this file since 924:c67e235c832f was 924:c67e235c832f, checked in by Peter Kovacs <kpeter@…>, 14 years ago

Bug fix in Suurballe (#323)

File size: 16.0 KB
Line
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 <limits>
29#include <lemon/bin_heap.h>
30#include <lemon/path.h>
31#include <lemon/list_graph.h>
32#include <lemon/maps.h>
33
34namespace lemon {
35
37  /// @{
38
39  /// \brief Algorithm for finding arc-disjoint paths between two nodes
40  /// having minimum total length.
41  ///
42  /// \ref lemon::Suurballe "Suurballe" implements an algorithm for
43  /// finding arc-disjoint paths having minimum total length (cost)
44  /// from a given source node to a given target node in a digraph.
45  ///
46  /// Note that this problem is a special case of the \ref min_cost_flow
47  /// "minimum cost flow problem". This implementation is actually an
48  /// efficient specialized version of the \ref CapacityScaling
49  /// "Successive Shortest Path" algorithm directly for this problem.
50  /// Therefore this class provides query functions for flow values and
51  /// node potentials (the dual solution) just like the minimum cost flow
52  /// algorithms.
53  ///
54  /// \tparam GR The digraph type the algorithm runs on.
55  /// \tparam LEN The type of the length map.
56  /// The default value is <tt>GR::ArcMap<int></tt>.
57  ///
58  /// \warning Length values should be \e non-negative \e integers.
59  ///
60  /// \note For finding node-disjoint paths this algorithm can be used
61  /// along with the \ref SplitNodes adaptor.
62#ifdef DOXYGEN
63  template <typename GR, typename LEN>
64#else
65  template < typename GR,
66             typename LEN = typename GR::template ArcMap<int> >
67#endif
68  class Suurballe
69  {
70    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
71
72    typedef ConstMap<Arc, int> ConstArcMap;
73    typedef typename GR::template NodeMap<Arc> PredMap;
74
75  public:
76
77    /// The type of the digraph the algorithm runs on.
78    typedef GR Digraph;
79    /// The type of the length map.
80    typedef LEN LengthMap;
81    /// The type of the lengths.
82    typedef typename LengthMap::Value Length;
83#ifdef DOXYGEN
84    /// The type of the flow map.
85    typedef GR::ArcMap<int> FlowMap;
86    /// The type of the potential map.
87    typedef GR::NodeMap<Length> PotentialMap;
88#else
89    /// The type of the flow map.
90    typedef typename Digraph::template ArcMap<int> FlowMap;
91    /// The type of the potential map.
92    typedef typename Digraph::template NodeMap<Length> PotentialMap;
93#endif
94
95    /// The type of the path structures.
96    typedef SimplePath<GR> Path;
97
98  private:
99
100    // ResidualDijkstra is a special implementation of the
101    // Dijkstra algorithm for finding shortest paths in the
102    // residual network with respect to the reduced arc lengths
103    // and modifying the node potentials according to the
104    // distance of the nodes.
105    class ResidualDijkstra
106    {
107      typedef typename Digraph::template NodeMap<int> HeapCrossRef;
108      typedef BinHeap<Length, HeapCrossRef> Heap;
109
110    private:
111
112      // The digraph the algorithm runs on
113      const Digraph &_graph;
114
115      // The main maps
116      const FlowMap &_flow;
117      const LengthMap &_length;
118      PotentialMap &_potential;
119
120      // The distance map
121      PotentialMap _dist;
122      // The pred arc map
123      PredMap &_pred;
124      // The processed (i.e. permanently labeled) nodes
125      std::vector<Node> _proc_nodes;
126
127      Node _s;
128      Node _t;
129
130    public:
131
132      /// Constructor.
133      ResidualDijkstra( const Digraph &graph,
134                        const FlowMap &flow,
135                        const LengthMap &length,
136                        PotentialMap &potential,
137                        PredMap &pred,
138                        Node s, Node t ) :
139        _graph(graph), _flow(flow), _length(length), _potential(potential),
140        _dist(graph), _pred(pred), _s(s), _t(t) {}
141
142      /// \brief Run the algorithm. It returns \c true if a path is found
143      /// from the source node to the target node.
