COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/capacity_scaling.h @ 2476:059dcdda37c5

Last change on this file since 2476:059dcdda37c5 was 2471:ed70b226cc48, checked in by Peter Kovacs, 12 years ago

Small changes in min. cost flow algorithms.

File size: 20.9 KB
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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2007
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_CAPACITY_SCALING_H
20#define LEMON_CAPACITY_SCALING_H
21
22/// \ingroup min_cost_flow
23///
24/// \file
25/// \brief The capacity scaling algorithm for finding a minimum cost
26/// flow.
27
28#include <vector>
29#include <lemon/dijkstra.h>
30#include <lemon/graph_adaptor.h>
31
32#define WITH_SCALING
33
34#ifdef WITH_SCALING
35#define SCALING_FACTOR    2
36#endif
37
38//#define _DEBUG_ITER_
39
40namespace lemon {
41
42  /// \addtogroup min_cost_flow
43  /// @{
44
45  /// \brief Implementation of the capacity scaling version of the
46  /// successive shortest path algorithm for finding a minimum cost flow.
47  ///
48  /// \ref lemon::CapacityScaling "CapacityScaling" implements a
49  /// capacity scaling algorithm for finding a minimum cost flow.
50  ///
51  /// \param Graph The directed graph type the algorithm runs on.
52  /// \param LowerMap The type of the lower bound map.
53  /// \param CapacityMap The type of the capacity (upper bound) map.
54  /// \param CostMap The type of the cost (length) map.
55  /// \param SupplyMap The type of the supply map.
56  ///
57  /// \warning
58  /// - Edge capacities and costs should be nonnegative integers.
59  ///   However \c CostMap::Value should be signed type.
60  /// - Supply values should be integers.
61  /// - \c LowerMap::Value must be convertible to
62  ///   \c CapacityMap::Value and \c CapacityMap::Value must be
63  ///   convertible to \c SupplyMap::Value.
64  ///
65  /// \author Peter Kovacs
66
67template < typename Graph,
68           typename LowerMap = typename Graph::template EdgeMap<int>,
69           typename CapacityMap = LowerMap,
70           typename CostMap = typename Graph::template EdgeMap<int>,
71           typename SupplyMap = typename Graph::template NodeMap
72                                <typename CapacityMap::Value> >
73  class CapacityScaling
74  {
75    typedef typename Graph::Node Node;
76    typedef typename Graph::NodeIt NodeIt;
77    typedef typename Graph::Edge Edge;
78    typedef typename Graph::EdgeIt EdgeIt;
79    typedef typename Graph::InEdgeIt InEdgeIt;
80    typedef typename Graph::OutEdgeIt OutEdgeIt;
81
82    typedef typename LowerMap::Value Lower;
83    typedef typename CapacityMap::Value Capacity;
84    typedef typename CostMap::Value Cost;
85    typedef typename SupplyMap::Value Supply;
86    typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap;
87    typedef typename Graph::template NodeMap<Supply> SupplyRefMap;
88
89    typedef ResGraphAdaptor< const Graph, Capacity,
90                             CapacityRefMap, CapacityRefMap > ResGraph;
91    typedef typename ResGraph::Node ResNode;
92    typedef typename ResGraph::NodeIt ResNodeIt;
93    typedef typename ResGraph::Edge ResEdge;
94    typedef typename ResGraph::EdgeIt ResEdgeIt;
95
96  public:
97
98    /// \brief The type of the flow map.
99    typedef CapacityRefMap FlowMap;
100    /// \brief The type of the potential map.
101    typedef typename Graph::template NodeMap<Cost> PotentialMap;
102
103  protected:
104
105    /// \brief Map adaptor class for handling reduced edge costs.
106    class ReducedCostMap : public MapBase<ResEdge, Cost>
107    {
108    private:
109
110      const ResGraph &gr;
111      const CostMap &cost_map;
112      const PotentialMap &pot_map;
113
114    public:
115
116      typedef typename MapBase<ResEdge, Cost>::Value Value;
117      typedef typename MapBase<ResEdge, Cost>::Key Key;
118
119      ReducedCostMap( const ResGraph &_gr,
120                      const CostMap &_cost,
121                      const PotentialMap &_pot ) :
122        gr(_gr), cost_map(_cost), pot_map(_pot) {}
123
124      Value operator[](const Key &e) const {
125        return ResGraph::forward(e) ?
