COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/edmonds_karp.h @ 2522:616c019215c4

Last change on this file since 2522:616c019215c4 was 2522:616c019215c4, checked in by Balazs Dezso, 13 years ago

Performance bug in Preflow
The initial relabeling moved each node to the lowest level
Doc bug fix

File size: 14.5 KB
Line 
1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2007
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_EDMONDS_KARP_H
20#define LEMON_EDMONDS_KARP_H
21
22/// \file
23/// \ingroup max_flow
24/// \brief Implementation of the Edmonds-Karp algorithm.
25
26#include <lemon/tolerance.h>
27#include <vector>
28
29namespace lemon {
30
31  /// \brief Default traits class of EdmondsKarp class.
32  ///
33  /// Default traits class of EdmondsKarp class.
34  /// \param _Graph Graph type.
35  /// \param _CapacityMap Type of capacity map.
36  template <typename _Graph, typename _CapacityMap>
37  struct EdmondsKarpDefaultTraits {
38
39    /// \brief The graph type the algorithm runs on.
40    typedef _Graph Graph;
41
42    /// \brief The type of the map that stores the edge capacities.
43    ///
44    /// The type of the map that stores the edge capacities.
45    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
46    typedef _CapacityMap CapacityMap;
47
48    /// \brief The type of the length of the edges.
49    typedef typename CapacityMap::Value Value;
50
51    /// \brief The map type that stores the flow values.
52    ///
53    /// The map type that stores the flow values.
54    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
55    typedef typename Graph::template EdgeMap<Value> FlowMap;
56
57    /// \brief Instantiates a FlowMap.
58    ///
59    /// This function instantiates a \ref FlowMap.
60    /// \param graph The graph, to which we would like to define the flow map.
61    static FlowMap* createFlowMap(const Graph& graph) {
62      return new FlowMap(graph);
63    }
64
65    /// \brief The tolerance used by the algorithm
66    ///
67    /// The tolerance used by the algorithm to handle inexact computation.
68    typedef Tolerance<Value> Tolerance;
69
70  };
71
72  /// \ingroup max_flow
73  ///
74  /// \brief Edmonds-Karp algorithms class.
75  ///
76  /// This class provides an implementation of the \e Edmonds-Karp \e
77  /// algorithm producing a flow of maximum value in a directed
78  /// graphs. The Edmonds-Karp algorithm is slower than the Preflow
79  /// algorithm but it has an advantage of the step-by-step execution
80  /// control with feasible flow solutions. The \e source node, the \e
81  /// target node, the \e capacity of the edges and the \e starting \e
82  /// flow value of the edges should be passed to the algorithm
83  /// through the constructor.
84  ///
85  /// The time complexity of the algorithm is \f$ O(nm^2) \f$ in
86  /// worst case.  Always try the preflow algorithm instead of this if
87  /// you just want to compute the optimal flow.
88  ///
89  /// \param _Graph The directed graph type the algorithm runs on.
90  /// \param _CapacityMap The capacity map type.
91  /// \param _Traits Traits class to set various data types used by
92  /// the algorithm.  The default traits class is \ref
93  /// EdmondsKarpDefaultTraits.  See \ref EdmondsKarpDefaultTraits for the
94  /// documentation of a Edmonds-Karp traits class.
95  ///
96  /// \author Balazs Dezso
97#ifdef DOXYGEN
98  template <typename _Graph, typename _CapacityMap, typename _Traits>
99#else
100  template <typename _Graph,
101            typename _CapacityMap = typename _Graph::template EdgeMap<int>,
102            typename _Traits = EdmondsKarpDefaultTraits<_Graph, _CapacityMap> >
103#endif
104  class EdmondsKarp {
105  public:
106
107    typedef _Traits Traits;
108    typedef typename Traits::Graph Graph;
109    typedef typename Traits::CapacityMap CapacityMap;
110    typedef typename Traits::Value Value;
111
112    typedef typename Traits::FlowMap FlowMap;
113    typedef typename Traits::Tolerance Tolerance;
114
115    /// \brief \ref Exception for the case when the source equals the target.
