COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/cycle_canceling.h @ 2620:8f41a3129746

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2008
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_CYCLE_CANCELING_H
20#define LEMON_CYCLE_CANCELING_H
21
22/// \ingroup min_cost_flow
23///
24/// \file
25/// \brief Cycle-canceling algorithm for finding a minimum cost flow.
26
27#include <vector>
28#include <lemon/graph_adaptor.h>
29#include <lemon/path.h>
30
31#include <lemon/circulation.h>
32#include <lemon/bellman_ford.h>
33#include <lemon/min_mean_cycle.h>
34
35namespace lemon {
36
37  /// \addtogroup min_cost_flow
38  /// @{
39
40  /// \brief Implementation of a cycle-canceling algorithm for
41  /// finding a minimum cost flow.
42  ///
43  /// \ref CycleCanceling implements a cycle-canceling algorithm for
44  /// finding a minimum cost flow.
45  ///
46  /// \tparam Graph The directed graph type the algorithm runs on.
47  /// \tparam LowerMap The type of the lower bound map.
48  /// \tparam CapacityMap The type of the capacity (upper bound) map.
49  /// \tparam CostMap The type of the cost (length) map.
50  /// \tparam SupplyMap The type of the supply map.
51  ///
52  /// \warning
53  /// - Edge capacities and costs should be \e non-negative \e integers.
54  /// - Supply values should be \e signed \e integers.
55  /// - The value types of the maps should be convertible to each other.
56  /// - \c CostMap::Value must be signed type.
57  ///
58  /// \note By default the \ref BellmanFord "Bellman-Ford" algorithm is
59  /// used for negative cycle detection with limited iteration number.
60  /// However \ref CycleCanceling also provides the "Minimum Mean
61  /// Cycle-Canceling" algorithm, which is \e strongly \e polynomial,
62  /// but rather slower in practice.
63  /// To use this version of the algorithm, call \ref run() with \c true
64  /// parameter.
65  ///
66  /// \author Peter Kovacs
67  template < typename Graph,
68             typename LowerMap = typename Graph::template EdgeMap<int>,
69             typename CapacityMap = typename Graph::template EdgeMap<int>,
70             typename CostMap = typename Graph::template EdgeMap<int>,
71             typename SupplyMap = typename Graph::template NodeMap<int> >
72  class CycleCanceling
73  {
74    GRAPH_TYPEDEFS(typename Graph);
75
76    typedef typename CapacityMap::Value Capacity;
77    typedef typename CostMap::Value Cost;
78    typedef typename SupplyMap::Value Supply;
79    typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap;
80    typedef typename Graph::template NodeMap<Supply> SupplyNodeMap;
81
82    typedef ResGraphAdaptor< const Graph, Capacity,
83                             CapacityEdgeMap, CapacityEdgeMap > ResGraph;
84    typedef typename ResGraph::Node ResNode;
85    typedef typename ResGraph::NodeIt ResNodeIt;
86    typedef typename ResGraph::Edge ResEdge;
87    typedef typename ResGraph::EdgeIt ResEdgeIt;
88
89  public:
90
91    /// The type of the flow map.
92    typedef typename Graph::template EdgeMap<Capacity> FlowMap;
93    /// The type of the potential map.
94    typedef typename Graph::template NodeMap<Cost> PotentialMap;
95
96  private:
97
98    /// \brief Map adaptor class for handling residual edge costs.
99    ///
100    /// Map adaptor class for handling residual edge costs.
101    class ResidualCostMap : public MapBase<ResEdge, Cost>
102    {
103    private:
104
105      const CostMap &_cost_map;
106
107    public:
108
109      ///\e
110      ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}
111
112      ///\e
113      Cost operator[](const ResEdge &e) const {
114        return ResGraph::forward(e) ? _cost_map[e] : -_cost_map[e];
115      }
116
117    }; //class ResidualCostMap
118
119  private:
120
121    // The maximum number of iterations for the first execution of the
122    // Bellman-Ford algorithm. It should be at least 2.
123    static const int BF_FIRST_LIMIT  = 2;
124    // The iteration limit for the Bellman-Ford algorithm is multiplied
125    // by BF_LIMIT_FACTOR/100 in every round.
126    static const int BF_LIMIT_FACTOR = 150;
127
128  private:
129
130    // The directed graph the algorithm runs on
131    const Graph &_graph;
132    // The original lower bound map
133    const LowerMap *_lower;
134    // The modified capacity map
135    CapacityEdgeMap _capacity;
136    // The original cost map
137    const CostMap &_cost;
138    // The modified supply map
139    SupplyNodeMap _supply;
140    bool _valid_supply;
141
142    // Edge map of the current flow
143    FlowMap *_flow;
144    bool _local_flow;
145    // Node map of the current potentials
146    PotentialMap *_potential;
147    bool _local_potential;
148
149    // The residual graph
150    ResGraph *_res_graph;
151    // The residual cost map
152    ResidualCostMap _res_cost;
153
154  public:
155
156    /// \brief General constructor (with lower bounds).