144      bool run() {
145        HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
146        Heap heap(heap_cross_ref);
147        heap.push(_s, 0);
148        _pred[_s] = INVALID;
149        _proc_nodes.clear();
150
151        // Process nodes
152        while (!heap.empty() && heap.top() != _t) {
153          Node u = heap.top(), v;
154          Length d = heap.prio() + _potential[u], nd;
155          _dist[u] = heap.prio();
156          heap.pop();
157          _proc_nodes.push_back(u);
158
159          // Traverse outgoing arcs
160          for (OutArcIt e(_graph, u); e != INVALID; ++e) {
161            if (_flow[e] == 0) {
162              v = _graph.target(e);
163              switch(heap.state(v)) {
164              case Heap::PRE_HEAP:
165                heap.push(v, d + _length[e] - _potential[v]);
166                _pred[v] = e;
167                break;
168              case Heap::IN_HEAP:
169                nd = d + _length[e] - _potential[v];
170                if (nd < heap[v]) {
171                  heap.decrease(v, nd);
172                  _pred[v] = e;
173                }
174                break;
175              case Heap::POST_HEAP:
176                break;
177              }
178            }
179          }
180
181          // Traverse incoming arcs
182          for (InArcIt e(_graph, u); e != INVALID; ++e) {
183            if (_flow[e] == 1) {
184              v = _graph.source(e);
185              switch(heap.state(v)) {
186              case Heap::PRE_HEAP:
187                heap.push(v, d - _length[e] - _potential[v]);
188                _pred[v] = e;
189                break;
190              case Heap::IN_HEAP:
191                nd = d - _length[e] - _potential[v];
192                if (nd < heap[v]) {
193                  heap.decrease(v, nd);
194                  _pred[v] = e;
195                }
196                break;
197              case Heap::POST_HEAP:
198                break;
199              }
200            }
201          }
202        }
203        if (heap.empty()) return false;
204
205        // Update potentials of processed nodes
206        Length t_dist = heap.prio();
207        for (int i = 0; i < int(_proc_nodes.size()); ++i)
208          _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
209        return true;
210      }
211
212    }; //class ResidualDijkstra
213
214  private:
215
216    // The digraph the algorithm runs on
217    const Digraph &_graph;
218    // The length map
219    const LengthMap &_length;
220
221    // Arc map of the current flow
222    FlowMap *_flow;
223    bool _local_flow;
224    // Node map of the current potentials
225    PotentialMap *_potential;
226    bool _local_potential;
227
228    // The source node
229    Node _source;
230    // The target node
231    Node _target;
232
233    // Container to store the found paths
234    std::vector< SimplePath<Digraph> > paths;
235    int _path_num;
236
237    // The pred arc map
238    PredMap _pred;
239    // Implementation of the Dijkstra algorithm for finding augmenting
240    // shortest paths in the residual network
241    ResidualDijkstra *_dijkstra;
242
243  public:
244
245    /// \brief Constructor.
246    ///
247    /// Constructor.
248    ///
249    /// \param graph The digraph the algorithm runs on.
250    /// \param length The length (cost) values of the arcs.
251    Suurballe( const Digraph &graph,
252               const LengthMap &length ) :
253      _graph(graph), _length(length), _flow(0), _local_flow(false),
254      _potential(0), _local_potential(false), _pred(graph)
255    {
256      LEMON_ASSERT(std::numeric_limits<Length>::is_integer,
257        "The length type of Suurballe must be integer");
258    }
259
260    /// Destructor.
261    ~Suurballe() {
262      if (_local_flow) delete _flow;
263      if (_local_potential) delete _potential;
264      delete _dijkstra;
265    }
266
267    /// \brief Set the flow map.
268    ///
269    /// This function sets the flow map.