116    ///
117    /// \ref Exception for the case when the source equals the target.
118    ///
119    class InvalidArgument : public lemon::LogicError {
120    public:
121      virtual const char* what() const throw() {
122        return "lemon::EdmondsKarp::InvalidArgument";
123      }
124    };
125
126
127  private:
128
129    GRAPH_TYPEDEFS(typename Graph);
130    typedef typename Graph::template NodeMap<Edge> PredMap;
131   
132    const Graph& _graph;
133    const CapacityMap* _capacity;
134
135    Node _source, _target;
136
137    FlowMap* _flow;
138    bool _local_flow;
139
140    PredMap* _pred;
141    std::vector<Node> _queue;
142   
143    Tolerance _tolerance;
144    Value _flow_value;
145
146    void createStructures() {
147      if (!_flow) {
148        _flow = Traits::createFlowMap(_graph);
149        _local_flow = true;
150      }
151      if (!_pred) {
152        _pred = new PredMap(_graph);
153      }
154      _queue.resize(countNodes(_graph));
155    }
156
157    void destroyStructures() {
158      if (_local_flow) {
159        delete _flow;
160      }
161      if (_pred) {
162        delete _pred;
163      }
164    }
165   
166  public:
167
168    ///\name Named template parameters
169
170    ///@{
171
172    template <typename _FlowMap>
173    struct DefFlowMapTraits : public Traits {
174      typedef _FlowMap FlowMap;
175      static FlowMap *createFlowMap(const Graph&) {
176        throw UninitializedParameter();
177      }
178    };
179
180    /// \brief \ref named-templ-param "Named parameter" for setting
181    /// FlowMap type
182    ///
183    /// \ref named-templ-param "Named parameter" for setting FlowMap
184    /// type
185    template <typename _FlowMap>
186    struct DefFlowMap
187      : public EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > {
188      typedef EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> >
189      Create;
190    };
191
192
193    /// @}
194
195    /// \brief The constructor of the class.
196    ///
197    /// The constructor of the class.
198    /// \param graph The directed graph the algorithm runs on.
199    /// \param capacity The capacity of the edges.
200    /// \param source The source node.
201    /// \param target The target node.
202    EdmondsKarp(const Graph& graph, const CapacityMap& capacity,
203                Node source, Node target)
204      : _graph(graph), _capacity(&capacity), _source(source), _target(target),
205        _flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value()
206    {
207      if (_source == _target) {
208        throw InvalidArgument();
209      }
210    }
211
212    /// \brief Destrcutor.
213    ///
214    /// Destructor.
215    ~EdmondsKarp() {
216      destroyStructures();
217    }
218
219    /// \brief Sets the capacity map.
220    ///
221    /// Sets the capacity map.
222    /// \return \c (*this)
223    EdmondsKarp& capacityMap(const CapacityMap& map) {
224      _capacity = &map;
225      return *this;
226    }
227
228    /// \brief Sets the flow map.
229    ///
230    /// Sets the flow map.
231    /// \return \c (*this)
232    EdmondsKarp& flowMap(FlowMap& map) {
233      if (_local_flow) {
234        delete _flow;
235        _local_flow = false;
236      }
237      _flow = &map;
238      return *this;
239    }
240
241    /// \brief Returns the flow map.
242    ///
243    /// \return The flow map.
244    const FlowMap& flowMap() {
245      return *_flow;
246    }
247
248    /// \brief Sets the source node.
249    ///
250    /// Sets the source node.
251    /// \return \c (*this)
252    EdmondsKarp& source(const Node& node) {
253      _source = node;
254      return *this;
255    }
256
257    /// \brief Sets the target node.
258    ///
259    /// Sets the target node.
260    /// \return \c (*this)
261    EdmondsKarp& target(const Node& node) {
262      _target = node;
263      return *this;
264    }
265
266    /// \brief Sets the tolerance used by algorithm.
