COIN-OR::LEMON - Graph Library

source: lemon/lemon/edmonds_karp.h @ 1229:473c71baff72

Last change on this file since 1229:473c71baff72 was 1229:473c71baff72, checked in by Peter Kovacs <kpeter@…>, 7 years ago

Avoid usage of alternative operator (#177)

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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    typedef EdmondsKarp Create;
171
172    ///\name Named template parameters
173
174    ///@{
175
176    template <typename T>
177    struct SetFlowMapTraits : public Traits {
178      typedef T FlowMap;
179      static FlowMap *createFlowMap(const Digraph&) {
180        LEMON_ASSERT(false, "FlowMap is not initialized");
181        return 0;
182      }
183    };
184
185    /// \brief \ref named-templ-param "Named parameter" for setting
186    /// FlowMap type
187    ///
188    /// \ref named-templ-param "Named parameter" for setting FlowMap
189    /// type
190    template <typename T>
191    struct SetFlowMap
192      : public EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > {
193      typedef EdmondsKarp<Digraph, CapacityMap, SetFlowMapTraits<T> > Create;
194    };
195
196    /// @}
197
198  protected:
199   
200    EdmondsKarp() {}
201
202  public:
203
204    /// \brief The constructor of the class.
205    ///
206    /// The constructor of the class.
207    /// \param digraph The digraph the algorithm runs on.
208    /// \param capacity The capacity of the arcs.
209    /// \param source The source node.
210    /// \param target The target node.
211    EdmondsKarp(const Digraph& digraph, const CapacityMap& capacity,
212                Node source, Node target)
213      : _graph(digraph), _capacity(&capacity), _source(source), _target(target),
214        _flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value()
215    {
216      LEMON_ASSERT(_source != _target,
217                   "Flow source and target are the same nodes.");
218    }
219
220    /// \brief Destructor.
221    ///
222    /// Destructor.
223    ~EdmondsKarp() {
224      destroyStructures();
225    }
226
227    /// \brief Sets the capacity map.
228    ///
229    /// Sets the capacity map.
230    /// \return <tt>(*this)</tt>
231    EdmondsKarp& capacityMap(const CapacityMap& map) {
232      _capacity = &map;
233      return *this;
234    }
235
236    /// \brief Sets the flow map.
237    ///
238    /// Sets the flow map.
239    /// If you don't use this function before calling \ref run() or
240    /// \ref init(), an instance will be allocated automatically.
241    /// The destructor deallocates this automatically allocated map,
242    /// of course.
243    /// \return <tt>(*this)</tt>
244    EdmondsKarp& flowMap(FlowMap& map) {
245      if (_local_flow) {
246        delete _flow;
247        _local_flow = false;
248      }
249      _flow = &map;
250      return *this;
251    }
252
253    /// \brief Sets the source node.
254    ///
255    /// Sets the source node.
256    /// \return <tt>(*this)</tt>
257    EdmondsKarp& source(const Node& node) {
258      _source = node;
259      return *this;
260    }
261
262    /// \brief Sets the target node.
263    ///
264    /// Sets the target node.
265    /// \return <tt>(*this)</tt>
266    EdmondsKarp& target(const Node& node) {
267      _target = node;
268      return *this;
269    }
270
271    /// \brief Sets the tolerance used by algorithm.
272    ///
273    /// Sets the tolerance used by algorithm.
274    /// \return <tt>(*this)</tt>
275    EdmondsKarp& tolerance(const Tolerance& tolerance) {
276      _tolerance = tolerance;
277      return *this;
278    }
279
280    /// \brief Returns a const reference to the tolerance.
281    ///
282    /// Returns a const reference to the tolerance object used by
283    /// the algorithm.
284    const Tolerance& tolerance() const {
285      return _tolerance;
286    }
287
288    /// \name Execution control
289    /// The simplest way to execute the algorithm is to use \ref run().\n
290    /// If you need better control on the initial solution or the execution,
291    /// you have to call one of the \ref init() functions first, then
292    /// \ref start() or multiple times the \ref augment() function.
293   
294    ///@{
295
296    /// \brief Initializes the algorithm.
297    ///
298    /// Initializes the internal data structures and sets the initial
299    /// flow to zero on each arc.