126           cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)] :
127          -cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)];
128      }
129
130    }; //class ReducedCostMap
131
132    /// \brief Map adaptor for \ref lemon::Dijkstra "Dijkstra" class to
133    /// update node potentials.
134    class PotentialUpdateMap : public MapBase<ResNode, Cost>
135    {
136    private:
137
138      PotentialMap *pot;
139      typedef std::pair<ResNode, Cost> Pair;
140      std::vector<Pair> data;
141
142    public:
143
144      typedef typename MapBase<ResNode, Cost>::Value Value;
145      typedef typename MapBase<ResNode, Cost>::Key Key;
146
147      void potentialMap(PotentialMap &_pot) {
148        pot = &_pot;
149      }
150
151      void init() {
152        data.clear();
153      }
154
155      void set(const Key &n, const Value &v) {
156        data.push_back(Pair(n, v));
157      }
158
159      void update() {
160        Cost val = data[data.size()-1].second;
161        for (int i = 0; i < data.size()-1; ++i)
162          (*pot)[data[i].first] += val - data[i].second;
163      }
164
165    }; //class PotentialUpdateMap
166
167#ifdef WITH_SCALING
168    /// \brief Map adaptor class for identifing deficit nodes.
169    class DeficitBoolMap : public MapBase<ResNode, bool>
170    {
171    private:
172
173      const SupplyRefMap &imb;
174      const Capacity &delta;
175
176    public:
177
178      DeficitBoolMap(const SupplyRefMap &_imb, const Capacity &_delta) :
179        imb(_imb), delta(_delta) {}
180
181      bool operator[](const ResNode &n) const {
182        return imb[n] <= -delta;
183      }
184
185    }; //class DeficitBoolMap
186
187    /// \brief Map adaptor class for filtering edges with at least
188    /// \c delta residual capacity
189    class DeltaFilterMap : public MapBase<ResEdge, bool>
190    {
191    private:
192
193      const ResGraph &gr;
194      const Capacity &delta;
195
196    public:
197
198      typedef typename MapBase<ResEdge, Cost>::Value Value;
199      typedef typename MapBase<ResEdge, Cost>::Key Key;
200
201      DeltaFilterMap(const ResGraph &_gr, const Capacity &_delta) :
202        gr(_gr), delta(_delta) {}
203
204      Value operator[](const Key &e) const {
205        return gr.rescap(e) >= delta;
206      }
207
208    }; //class DeltaFilterMap
209
210    typedef EdgeSubGraphAdaptor<const ResGraph, const DeltaFilterMap>
211      DeltaResGraph;
212
213    /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class.
214    class ResDijkstraTraits :
215      public DijkstraDefaultTraits<DeltaResGraph, ReducedCostMap>
216    {
217    public:
218
219      typedef PotentialUpdateMap DistMap;
220
221      static DistMap *createDistMap(const DeltaResGraph&) {
222        return new DistMap();
223      }
224
225    }; //class ResDijkstraTraits
226
227#else //WITHOUT_CAPACITY_SCALING
228    /// \brief Map adaptor class for identifing deficit nodes.
229    class DeficitBoolMap : public MapBase<ResNode, bool>
230    {
231    private:
232
233      const SupplyRefMap &imb;
234
235    public:
236
237      DeficitBoolMap(const SupplyRefMap &_imb) : imb(_imb) {}
238
239      bool operator[](const ResNode &n) const {
240        return imb[n] < 0;
241      }
242
243    }; //class DeficitBoolMap
244
245    /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class.
246    class ResDijkstraTraits :
247      public DijkstraDefaultTraits<ResGraph, ReducedCostMap>
248    {
249    public:
250
251      typedef PotentialUpdateMap DistMap;
252
253      static DistMap *createDistMap(const ResGraph&) {
254        return new DistMap();
255      }
256
257    }; //class ResDijkstraTraits
258#endif
259
260  protected:
261
262    /// \brief The directed graph the algorithm runs on.
263    const Graph &graph;
264    /// \brief The original lower bound map.
265    const LowerMap *lower;
266    /// \brief The modified capacity map.
267    CapacityRefMap capacity;
268    /// \brief The cost map.
269    const CostMap &cost;
270    /// \brief The modified supply map.
271    SupplyRefMap supply;
272    /// \brief The sum of supply values equals zero.
273    bool valid_supply;
274
275    /// \brief The edge map of the current flow.
276    FlowMap flow;
277    /// \brief The potential node map.
278    PotentialMap potential;
279    /// \brief The residual graph.
280    ResGraph res_graph;
281    /// \brief The reduced cost map.
