COIN-OR::LEMON - Graph Library

source: lemon/lemon/edmonds_karp.h @ 1227:08f2dc76e82e

Last change on this file since 1227:08f2dc76e82e was 1227:08f2dc76e82e, checked in by Peter Kovacs <kpeter@…>, 7 years ago

Rename flow init functions according to Preflow (#177)

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 *
5 * Copyright (C) 2003-2010
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 GR Digraph type.
35  /// \param CAP Type of capacity map.
36  template <typename GR, typename CAP>
37  struct EdmondsKarpDefaultTraits {
38
39    /// \brief The digraph type the algorithm runs on.
40    typedef GR Digraph;
41
42    /// \brief The type of the map that stores the arc capacities.
43    ///
44    /// The type of the map that stores the arc capacities.
45    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
46    typedef CAP CapacityMap;
47
48    /// \brief The type of the flow values.
49    typedef typename CapacityMap::Value Value;
50
51    /// \brief The type of the map that stores the flow values.
52    ///
53    /// The type of the map that stores the flow values.
54    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
55#ifdef DOXYGEN
56    typedef GR::ArcMap<Value> FlowMap;
57#else
58    typedef typename Digraph::template ArcMap<Value> FlowMap;
59#endif
60
61    /// \brief Instantiates a FlowMap.
62    ///
63    /// This function instantiates a \ref FlowMap.
64    /// \param digraph The digraph for which we would like to define
65    /// the flow map.
66    static FlowMap* createFlowMap(const Digraph& digraph) {
67      return new FlowMap(digraph);
68    }
69
70    /// \brief The tolerance used by the algorithm
71    ///
72    /// The tolerance used by the algorithm to handle inexact computation.
73    typedef lemon::Tolerance<Value> Tolerance;
74
75  };
76
77  /// \ingroup max_flow
78  ///
79  /// \brief Edmonds-Karp algorithms class.
80  ///
81  /// This class provides an implementation of the \e Edmonds-Karp \e
82  /// algorithm producing a \ref max_flow "flow of maximum value" in a
83  /// digraph \ref clrs01algorithms, \ref amo93networkflows,
84  /// \ref edmondskarp72theoretical.
85  /// The Edmonds-Karp algorithm is slower than the Preflow
86  /// algorithm, but it has an advantage of the step-by-step execution
87  /// control with feasible flow solutions. The \e source node, the \e
88  /// target node, the \e capacity of the arcs and the \e starting \e
89  /// flow value of the arcs should be passed to the algorithm
90  /// through the constructor.
91  ///
92  /// The time complexity of the algorithm is \f$ O(nm^2) \f$ in
93  /// worst case. Always try the Preflow algorithm instead of this if
94  /// you just want to compute the optimal flow.
95  ///
96  /// \tparam GR The type of the digraph the algorithm runs on.
97  /// \tparam CAP The type of the capacity map. The default map
98  /// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
99  /// \tparam TR The traits class that defines various types used by the
100  /// algorithm. By default, it is \ref EdmondsKarpDefaultTraits
101  /// "EdmondsKarpDefaultTraits<GR, CAP>".
102  /// In most cases, this parameter should not be set directly,
103  /// consider to use the named template parameters instead.
104
105#ifdef DOXYGEN
106  template <typename GR, typename CAP, typename TR>
107#else
108  template <typename GR,
109            typename CAP = typename GR::template ArcMap<int>,
110            typename TR = EdmondsKarpDefaultTraits<GR, CAP> >
111#endif
112  class EdmondsKarp {
113  public:
114
115    /// The \ref EdmondsKarpDefaultTraits "traits class" of the algorithm.
116    typedef TR Traits;
117    /// The type of the digraph the algorithm runs on.
118    typedef typename Traits::Digraph Digraph;
119    /// The type of the capacity map.
120    typedef typename Traits::CapacityMap CapacityMap;
121    /// The type of the flow values.
122    typedef typename Traits::Value Value;
123
124    /// The type of the flow map.
125    typedef typename Traits::FlowMap FlowMap;
126    /// The type of the tolerance.