300    void init() {
301      createStructures();
302      for (ArcIt it(_graph); it != INVALID; ++it) {
303        _flow->set(it, 0);
304      }
305      _flow_value = 0;
306    }
307   
308    /// \brief Initializes the algorithm using the given flow map.
309    ///
310    /// Initializes the internal data structures and sets the initial
311    /// flow to the given \c flowMap. The \c flowMap should
312    /// contain a feasible flow, i.e. at each node excluding the source
313    /// and the target, the incoming flow should be equal to the
314    /// outgoing flow.
315    template <typename FlowMap>
316    void init(const FlowMap& flowMap) {
317      createStructures();
318      for (ArcIt e(_graph); e != INVALID; ++e) {
319        _flow->set(e, flowMap[e]);
320      }
321      _flow_value = 0;
322      for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) {
323        _flow_value += (*_flow)[jt];
324      }
325      for (InArcIt jt(_graph, _source); jt != INVALID; ++jt) {
326        _flow_value -= (*_flow)[jt];
327      }
328    }
329
330    /// \brief Initializes the algorithm using the given flow map.
331    ///
332    /// Initializes the internal data structures and sets the initial
333    /// flow to the given \c flowMap. The \c flowMap should
334    /// contain a feasible flow, i.e. at each node excluding the source
335    /// and the target, the incoming flow should be equal to the
336    /// outgoing flow.
337    /// \return \c false when the given \c flowMap does not contain a
338    /// feasible flow.
339    template <typename FlowMap>
340    bool checkedInit(const FlowMap& flowMap) {
341      createStructures();
342      for (ArcIt e(_graph); e != INVALID; ++e) {
343        _flow->set(e, flowMap[e]);
344      }
345      for (NodeIt it(_graph); it != INVALID; ++it) {
346        if (it == _source || it == _target) continue;
347        Value outFlow = 0;
348        for (OutArcIt jt(_graph, it); jt != INVALID; ++jt) {
349          outFlow += (*_flow)[jt];
350        }
351        Value inFlow = 0;
352        for (InArcIt jt(_graph, it); jt != INVALID; ++jt) {
353          inFlow += (*_flow)[jt];
354        }
355        if (_tolerance.different(outFlow, inFlow)) {
356          return false;
357        }
358      }
359      for (ArcIt it(_graph); it != INVALID; ++it) {
360        if (_tolerance.less((*_flow)[it], 0)) return false;
361        if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false;
362      }
363      _flow_value = 0;
364      for (OutArcIt jt(_graph, _source); jt != INVALID; ++jt) {
365        _flow_value += (*_flow)[jt];
366      }
367      for (InArcIt jt(_graph, _source); jt != INVALID; ++jt) {
368        _flow_value -= (*_flow)[jt];
369      }
370      return true;
371    }
372
373    /// \brief Augments the solution along a shortest path.
374    ///
375    /// Augments the solution along a shortest path. This function searches a
376    /// shortest path between the source and the target
377    /// in the residual digraph by the Bfs algoritm.
378    /// Then it increases the flow on this path with the minimal residual
379    /// capacity on the path. If there is no such path, it gives back
380    /// false.
381    /// \return \c false when the augmenting did not success, i.e. the
382    /// current flow is a feasible and optimal solution.
