# source:lemon/lemon/suurballe.h@925:30c77d1c0cba

Last change on this file since 925:30c77d1c0cba was 925:30c77d1c0cba, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Remove unnecessary integer requirement in Suurballe (#323)

File size: 15.9 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.
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
257    /// Destructor.
258    ~Suurballe() {
259      if (_local_flow) delete _flow;
260      if (_local_potential) delete _potential;
261      delete _dijkstra;
262    }
263
264    /// \brief Set the flow map.
265    ///
266    /// This function sets the flow map.
267    /// If it is not used before calling \ref run() or \ref init(),
268    /// an instance will be allocated automatically. The destructor
269    /// deallocates this automatically allocated map, of course.
270    ///
271    /// The found flow contains only 0 and 1 values, since it is the
272    /// union of the found arc-disjoint paths.
273    ///
274    /// \return <tt>(*this)</tt>
275    Suurballe& flowMap(FlowMap &map) {
276      if (_local_flow) {
277        delete _flow;
278        _local_flow = false;
279      }
280      _flow = &map;
281      return *this;
282    }
283
284    /// \brief Set the potential map.
285    ///
286    /// This function sets the potential map.
287    /// If it is not used before calling \ref run() or \ref init(),
288    /// an instance will be allocated automatically. The destructor
289    /// deallocates this automatically allocated map, of course.
290    ///
291    /// The node potentials provide the dual solution of the underlying
292    /// \ref min_cost_flow "minimum cost flow problem".
293    ///
294    /// \return <tt>(*this)</tt>
295    Suurballe& potentialMap(PotentialMap &map) {
296      if (_local_potential) {
297        delete _potential;
298        _local_potential = false;
299      }
300      _potential = &map;
301      return *this;
302    }
303
304    /// \name Execution Control
305    /// The simplest way to execute the algorithm is to call the run()
306    /// function.
307    /// \n
308    /// If you only need the flow that is the union of the found
309    /// arc-disjoint paths, you may call init() and findFlow().
310
311    /// @{
312
313    /// \brief Run the algorithm.
314    ///
315    /// This function runs the algorithm.
316    ///
317    /// \param s The source node.
318    /// \param t The target node.
319    /// \param k The number of paths to be found.
320    ///
321    /// \return \c k if there are at least \c k arc-disjoint paths from
322    /// \c s to \c t in the digraph. Otherwise it returns the number of
323    /// arc-disjoint paths found.
324    ///
325    /// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is
326    /// just a shortcut of the following code.
327    /// \code
328    ///   s.init(s);
329    ///   s.findFlow(t, k);
330    ///   s.findPaths();
331    /// \endcode
332    int run(const Node& s, const Node& t, int k = 2) {
333      init(s);
334      findFlow(t, k);
335      findPaths();
336      return _path_num;
337    }
338
339    /// \brief Initialize the algorithm.
340    ///
341    /// This function initializes the algorithm.
342    ///
343    /// \param s The source node.
344    void init(const Node& s) {
345      _source = s;
346
347      // Initialize maps
348      if (!_flow) {
349        _flow = new FlowMap(_graph);
350        _local_flow = true;
351      }
352      if (!_potential) {
353        _potential = new PotentialMap(_graph);
354        _local_potential = true;
355      }
356      for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
357      for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
358    }
359
360    /// \brief Execute the algorithm to find an optimal flow.
361    ///
362    /// This function executes the successive shortest path algorithm to
363    /// find a minimum cost flow, which is the union of \c k (or less)
364    /// arc-disjoint paths.
365    ///
366    /// \param t The target node.
367    /// \param k The number of paths to be found.
368    ///
369    /// \return \c k if there are at least \c k arc-disjoint paths from
370    /// the source node to the given node \c t in the digraph.
371    /// Otherwise it returns the number of arc-disjoint paths found.
372    ///
373    /// \pre \ref init() must be called before using this function.