267    ///
268    /// Sets the tolerance used by algorithm.
269    EdmondsKarp& tolerance(const Tolerance& tolerance) const {
270      _tolerance = tolerance;
271      return *this;
272    }
273
274    /// \brief Returns the tolerance used by algorithm.
275    ///
276    /// Returns the tolerance used by algorithm.
277    const Tolerance& tolerance() const {
278      return tolerance;
279    }
280
281    /// \name Execution control The simplest way to execute the
282    /// algorithm is to use the \c run() member functions.
283    /// \n
284    /// If you need more control on initial solution or
285    /// execution then you have to call one \ref init() function and then
286    /// the start() or multiple times the \c augment() member function. 
287   
288    ///@{
289
290    /// \brief Initializes the algorithm
291    ///
292    /// It sets the flow to empty flow.
293    void init() {
294      createStructures();
295      for (EdgeIt it(_graph); it != INVALID; ++it) {
296        _flow->set(it, 0);
297      }
298      _flow_value = 0;
299    }
300   
301    /// \brief Initializes the algorithm
302    ///
303    /// Initializes the flow to the \c flowMap. The \c flowMap should
304    /// contain a feasible flow, ie. in each node excluding the source
305    /// and the target the incoming flow should be equal to the
306    /// outgoing flow.
307    template <typename FlowMap>
308    void flowInit(const FlowMap& flowMap) {
309      createStructures();
310      for (EdgeIt e(_graph); e != INVALID; ++e) {
311        _flow->set(e, flowMap[e]);
312      }
313      _flow_value = 0;
314      for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
315        _flow_value += (*_flow)[jt];
316      }
317      for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
318        _flow_value -= (*_flow)[jt];
319      }
320    }
321
322    /// \brief Initializes the algorithm
323    ///
324    /// Initializes the flow to the \c flowMap. The \c flowMap should
325    /// contain a feasible flow, ie. in each node excluding the source
326    /// and the target the incoming flow should be equal to the
327    /// outgoing flow. 
328    /// \return %False when the given flowMap does not contain
329    /// feasible flow.
330    template <typename FlowMap>
331    bool checkedFlowInit(const FlowMap& flowMap) {
332      createStructures();
333      for (EdgeIt e(_graph); e != INVALID; ++e) {
334        _flow->set(e, flowMap[e]);
335      }
336      for (NodeIt it(_graph); it != INVALID; ++it) {
337        if (it == _source || it == _target) continue;
338        Value outFlow = 0;
339        for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) {
340          outFlow += (*_flow)[jt];
341        }
342        Value inFlow = 0;
343        for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) {
344          inFlow += (*_flow)[jt];
345        }
346        if (_tolerance.different(outFlow, inFlow)) {
347          return false;
348        }
349      }
350      for (EdgeIt it(_graph); it != INVALID; ++it) {
351        if (_tolerance.less((*_flow)[it], 0)) return false;
352        if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false;
353      }
354      _flow_value = 0;
355      for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
356        _flow_value += (*_flow)[jt];
357      }
358      for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) {
359        _flow_value -= (*_flow)[jt];
360      }
361      return true;
362    }
363
364    /// \brief Augment the solution on an edge shortest path.
365    ///
366    /// Augment the solution on an edge shortest path. It search an
367    /// edge shortest path between the source and the target
368    /// in the residual graph with the bfs algoritm.
369    /// Then it increase the flow on this path with the minimal residual
370    /// capacity on the path. If there is not such path it gives back
371    /// false.
372    /// \return %False when the augmenting is not success so the
373    /// current flow is a feasible and optimal solution.