127    typedef typename Traits::Tolerance Tolerance;
128
129  private:
130
131    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
132    typedef typename Digraph::template NodeMap<Arc> PredMap;
133   
134    const Digraph& _graph;
135    const CapacityMap* _capacity;
136
137    Node _source, _target;
138
139    FlowMap* _flow;
140    bool _local_flow;
141
142    PredMap* _pred;
143    std::vector<Node> _queue;
144   
145    Tolerance _tolerance;
146    Value _flow_value;
147
148    void createStructures() {
149      if (!_flow) {
150        _flow = Traits::createFlowMap(_graph);
151        _local_flow = true;
152      }
153      if (!_pred) {
154        _pred = new PredMap(_graph);
155      }
156      _queue.resize(countNodes(_graph));
157    }
158
159    void destroyStructures() {
160      if (_local_flow) {
161        delete _flow;
162      }
163      if (_pred) {
164        delete _pred;
165      }
166    }
167   
168  public:
169
170    ///\name Named template parameters
171
172    ///@{
173
174    template <typename T>
175    struct SetFlowMapTraits : public Traits {
176      typedef T FlowMap;
177      static FlowMap *createFlowMap(const Digraph&) {
178        LEMON_ASSERT(false, "FlowMap is not initialized");
179        return 0;
180      }
181    };
182
183    /// \brief \ref named-templ-param "Named parameter" for setting
184    /// FlowMap type
185    ///
186    /// \ref named-templ-param "Named parameter" for setting FlowMap
187    /// type
188    template <typename T>
189    struct SetFlowMap
190      : public EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > {
191      typedef EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > Create;
192    };
193
194    /// @}
195
196  protected:
197   
198    EdmondsKarp() {}
199
200  public:
201
202    /// \brief The constructor of the class.
203    ///
204    /// The constructor of the class.
205    /// \param digraph The digraph the algorithm runs on.
206    /// \param capacity The capacity of the arcs.
207    /// \param source The source node.
208    /// \param target The target node.
209    EdmondsKarp(const Digraph& digraph, const CapacityMap& capacity,
210                Node source, Node target)
211      : _graph(digraph), _capacity(&capacity), _source(source), _target(target),
212        _flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value()
213    {
214      LEMON_ASSERT(_source != _target,
215                   "Flow source and target are the same nodes.");
216    }
217
218    /// \brief Destructor.
219    ///
220    /// Destructor.
221    ~EdmondsKarp() {
222      destroyStructures();
223    }
224
225    /// \brief Sets the capacity map.
226    ///
227    /// Sets the capacity map.
228    /// \return <tt>(*this)</tt>
229    EdmondsKarp& capacityMap(const CapacityMap& map) {
230      _capacity = &map;
231      return *this;
232    }
233
234    /// \brief Sets the flow map.
235    ///
236    /// Sets the flow map.
237    /// If you don't use this function before calling \ref run() or
238    /// \ref init(), an instance will be allocated automatically.
239    /// The destructor deallocates this automatically allocated map,
240    /// of course.
241    /// \return <tt>(*this)</tt>
242    EdmondsKarp& flowMap(FlowMap& map) {
243      if (_local_flow) {
244        delete _flow;
245        _local_flow = false;
246      }
247      _flow = &map;
248      return *this;
249    }
250
251    /// \brief Sets the source node.
252    ///
253    /// Sets the source node.
254    /// \return <tt>(*this)</tt>
255    EdmondsKarp& source(const Node& node) {
256      _source = node;
257      return *this;
258    }
259
260    /// \brief Sets the target node.
261    ///
262    /// Sets the target node.
263    /// \return <tt>(*this)</tt>
264    EdmondsKarp& target(const Node& node) {
265      _target = node;
266      return *this;
267    }
268
269    /// \brief Sets the tolerance used by algorithm.
270    ///
271    /// Sets the tolerance used by algorithm.
272    /// \return <tt>(*this)</tt>
273    EdmondsKarp& tolerance(const Tolerance& tolerance) {
274      _tolerance = tolerance;
275      return *this;
276    }
277
278    /// \brief Returns a const reference to the tolerance.
279    ///
280    /// Returns a const reference to the tolerance object used by
281    /// the algorithm.
282    const Tolerance& tolerance() const {
283      return _tolerance;
284    }
285
286    /// \name Execution control
287    /// The simplest way to execute the algorithm is to use \ref run().\n
288    /// If you need better control on the initial solution or the execution,
289    /// you have to call one of the \ref init() functions first, then
290    /// \ref start() or multiple times the \ref augment() function.