270    /// If it is not used before calling \ref run() or \ref init(),
271    /// an instance will be allocated automatically. The destructor
272    /// deallocates this automatically allocated map, of course.
273    ///
274    /// The found flow contains only 0 and 1 values, since it is the
275    /// union of the found arc-disjoint paths.
276    ///
277    /// \return <tt>(*this)</tt>
278    Suurballe& flowMap(FlowMap &map) {
279      if (_local_flow) {
280        delete _flow;
281        _local_flow = false;
282      }
283      _flow = &map;
284      return *this;
285    }
286
287    /// \brief Set the potential map.
288    ///
289    /// This function sets the potential map.
290    /// If it is not used before calling \ref run() or \ref init(),
291    /// an instance will be allocated automatically. The destructor
292    /// deallocates this automatically allocated map, of course.
293    ///
294    /// The node potentials provide the dual solution of the underlying
295    /// \ref min_cost_flow "minimum cost flow problem".
296    ///
297    /// \return <tt>(*this)</tt>
298    Suurballe& potentialMap(PotentialMap &map) {
299      if (_local_potential) {
300        delete _potential;
301        _local_potential = false;
302      }
303      _potential = &map;
304      return *this;
305    }
306
307    /// \name Execution Control
308    /// The simplest way to execute the algorithm is to call the run()
309    /// function.
310    /// \n
311    /// If you only need the flow that is the union of the found
312    /// arc-disjoint paths, you may call init() and findFlow().
313
314    /// @{
315
316    /// \brief Run the algorithm.
317    ///
318    /// This function runs the algorithm.
319    ///
320    /// \param s The source node.
321    /// \param t The target node.
322    /// \param k The number of paths to be found.
323    ///
324    /// \return \c k if there are at least \c k arc-disjoint paths from
325    /// \c s to \c t in the digraph. Otherwise it returns the number of
326    /// arc-disjoint paths found.
327    ///
328    /// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is
329    /// just a shortcut of the following code.
330    /// \code
331    ///   s.init(s);
332    ///   s.findFlow(t, k);
333    ///   s.findPaths();
334    /// \endcode
335    int run(const Node& s, const Node& t, int k = 2) {
336      init(s);
337      findFlow(t, k);
338      findPaths();
339      return _path_num;
340    }
341
342    /// \brief Initialize the algorithm.
343    ///
344    /// This function initializes the algorithm.
345    ///
346    /// \param s The source node.
347    void init(const Node& s) {
348      _source = s;
349
350      // Initialize maps
351      if (!_flow) {
352        _flow = new FlowMap(_graph);
353        _local_flow = true;
354      }
355      if (!_potential) {
356        _potential = new PotentialMap(_graph);
357        _local_potential = true;
358      }
359      for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
360      for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
361    }
362
363    /// \brief Execute the algorithm to find an optimal flow.
364    ///
365    /// This function executes the successive shortest path algorithm to
366    /// find a minimum cost flow, which is the union of \c k (or less)
367    /// arc-disjoint paths.
368    ///
369    /// \param t The target node.
370    /// \param k The number of paths to be found.
371    ///
372    /// \return \c k if there are at least \c k arc-disjoint paths from
373    /// the source node to the given node \c t in the digraph.
374    /// Otherwise it returns the number of arc-disjoint paths found.
375    ///
376    /// \pre \ref init() must be called before using this function.
377    int findFlow(const Node& t, int k = 2) {
378      _target = t;
379      _dijkstra =
380        new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
381                              _source, _target );
382
383      // Find shortest paths
384      _path_num = 0;
385      while (_path_num < k) {
386        // Run Dijkstra
387        if (!_dijkstra->run()) break;
388        ++_path_num;
389
390        // Set the flow along the found shortest path
391        Node u = _target;
392        Arc e;
393        while ((e = _pred[u]) != INVALID) {
394          if (u == _graph.target(e)) {
395            (*_flow)[e] = 1;
396            u = _graph.source(e);
397          } else {
398            (*_flow)[e] = 0;
399            u = _graph.target(e);
400          }
401        }
402      }
403      return _path_num;
404    }
405
406    /// \brief Compute the paths from the flow.