374    int findFlow(const Node& t, int k = 2) {
375      _target = t;
376      _dijkstra =
377        new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
378                              _source, _target );
379
380      // Find shortest paths
381      _path_num = 0;
382      while (_path_num < k) {
383        // Run Dijkstra
384        if (!_dijkstra->run()) break;
385        ++_path_num;
386
387        // Set the flow along the found shortest path
388        Node u = _target;
389        Arc e;
390        while ((e = _pred[u]) != INVALID) {
391          if (u == _graph.target(e)) {
392            (*_flow)[e] = 1;
393            u = _graph.source(e);
394          } else {
395            (*_flow)[e] = 0;
396            u = _graph.target(e);
397          }
398        }
399      }
400      return _path_num;
401    }
402
403    /// \brief Compute the paths from the flow.
404    ///
405    /// This function computes the paths from the found minimum cost flow,
406    /// which is the union of some arc-disjoint paths.
407    ///
408    /// \pre \ref init() and \ref findFlow() must be called before using
409    /// this function.
410    void findPaths() {
411      FlowMap res_flow(_graph);
412      for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
413
414      paths.clear();
415      paths.resize(_path_num);
416      for (int i = 0; i < _path_num; ++i) {
417        Node n = _source;
418        while (n != _target) {
419          OutArcIt e(_graph, n);
420          for ( ; res_flow[e] == 0; ++e) ;
421          n = _graph.target(e);
423          res_flow[e] = 0;
424        }
425      }
426    }
427
428    /// @}
429
430    /// \name Query Functions
431    /// The results of the algorithm can be obtained using these
432    /// functions.
433    /// \n The algorithm should be executed before using them.
434
435    /// @{
436
437    /// \brief Return the total length of the found paths.
438    ///
439    /// This function returns the total length of the found paths, i.e.
440    /// the total cost of the found flow.
441    /// The complexity of the function is O(e).
442    ///
443    /// \pre \ref run() or \ref findFlow() must be called before using
444    /// this function.
445    Length totalLength() const {
446      Length c = 0;
447      for (ArcIt e(_graph); e != INVALID; ++e)
448        c += (*_flow)[e] * _length[e];
449      return c;
450    }
451
452    /// \brief Return the flow value on the given arc.
453    ///
454    /// This function returns the flow value on the given arc.
455    /// It is \c 1 if the arc is involved in one of the found arc-disjoint
456    /// paths, otherwise it is \c 0.
457    ///
458    /// \pre \ref run() or \ref findFlow() must be called before using
459    /// this function.
460    int flow(const Arc& arc) const {
461      return (*_flow)[arc];
462    }
463
464    /// \brief Return a const reference to an arc map storing the
465    /// found flow.
466    ///
467    /// This function returns a const reference to an arc map storing
468    /// the flow that is the union of the found arc-disjoint paths.
469    ///
470    /// \pre \ref run() or \ref findFlow() must be called before using
471    /// this function.
472    const FlowMap& flowMap() const {
473      return *_flow;
474    }
475
476    /// \brief Return the potential of the given node.
477    ///
478    /// This function returns the potential of the given node.
479    /// The node potentials provide the dual solution of the
480    /// underlying \ref min_cost_flow "minimum cost flow problem".
481    ///
482    /// \pre \ref run() or \ref findFlow() must be called before using
483    /// this function.
484    Length potential(const Node& node) const {
485      return (*_potential)[node];
486    }
487
488    /// \brief Return a const reference to a node map storing the
489    /// found potentials (the dual solution).
490    ///
491    /// This function returns a const reference to a node map storing
492    /// the found potentials that provide the dual solution of the
493    /// underlying \ref min_cost_flow "minimum cost flow problem".
494    ///
495    /// \pre \ref run() or \ref findFlow() must be called before using
496    /// this function.
497    const PotentialMap& potentialMap() const {
498      return *_potential;
499    }
500
501    /// \brief Return the number of the found paths.
502    ///
503    /// This function returns the number of the found paths.
504    ///
505    /// \pre \ref run() or \ref findFlow() must be called before using
506    /// this function.
507    int pathNum() const {
508      return _path_num;
509    }
510
511    /// \brief Return a const reference to the specified path.
512    ///
513    /// This function returns a const reference to the specified path.
514    ///
515    /// \param i The function returns the <tt>i</tt>-th path.
516    /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
517    ///
518    /// \pre \ref run() or \ref findPaths() must be called before using
519    /// this function.
520    const Path& path(int i) const {
521      return paths[i];
522    }
523
524    /// @}
525
526  }; //class Suurballe
527
528  ///@}
529
530} //namespace lemon
531
532#endif //LEMON_SUURBALLE_H
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