157    ///
158    /// General constructor (with lower bounds).
159    ///
160    /// \param graph The directed graph the algorithm runs on.
161    /// \param lower The lower bounds of the edges.
162    /// \param capacity The capacities (upper bounds) of the edges.
163    /// \param cost The cost (length) values of the edges.
164    /// \param supply The supply values of the nodes (signed).
165    CycleCanceling( const Graph &graph,
166                    const LowerMap &lower,
167                    const CapacityMap &capacity,
168                    const CostMap &cost,
169                    const SupplyMap &supply ) :
170      _graph(graph), _lower(&lower), _capacity(graph), _cost(cost),
171      _supply(graph), _flow(0), _local_flow(false),
172      _potential(0), _local_potential(false), _res_cost(_cost)
173    {
174      // Removing non-zero lower bounds
175      _capacity = subMap(capacity, lower);
176      Supply sum = 0;
177      for (NodeIt n(_graph); n != INVALID; ++n) {
178        Supply s = supply[n];
179        for (InEdgeIt e(_graph, n); e != INVALID; ++e)
180          s += lower[e];
181        for (OutEdgeIt e(_graph, n); e != INVALID; ++e)
182          s -= lower[e];
183        sum += (_supply[n] = s);
184      }
185      _valid_supply = sum == 0;
186    }
187
188    /// \brief General constructor (without lower bounds).
189    ///
190    /// General constructor (without lower bounds).
191    ///
192    /// \param graph The directed graph the algorithm runs on.
193    /// \param capacity The capacities (upper bounds) of the edges.
194    /// \param cost The cost (length) values of the edges.
195    /// \param supply The supply values of the nodes (signed).
196    CycleCanceling( const Graph &graph,
197                    const CapacityMap &capacity,
198                    const CostMap &cost,
199                    const SupplyMap &supply ) :
200      _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),
201      _supply(supply), _flow(0), _local_flow(false),
202      _potential(0), _local_potential(false), _res_cost(_cost)
203    {
204      // Checking the sum of supply values
205      Supply sum = 0;
206      for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
207      _valid_supply = sum == 0;
208    }
209
210    /// \brief Simple constructor (with lower bounds).
211    ///
212    /// Simple constructor (with lower bounds).
213    ///
214    /// \param graph The directed graph the algorithm runs on.
215    /// \param lower The lower bounds of the edges.
216    /// \param capacity The capacities (upper bounds) of the edges.
217    /// \param cost The cost (length) values of the edges.
218    /// \param s The source node.
219    /// \param t The target node.
220    /// \param flow_value The required amount of flow from node \c s
221    /// to node \c t (i.e. the supply of \c s and the demand of \c t).
222    CycleCanceling( const Graph &graph,
223                    const LowerMap &lower,
224                    const CapacityMap &capacity,
225                    const CostMap &cost,
226                    Node s, Node t,
227                    Supply flow_value ) :
228      _graph(graph), _lower(&lower), _capacity(graph), _cost(cost),
229      _supply(graph), _flow(0), _local_flow(false),
230      _potential(0), _local_potential(false), _res_cost(_cost)
231    {
232      // Removing non-zero lower bounds
233      _capacity = subMap(capacity, lower);
234      for (NodeIt n(_graph); n != INVALID; ++n) {
235        Supply sum = 0;
236        if (n == s) sum =  flow_value;
237        if (n == t) sum = -flow_value;
238        for (InEdgeIt e(_graph, n); e != INVALID; ++e)
239          sum += lower[e];
240        for (OutEdgeIt e(_graph, n); e != INVALID; ++e)
241          sum -= lower[e];
242        _supply[n] = sum;
243      }
244      _valid_supply = true;
245    }
246
247    /// \brief Simple constructor (without lower bounds).
248    ///
249    /// Simple constructor (without lower bounds).
250    ///
251    /// \param graph The directed graph the algorithm runs on.
252    /// \param capacity The capacities (upper bounds) of the edges.
253    /// \param cost The cost (length) values of the edges.
254    /// \param s The source node.
255    /// \param t The target node.
256    /// \param flow_value The required amount of flow from node \c s
257    /// to node \c t (i.e. the supply of \c s and the demand of \c t).