407    ///
408    /// This function computes the paths from the found minimum cost flow,
409    /// which is the union of some arc-disjoint paths.
410    ///
411    /// \pre \ref init() and \ref findFlow() must be called before using
412    /// this function.
413    void findPaths() {
414      FlowMap res_flow(_graph);
415      for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
416
417      paths.clear();
418      paths.resize(_path_num);
419      for (int i = 0; i < _path_num; ++i) {
420        Node n = _source;
421        while (n != _target) {
422          OutArcIt e(_graph, n);
423          for ( ; res_flow[e] == 0; ++e) ;
424          n = _graph.target(e);
426          res_flow[e] = 0;
427        }
428      }
429    }
430
431    /// @}
432
433    /// \name Query Functions
434    /// The results of the algorithm can be obtained using these
435    /// functions.
436    /// \n The algorithm should be executed before using them.
437
438    /// @{
439
440    /// \brief Return the total length of the found paths.
441    ///
442    /// This function returns the total length of the found paths, i.e.
443    /// the total cost of the found flow.
444    /// The complexity of the function is O(e).
445    ///
446    /// \pre \ref run() or \ref findFlow() must be called before using
447    /// this function.
448    Length totalLength() const {
449      Length c = 0;
450      for (ArcIt e(_graph); e != INVALID; ++e)
451        c += (*_flow)[e] * _length[e];
452      return c;
453    }
454
455    /// \brief Return the flow value on the given arc.
456    ///
457    /// This function returns the flow value on the given arc.
458    /// It is \c 1 if the arc is involved in one of the found arc-disjoint
459    /// paths, otherwise it is \c 0.
460    ///
461    /// \pre \ref run() or \ref findFlow() must be called before using
462    /// this function.
463    int flow(const Arc& arc) const {
464      return (*_flow)[arc];
465    }
466
467    /// \brief Return a const reference to an arc map storing the
468    /// found flow.
469    ///
470    /// This function returns a const reference to an arc map storing
471    /// the flow that is the union of the found arc-disjoint paths.
472    ///
473    /// \pre \ref run() or \ref findFlow() must be called before using
474    /// this function.
475    const FlowMap& flowMap() const {
476      return *_flow;
477    }
478
479    /// \brief Return the potential of the given node.
480    ///
481    /// This function returns the potential of the given node.
482    /// The node potentials provide the dual solution of the
483    /// underlying \ref min_cost_flow "minimum cost flow problem".
484    ///
485    /// \pre \ref run() or \ref findFlow() must be called before using
486    /// this function.
487    Length potential(const Node& node) const {
488      return (*_potential)[node];
489    }
490
491    /// \brief Return a const reference to a node map storing the
492    /// found potentials (the dual solution).
493    ///
494    /// This function returns a const reference to a node map storing
495    /// the found potentials that provide the dual solution of the
496    /// underlying \ref min_cost_flow "minimum cost flow problem".
497    ///
498    /// \pre \ref run() or \ref findFlow() must be called before using
499    /// this function.
500    const PotentialMap& potentialMap() const {
501      return *_potential;
502    }
503
504    /// \brief Return the number of the found paths.
505    ///
506    /// This function returns the number of the found paths.
507    ///
508    /// \pre \ref run() or \ref findFlow() must be called before using
509    /// this function.
510    int pathNum() const {
511      return _path_num;
512    }
513
514    /// \brief Return a const reference to the specified path.
515    ///
516    /// This function returns a const reference to the specified path.
517    ///
518    /// \param i The function returns the <tt>i</tt>-th path.
519    /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
520    ///
521    /// \pre \ref run() or \ref findPaths() must be called before using
522    /// this function.
523    const Path& path(int i) const {
524      return paths[i];
525    }
526
527    /// @}
528
529  }; //class Suurballe
530
531  ///@}
532
533} //namespace lemon
534
535#endif //LEMON_SUURBALLE_H
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