374    bool augment() {
375      for (NodeIt n(_graph); n != INVALID; ++n) {
376        _pred->set(n, INVALID);
377      }
378     
379      int first = 0, last = 1;
380     
381      _queue[0] = _source;
382      _pred->set(_source, OutEdgeIt(_graph, _source));
383
384      while (first != last && (*_pred)[_target] == INVALID) {
385        Node n = _queue[first++];
386       
387        for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
388          Value rem = (*_capacity)[e] - (*_flow)[e];
389          Node t = _graph.target(e);
390          if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
391            _pred->set(t, e);
392            _queue[last++] = t;
393          }
394        }
395        for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
396          Value rem = (*_flow)[e];
397          Node t = _graph.source(e);
398          if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
399            _pred->set(t, e);
400            _queue[last++] = t;
401          }
402        }
403      }
404
405      if ((*_pred)[_target] != INVALID) {
406        Node n = _target;
407        Edge e = (*_pred)[n];
408
409        Value prem = (*_capacity)[e] - (*_flow)[e];
410        n = _graph.source(e);
411        while (n != _source) {
412          e = (*_pred)[n];
413          if (_graph.target(e) == n) {
414            Value rem = (*_capacity)[e] - (*_flow)[e];
415            if (rem < prem) prem = rem;
416            n = _graph.source(e);
417          } else {
418            Value rem = (*_flow)[e];
419            if (rem < prem) prem = rem;
420            n = _graph.target(e);   
421          }
422        }
423
424        n = _target;
425        e = (*_pred)[n];
426
427        _flow->set(e, (*_flow)[e] + prem);
428        n = _graph.source(e);
429        while (n != _source) {
430          e = (*_pred)[n];
431          if (_graph.target(e) == n) {
432            _flow->set(e, (*_flow)[e] + prem);
433            n = _graph.source(e);
434          } else {
435            _flow->set(e, (*_flow)[e] - prem);
436            n = _graph.target(e);   
437          }
438        }
439
440        _flow_value += prem;   
441        return true;
442      } else {
443        return false;
444      }
445    }
446
447    /// \brief Executes the algorithm
448    ///
449    /// It runs augmenting phases until the optimal solution is reached.
450    void start() {
451      while (augment()) {}
452    }
453
454    /// \brief runs the algorithm.
455    ///
456    /// It is just a shorthand for:
457    ///
458    ///\code
459    /// ek.init();
460    /// ek.start();
461    ///\endcode
462    void run() {
463      init();
464      start();
465    }
466
467    /// @}
468
469    /// \name Query Functions
470    /// The result of the Edmonds-Karp algorithm can be obtained using these
471    /// functions.\n
472    /// Before the use of these functions,
473    /// either run() or start() must be called.
474   
475    ///@{
476
477    /// \brief Returns the value of the maximum flow.
478    ///
479    /// Returns the value of the maximum flow by returning the excess
480    /// of the target node \c t. This value equals to the value of
481    /// the maximum flow already after the first phase.
482    Value flowValue() const {
483      return _flow_value;
484    }
485
486
487    /// \brief Returns the flow on the edge.
488    ///
489    /// Sets the \c flowMap to the flow on the edges. This method can
490    /// be called after the second phase of algorithm.
491    Value flow(const Edge& edge) const {
492      return (*_flow)[edge];
493    }
494
495    /// \brief Returns true when the node is on the source side of minimum cut.
496    ///
497
498    /// Returns true when the node is on the source side of minimum
499    /// cut. This method can be called both after running \ref
500    /// startFirstPhase() and \ref startSecondPhase().
501    bool minCut(const Node& node) const {
502      return (*_pred)[node] != INVALID;
503    }
504
505    /// \brief Returns a minimum value cut.
506    ///
507    /// Sets \c cut to the characteristic vector of a minimum value cut
508    /// It simply calls the minMinCut member.
509    /// \retval cut Write node bool map.
510    template <typename CutMap>
511    void minCutMap(CutMap& cutMap) const {
512      for (NodeIt n(_graph); n != INVALID; ++n) {
513        cutMap.set(n, (*_pred)[n] != INVALID);
514      }
515      cutMap.set(_source, true);
516    }   
517
518    /// @}
519
520  };
521
522}
523
524#endif
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