258    CycleCanceling( const Graph &graph,
259                    const CapacityMap &capacity,
260                    const CostMap &cost,
261                    Node s, Node t,
262                    Supply flow_value ) :
263      _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),
264      _supply(graph, 0), _flow(0), _local_flow(false),
265      _potential(0), _local_potential(false), _res_cost(_cost)
266    {
267      _supply[s] =  flow_value;
268      _supply[t] = -flow_value;
269      _valid_supply = true;
270    }
271
272    /// Destructor.
273    ~CycleCanceling() {
274      if (_local_flow) delete _flow;
275      if (_local_potential) delete _potential;
276      delete _res_graph;
277    }
278
279    /// \brief Set the flow map.
280    ///
281    /// Set the flow map.
282    ///
283    /// \return \c (*this)
284    CycleCanceling& flowMap(FlowMap &map) {
285      if (_local_flow) {
286        delete _flow;
287        _local_flow = false;
288      }
289      _flow = &map;
290      return *this;
291    }
292
293    /// \brief Set the potential map.
294    ///
295    /// Set the potential map.
296    ///
297    /// \return \c (*this)
298    CycleCanceling& 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
309    /// @{
310
311    /// \brief Run the algorithm.
312    ///
313    /// Run the algorithm.
314    ///
315    /// \param min_mean_cc Set this parameter to \c true to run the
316    /// "Minimum Mean Cycle-Canceling" algorithm, which is strongly
317    /// polynomial, but rather slower in practice.
318    ///
319    /// \return \c true if a feasible flow can be found.
320    bool run(bool min_mean_cc = false) {
321      return init() && start(min_mean_cc);
322    }
323
324    /// @}
325
326    /// \name Query Functions
327    /// The result of the algorithm can be obtained using these
328    /// functions.\n
329    /// \ref lemon::CycleCanceling::run() "run()" must be called before
330    /// using them.
331
332    /// @{
333
334    /// \brief Return a const reference to the edge map storing the
335    /// found flow.
336    ///
337    /// Return a const reference to the edge map storing the found flow.
338    ///
339    /// \pre \ref run() must be called before using this function.
340    const FlowMap& flowMap() const {
341      return *_flow;
342    }
343
344    /// \brief Return a const reference to the node map storing the
345    /// found potentials (the dual solution).
346    ///
347    /// Return a const reference to the node map storing the found
348    /// potentials (the dual solution).
349    ///
350    /// \pre \ref run() must be called before using this function.
351    const PotentialMap& potentialMap() const {
352      return *_potential;
353    }
354
355    /// \brief Return the flow on the given edge.
356    ///
357    /// Return the flow on the given edge.
358    ///
359    /// \pre \ref run() must be called before using this function.
360    Capacity flow(const Edge& edge) const {
361      return (*_flow)[edge];
362    }
363
364    /// \brief Return the potential of the given node.
365    ///
366    /// Return the potential of the given node.
367    ///
368    /// \pre \ref run() must be called before using this function.
369    Cost potential(const Node& node) const {
370      return (*_potential)[node];
371    }
372
373    /// \brief Return the total cost of the found flow.
374    ///
375    /// Return the total cost of the found flow. The complexity of the
376    /// function is \f$ O(e) \f$.
377    ///
378    /// \pre \ref run() must be called before using this function.
379    Cost totalCost() const {
380      Cost c = 0;
381      for (EdgeIt e(_graph); e != INVALID; ++e)
382        c += (*_flow)[e] * _cost[e];
383      return c;
384    }
385
386    /// @}
387
388  private:
389
390    /// Initialize the algorithm.
391    bool init() {
392      if (!_valid_supply) return false;
393
394      // Initializing flow and potential maps
395      if (!_flow) {
396        _flow = new FlowMap(_graph);
397        _local_flow = true;
398      }
399      if (!_potential) {
400        _potential = new PotentialMap(_graph);
401        _local_potential = true;
402      }
403
404      _res_graph = new ResGraph(_graph, _capacity, *_flow);
405
406      // Finding a feasible flow using Circulation
407      Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap,
408                   SupplyMap >
409        circulation( _graph, constMap<Edge>(Capacity(0)), _capacity,
410                     _supply );
411      return circulation.flowMap(*_flow).run();
412    }
413
414    bool start(bool min_mean_cc) {
415      if (min_mean_cc)
416        startMinMean();
417      else
418        start();
419
420      // Handling non-zero lower bounds
421      if (_lower) {
422        for (EdgeIt e(_graph); e != INVALID; ++e)
423          (*_flow)[e] += (*_lower)[e];
424      }
425      return true;
426    }
427
428    /// \brief Execute the algorithm using \ref BellmanFord.