383    bool augment() {
384      for (NodeIt n(_graph); n != INVALID; ++n) {
385        _pred->set(n, INVALID);
386      }
387     
388      int first = 0, last = 1;
389     
390      _queue[0] = _source;
391      _pred->set(_source, OutArcIt(_graph, _source));
392
393      while (first != last && (*_pred)[_target] == INVALID) {
394        Node n = _queue[first++];
395       
396        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
397          Value rem = (*_capacity)[e] - (*_flow)[e];
398          Node t = _graph.target(e);
399          if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
400            _pred->set(t, e);
401            _queue[last++] = t;
402          }
403        }
404        for (InArcIt e(_graph, n); e != INVALID; ++e) {
405          Value rem = (*_flow)[e];
406          Node t = _graph.source(e);
407          if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) {
408            _pred->set(t, e);
409            _queue[last++] = t;
410          }
411        }
412      }
413
414      if ((*_pred)[_target] != INVALID) {
415        Node n = _target;
416        Arc e = (*_pred)[n];
417
418        Value prem = (*_capacity)[e] - (*_flow)[e];
419        n = _graph.source(e);
420        while (n != _source) {
421          e = (*_pred)[n];
422          if (_graph.target(e) == n) {
423            Value rem = (*_capacity)[e] - (*_flow)[e];
424            if (rem < prem) prem = rem;
425            n = _graph.source(e);
426          } else {
427            Value rem = (*_flow)[e];
428            if (rem < prem) prem = rem;
429            n = _graph.target(e);   
430          }
431        }
432
433        n = _target;
434        e = (*_pred)[n];
435
436        _flow->set(e, (*_flow)[e] + prem);
437        n = _graph.source(e);
438        while (n != _source) {
439          e = (*_pred)[n];
440          if (_graph.target(e) == n) {
441            _flow->set(e, (*_flow)[e] + prem);
442            n = _graph.source(e);
443          } else {
444            _flow->set(e, (*_flow)[e] - prem);
445            n = _graph.target(e);   
446          }
447        }
448
449        _flow_value += prem;   
450        return true;
451      } else {
452        return false;
453      }
454    }
455
456    /// \brief Executes the algorithm
457    ///
458    /// Executes the algorithm by performing augmenting phases until the
459    /// optimal solution is reached.
460    /// \pre One of the \ref init() functions must be called before
461    /// using this function.
462    void start() {
463      while (augment()) {}
464    }
465
466    /// \brief Runs the algorithm.
467    ///
468    /// Runs the Edmonds-Karp algorithm.
469    /// \note ek.run() is just a shortcut of the following code.
470    ///\code
471    /// ek.init();
472    /// ek.start();
473    ///\endcode
474    void run() {
475      init();
476      start();
477    }
478
479    /// @}
480
481    /// \name Query Functions
482    /// The result of the Edmonds-Karp algorithm can be obtained using these
483    /// functions.\n
484    /// Either \ref run() or \ref start() should be called before using them.
485   
486    ///@{
487
488    /// \brief Returns the value of the maximum flow.
489    ///
490    /// Returns the value of the maximum flow found by the algorithm.
491    ///
492    /// \pre Either \ref run() or \ref init() must be called before
493    /// using this function.
494    Value flowValue() const {
495      return _flow_value;
496    }
497
498    /// \brief Returns the flow value on the given arc.
499    ///
500    /// Returns the flow value on the given arc.
501    ///
502    /// \pre Either \ref run() or \ref init() must be called before
503    /// using this function.
504    Value flow(const Arc& arc) const {
505      return (*_flow)[arc];
506    }
507
508    /// \brief Returns a const reference to the flow map.
509    ///
510    /// Returns a const reference to the arc map storing the found flow.
511    ///
512    /// \pre Either \ref run() or \ref init() must be called before
513    /// using this function.
514    const FlowMap& flowMap() const {
515      return *_flow;
516    }
517
518    /// \brief Returns \c true when the node is on the source side of the
519    /// minimum cut.
520    ///
521    /// Returns true when the node is on the source side of the found
522    /// minimum cut.
523    ///
524    /// \pre Either \ref run() or \ref init() must be called before
525    /// using this function.
526    bool minCut(const Node& node) const {
527      return ((*_pred)[node] != INVALID) || node == _source;
528    }
529
530    /// \brief Gives back a minimum value cut.
531    ///
532    /// Sets \c cutMap to the characteristic vector of a minimum value
533    /// cut. \c cutMap should be a \ref concepts::WriteMap "writable"
534    /// node map with \c bool (or convertible) value type.
535    ///
536    /// \note This function calls \ref minCut() for each node, so it runs in
537    /// O(n) time.
538    ///
539    /// \pre Either \ref run() or \ref init() must be called before
540    /// using this function.
541    template <typename CutMap>
542    void minCutMap(CutMap& cutMap) const {
543      for (NodeIt n(_graph); n != INVALID; ++n) {
544        cutMap.set(n, (*_pred)[n] != INVALID);
545      }
546      cutMap.set(_source, true);
547    }   
548
549    /// @}
550
551  };
552
553}
554
555#endif
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