282    ReducedCostMap red_cost;
283
284    /// \brief The imbalance map.
285    SupplyRefMap imbalance;
286    /// \brief The excess nodes.
287    std::vector<ResNode> excess_nodes;
288    /// \brief The index of the next excess node.
289    int next_node;
290
291#ifdef WITH_SCALING
292    typedef Dijkstra<DeltaResGraph, ReducedCostMap, ResDijkstraTraits>
293      ResDijkstra;
294    /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding
295    /// shortest paths in the residual graph with respect to the
296    /// reduced edge costs.
297    ResDijkstra dijkstra;
298
299    /// \brief The delta parameter used for capacity scaling.
300    Capacity delta;
301    /// \brief Edge filter map.
302    DeltaFilterMap delta_filter;
303    /// \brief The delta residual graph.
304    DeltaResGraph dres_graph;
305    /// \brief Map for identifing deficit nodes.
306    DeficitBoolMap delta_deficit;
307
308    /// \brief The deficit nodes.
309    std::vector<ResNode> deficit_nodes;
310
311#else //WITHOUT_CAPACITY_SCALING
312    typedef Dijkstra<ResGraph, ReducedCostMap, ResDijkstraTraits>
313      ResDijkstra;
314    /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding
315    /// shortest paths in the residual graph with respect to the
316    /// reduced edge costs.
317    ResDijkstra dijkstra;
318    /// \brief Map for identifing deficit nodes.
319    DeficitBoolMap has_deficit;
320#endif
321
322    /// \brief Pred map for the \ref lemon::Dijkstra "Dijkstra" class.
323    typename ResDijkstra::PredMap pred;
324    /// \brief Dist map for the \ref lemon::Dijkstra "Dijkstra" class to
325    /// update node potentials.
326    PotentialUpdateMap updater;
327
328  public :
329
330    /// \brief General constructor of the class (with lower bounds).
331    ///
332    /// General constructor of the class (with lower bounds).
333    ///
334    /// \param _graph The directed graph the algorithm runs on.
335    /// \param _lower The lower bounds of the edges.
336    /// \param _capacity The capacities (upper bounds) of the edges.
337    /// \param _cost The cost (length) values of the edges.
338    /// \param _supply The supply values of the nodes (signed).
339    CapacityScaling( const Graph &_graph,
340                     const LowerMap &_lower,
341                     const CapacityMap &_capacity,
342                     const CostMap &_cost,
343                     const SupplyMap &_supply ) :
344      graph(_graph), lower(&_lower), capacity(_graph), cost(_cost),
345      supply(_graph), flow(_graph, 0), potential(_graph, 0),
346      res_graph(_graph, capacity, flow),
347      red_cost(res_graph, cost, potential), imbalance(_graph),
348#ifdef WITH_SCALING
349      delta(0), delta_filter(res_graph, delta),
350      dres_graph(res_graph, delta_filter),
351      dijkstra(dres_graph, red_cost), pred(dres_graph),
352      delta_deficit(imbalance, delta)
353#else //WITHOUT_CAPACITY_SCALING
354      dijkstra(res_graph, red_cost), pred(res_graph),
355      has_deficit(imbalance)
356#endif
357    {
358      // Removing nonzero lower bounds
359      capacity = subMap(_capacity, _lower);
360      Supply sum = 0;
361      for (NodeIt n(graph); n != INVALID; ++n) {
362        Supply s = _supply[n];
363        for (InEdgeIt e(graph, n); e != INVALID; ++e)
364          s += _lower[e];
365        for (OutEdgeIt e(graph, n); e != INVALID; ++e)
366          s -= _lower[e];
367        supply[n] = imbalance[n] = s;
368        sum += s;
369      }
370      valid_supply = sum == 0;
371    }
372
373    /// \brief General constructor of the class (without lower bounds).
374    ///
375    /// General constructor of the class (without lower bounds).
376    ///
377    /// \param _graph The directed graph the algorithm runs on.
378    /// \param _capacity The capacities (upper bounds) of the edges.
379    /// \param _cost The cost (length) values of the edges.
380    /// \param _supply The supply values of the nodes (signed).