429    ///
430    /// Execute the algorithm using the \ref BellmanFord
431    /// "Bellman-Ford" algorithm for negative cycle detection with
432    /// successively larger limit for the number of iterations.
433    void start() {
434      typename BellmanFord<ResGraph, ResidualCostMap>::PredMap pred(*_res_graph);
435      typename ResGraph::template NodeMap<int> visited(*_res_graph);
436      std::vector<ResEdge> cycle;
437      int node_num = countNodes(_graph);
438
439      int length_bound = BF_FIRST_LIMIT;
440      bool optimal = false;
441      while (!optimal) {
442        BellmanFord<ResGraph, ResidualCostMap> bf(*_res_graph, _res_cost);
443        bf.predMap(pred);
444        bf.init(0);
445        int iter_num = 0;
446        bool cycle_found = false;
447        while (!cycle_found) {
448          int curr_iter_num = iter_num + length_bound <= node_num ?
449                              length_bound : node_num - iter_num;
450          iter_num += curr_iter_num;
451          int real_iter_num = curr_iter_num;
452          for (int i = 0; i < curr_iter_num; ++i) {
453            if (bf.processNextWeakRound()) {
454              real_iter_num = i;
455              break;
456            }
457          }
458          if (real_iter_num < curr_iter_num) {
459            // Optimal flow is found
460            optimal = true;
461            // Setting node potentials
462            for (NodeIt n(_graph); n != INVALID; ++n)
463              (*_potential)[n] = bf.dist(n);
464            break;
465          } else {
466            // Searching for node disjoint negative cycles
467            for (ResNodeIt n(*_res_graph); n != INVALID; ++n)
468              visited[n] = 0;
469            int id = 0;
470            for (ResNodeIt n(*_res_graph); n != INVALID; ++n) {
471              if (visited[n] > 0) continue;
472              visited[n] = ++id;
473              ResNode u = pred[n] == INVALID ?
474                          INVALID : _res_graph->source(pred[n]);
475              while (u != INVALID && visited[u] == 0) {
476                visited[u] = id;
477                u = pred[u] == INVALID ?
478                    INVALID : _res_graph->source(pred[u]);
479              }
480              if (u != INVALID && visited[u] == id) {
481                // Finding the negative cycle
482                cycle_found = true;
483                cycle.clear();
484                ResEdge e = pred[u];
485                cycle.push_back(e);
486                Capacity d = _res_graph->rescap(e);
487                while (_res_graph->source(e) != u) {
488                  cycle.push_back(e = pred[_res_graph->source(e)]);
489                  if (_res_graph->rescap(e) < d)
490                    d = _res_graph->rescap(e);
491                }
492
493                // Augmenting along the cycle
494                for (int i = 0; i < int(cycle.size()); ++i)
495                  _res_graph->augment(cycle[i], d);
496              }
497            }
498          }
499
500          if (!cycle_found)
501            length_bound = length_bound * BF_LIMIT_FACTOR / 100;
502        }
503      }
504    }
505
506    /// \brief Execute the algorithm using \ref MinMeanCycle.
507    ///
508    /// Execute the algorithm using \ref MinMeanCycle for negative
509    /// cycle detection.
510    void startMinMean() {
511      typedef Path<ResGraph> ResPath;
512      MinMeanCycle<ResGraph, ResidualCostMap> mmc(*_res_graph, _res_cost);
513      ResPath cycle;
514
515      mmc.cyclePath(cycle).init();
516      if (mmc.findMinMean()) {
517        while (mmc.cycleLength() < 0) {
518          // Finding the cycle
519          mmc.findCycle();
520
521          // Finding the largest flow amount that can be augmented
522          // along the cycle
523          Capacity delta = 0;
524          for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) {
525            if (delta == 0 || _res_graph->rescap(e) < delta)
526              delta = _res_graph->rescap(e);
527          }
528
529          // Augmenting along the cycle
530          for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e)
531            _res_graph->augment(e, delta);
532
533          // Finding the minimum cycle mean for the modified residual
534          // graph
535          mmc.reset();
536          if (!mmc.findMinMean()) break;
537        }
538      }
539
540      // Computing node potentials
541      BellmanFord<ResGraph, ResidualCostMap> bf(*_res_graph, _res_cost);
542      bf.init(0); bf.start();
543      for (NodeIt n(_graph); n != INVALID; ++n)
544        (*_potential)[n] = bf.dist(n);
545    }
546
547  }; //class CycleCanceling
548
549  ///@}
550
551} //namespace lemon
552
553#endif //LEMON_CYCLE_CANCELING_H
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