291   
292    ///@{
293
294    /// \brief Initializes the algorithm.
295    ///
296    /// Initializes the internal data structures and sets the initial
297    /// flow to zero on each arc.
298    void init() {
299      createStructures();
300      for (ArcIt it(_graph); it != INVALID; ++it) {
301        _flow->set(it, 0);
302      }
303      _flow_value = 0;
304    }
305   
306    /// \brief Initializes the algorithm using the given flow map.
307    ///
308    /// Initializes the internal data structures and sets the initial
309    /// flow to the given \c flowMap. The \c flowMap should
310    /// contain a feasible flow, i.e. at each node excluding the source
311    /// and the target, the incoming flow should be equal to the
312    /// outgoing flow.
313    template <typename FlowMap>
314    void init(const FlowMap& flowMap) {
315      createStructures();
316      for (ArcIt e(_graph); e != INVALID; ++e) {
317        _flow->set(e, flowMap[e]);
318      }
319      _flow_value = 0;
320      for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) {
321        _flow_value += (*_flow)[jt];
322      }
323      for (InArcIt jt(_graph, _source); jt != INVALID; ++jt) {
324        _flow_value -= (*_flow)[jt];
325      }
326    }
327
328    /// \brief Initializes the algorithm using the given flow map.
329    ///
330    /// Initializes the internal data structures and sets the initial
331    /// flow to the given \c flowMap. The \c flowMap should
332    /// contain a feasible flow, i.e. at each node excluding the source
333    /// and the target, the incoming flow should be equal to the
334    /// outgoing flow.
335    /// \return \c false when the given \c flowMap does not contain a
336    /// feasible flow.
337    template <typename FlowMap>
338    bool checkedInit(const FlowMap& flowMap) {
339      createStructures();
340      for (ArcIt e(_graph); e != INVALID; ++e) {
341        _flow->set(e, flowMap[e]);
342      }
343      for (NodeIt it(_graph); it != INVALID; ++it) {
344        if (it == _source || it == _target) continue;
345        Value outFlow = 0;
346        for (OutArcIt jt(_graph, it); jt != INVALID; ++jt) {
347          outFlow += (*_flow)[jt];
348        }
349        Value inFlow = 0;
350        for (InArcIt jt(_graph, it); jt != INVALID; ++jt) {
351          inFlow += (*_flow)[jt];
352        }
353        if (_tolerance.different(outFlow, inFlow)) {
354          return false;
355        }
356      }
357      for (ArcIt it(_graph); it != INVALID; ++it) {
358        if (_tolerance.less((*_flow)[it], 0)) return false;
359        if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false;
360      }
361      _flow_value = 0;
362      for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) {
363        _flow_value += (*_flow)[jt];
364      }
365      for (InArcIt jt(_graph, _source); jt != INVALID; ++jt) {
366        _flow_value -= (*_flow)[jt];
367      }
368      return true;
369    }
370
371    /// \brief Augments the solution along a shortest path.
372    ///
373    /// Augments the solution along a shortest path. This function searches a
374    /// shortest path between the source and the target
375    /// in the residual digraph by the Bfs algoritm.
376    /// Then it increases the flow on this path with the minimal residual
377    /// capacity on the path. If there is no such path, it gives back
378    /// false.
379    /// \return \c false when the augmenting did not success, i.e. the
380    /// current flow is a feasible and optimal solution.
381    bool augment() {
382      for (NodeIt n(_graph); n != INVALID; ++n) {
383        _pred->set(n, INVALID);
384      }
385     
386      int first = 0, last = 1;
387     
388      _queue[0] = _source;
389      _pred->set(_source, OutArcIt(_graph, _source));
390
391      while (first != last && (*_pred)[_target] == INVALID) {
392        Node n = _queue[first++];
393       
394        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
395          Value rem = (*_capacity)[e] - (*_flow)[e];
396          Node t = _graph.target(e);
397          if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
398            _pred->set(t, e);
399            _queue[last++] = t;
400          }
401        }
402        for (InArcIt e(_graph, n); e != INVALID; ++e) {
403          Value rem = (*_flow)[e];
404          Node t = _graph.source(e);
405          if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
406            _pred->set(t, e);
407            _queue[last++] = t;
408          }
409        }
410      }
411
412      if ((*_pred)[_target] != INVALID) {
413        Node n = _target;
414        Arc e = (*_pred)[n];
415
416        Value prem = (*_capacity)[e] - (*_flow)[e];
417        n = _graph.source(e);
418        while (n != _source) {
419          e = (*_pred)[n];
420          if (_graph.target(e) == n) {
421            Value rem = (*_capacity)[e] - (*_flow)[e];
422            if (rem < prem) prem = rem;
423            n = _graph.source(e);
424          } else {
425            Value rem = (*_flow)[e];
426            if (rem < prem) prem = rem;
427            n = _graph.target(e);   
428          }
429        }
430
431        n = _target;
432        e = (*_pred)[n];
433
434        _flow->set(e, (*_flow)[e] + prem);
435        n = _graph.source(e);
436        while (n != _source) {
437          e = (*_pred)[n];
438          if (_graph.target(e) == n) {
439            _flow->set(e, (*_flow)[e] + prem);
440            n = _graph.source(e);
441          } else {
442            _flow->set(e, (*_flow)[e] - prem);
443            n = _graph.target(e);   
444          }
445        }
446
447        _flow_value += prem;   
448        return true;
449      } else {
450        return false;
451      }
452    }
453
454    /// \brief Executes the algorithm
455    ///
456    /// Executes the algorithm by performing augmenting phases until the
457    /// optimal solution is reached.
458    /// \pre One of the \ref init() functions must be called before
459    /// using this function.
460    void start() {
461      while (augment()) {}
462    }
463
464    /// \brief Runs the algorithm.
465    ///
466    /// Runs the Edmonds-Karp algorithm.
467    /// \note ek.run() is just a shortcut of the following code.
468    ///\code
469    /// ek.init();
470    /// ek.start();
471    ///\endcode
472    void run() {
473      init();
474      start();
475    }
476
477    /// @}
478
479    /// \name Query Functions
480    /// The result of the Edmonds-Karp algorithm can be obtained using these
481    /// functions.\n
482    /// Either \ref run() or \ref start() should be called before using them.
483   
484    ///@{
485
486    /// \brief Returns the value of the maximum flow.
487    ///
488    /// Returns the value of the maximum flow found by the algorithm.
489    ///
490    /// \pre Either \ref run() or \ref init() must be called before
491    /// using this function.
492    Value flowValue() const {
493      return _flow_value;
494    }
495
496    /// \brief Returns the flow value on the given arc.
497    ///
498    /// Returns the flow value on the given arc.
499    ///
500    /// \pre Either \ref run() or \ref init() must be called before
501    /// using this function.
502    Value flow(const Arc& arc) const {
503      return (*_flow)[arc];
504    }
505
506    /// \brief Returns a const reference to the flow map.
507    ///
508    /// Returns a const reference to the arc map storing the found flow.
509    ///
510    /// \pre Either \ref run() or \ref init() must be called before
511    /// using this function.
512    const FlowMap& flowMap() const {
513      return *_flow;
514    }
515
516    /// \brief Returns \c true when the node is on the source side of the
517    /// minimum cut.
518    ///
519    /// Returns true when the node is on the source side of the found
520    /// minimum cut.
521    ///
522    /// \pre Either \ref run() or \ref init() must be called before
523    /// using this function.
524    bool minCut(const Node& node) const {
525      return ((*_pred)[node] != INVALID) or node == _source;
526    }
527
528    /// \brief Gives back a minimum value cut.
529    ///
530    /// Sets \c cutMap to the characteristic vector of a minimum value
531    /// cut. \c cutMap should be a \ref concepts::WriteMap "writable"
532    /// node map with \c bool (or convertible) value type.
533    ///
534    /// \note This function calls \ref minCut() for each node, so it runs in
535    /// O(n) time.
536    ///
537    /// \pre Either \ref run() or \ref init() must be called before
538    /// using this function.
539    template <typename CutMap>
540    void minCutMap(CutMap& cutMap) const {
541      for (NodeIt n(_graph); n != INVALID; ++n) {
542        cutMap.set(n, (*_pred)[n] != INVALID);
543      }
544      cutMap.set(_source, true);
545    }   
546
547    /// @}
548
549  };
550
551}
552
553#endif
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