381    CapacityScaling( const Graph &_graph,
382                     const CapacityMap &_capacity,
383                     const CostMap &_cost,
384                     const SupplyMap &_supply ) :
385      graph(_graph), lower(NULL), capacity(_capacity), cost(_cost),
386      supply(_supply), flow(_graph, 0), potential(_graph, 0),
387      res_graph(_graph, capacity, flow),
388      red_cost(res_graph, cost, potential), imbalance(_graph),
389#ifdef WITH_SCALING
390      delta(0), delta_filter(res_graph, delta),
391      dres_graph(res_graph, delta_filter),
392      dijkstra(dres_graph, red_cost), pred(dres_graph),
393      delta_deficit(imbalance, delta)
394#else //WITHOUT_CAPACITY_SCALING
395      dijkstra(res_graph, red_cost), pred(res_graph),
396      has_deficit(imbalance)
397#endif
398    {
399      // Checking the sum of supply values
400      Supply sum = 0;
401      for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n];
402      valid_supply = sum == 0;
403    }
404
405    /// \brief Simple constructor of the class (with lower bounds).
406    ///
407    /// Simple constructor of the class (with lower bounds).
408    ///
409    /// \param _graph The directed graph the algorithm runs on.
410    /// \param _lower The lower bounds of the edges.
411    /// \param _capacity The capacities (upper bounds) of the edges.
412    /// \param _cost The cost (length) values of the edges.
413    /// \param _s The source node.
414    /// \param _t The target node.
415    /// \param _flow_value The required amount of flow from node \c _s
416    /// to node \c _t (i.e. the supply of \c _s and the demand of
417    /// \c _t).
418    CapacityScaling( const Graph &_graph,
419                     const LowerMap &_lower,
420                     const CapacityMap &_capacity,
421                     const CostMap &_cost,
422                     Node _s, Node _t,
423                     Supply _flow_value ) :
424      graph(_graph), lower(&_lower), capacity(_graph), cost(_cost),
425      supply(_graph), flow(_graph, 0), potential(_graph, 0),
426      res_graph(_graph, capacity, flow),
427      red_cost(res_graph, cost, potential), imbalance(_graph),
428#ifdef WITH_SCALING
429      delta(0), delta_filter(res_graph, delta),
430      dres_graph(res_graph, delta_filter),
431      dijkstra(dres_graph, red_cost), pred(dres_graph),
432      delta_deficit(imbalance, delta)
433#else //WITHOUT_CAPACITY_SCALING
434      dijkstra(res_graph, red_cost), pred(res_graph),
435      has_deficit(imbalance)
436#endif
437    {
438      // Removing nonzero lower bounds
439      capacity = subMap(_capacity, _lower);
440      for (NodeIt n(graph); n != INVALID; ++n) {
441        Supply s = 0;
442        if (n == _s) s =  _flow_value;
443        if (n == _t) s = -_flow_value;
444        for (InEdgeIt e(graph, n); e != INVALID; ++e)
445          s += _lower[e];
446        for (OutEdgeIt e(graph, n); e != INVALID; ++e)
447          s -= _lower[e];
448        supply[n] = imbalance[n] = s;
449      }
450      valid_supply = true;
451    }
452
453    /// \brief Simple constructor of the class (without lower bounds).
454    ///
455    /// Simple constructor of the class (without lower bounds).
456    ///
457    /// \param _graph The directed graph the algorithm runs on.
458    /// \param _capacity The capacities (upper bounds) of the edges.
459    /// \param _cost The cost (length) values of the edges.
460    /// \param _s The source node.
461    /// \param _t The target node.
462    /// \param _flow_value The required amount of flow from node \c _s
463    /// to node \c _t (i.e. the supply of \c _s and the demand of
464    /// \c _t).
465    CapacityScaling( const Graph &_graph,
466                     const CapacityMap &_capacity,
467                     const CostMap &_cost,
468                     Node _s, Node _t,
469                     Supply _flow_value ) :
470      graph(_graph), lower(NULL), capacity(_capacity), cost(_cost),
471      supply(_graph, 0), flow(_graph, 0), potential(_graph, 0),
472      res_graph(_graph, capacity, flow),
473      red_cost(res_graph, cost, potential), imbalance(_graph),
474#ifdef WITH_SCALING
475      delta(0), delta_filter(res_graph, delta),
476      dres_graph(res_graph, delta_filter),
477      dijkstra(dres_graph, red_cost), pred(dres_graph),
478      delta_deficit(imbalance, delta)
479#else //WITHOUT_CAPACITY_SCALING
480      dijkstra(res_graph, red_cost), pred(res_graph),
481      has_deficit(imbalance)
482#endif
483    {
484      supply[_s] =  _flow_value;
485      supply[_t] = -_flow_value;
486      valid_supply = true;
487    }
488
489    /// \brief Returns a const reference to the flow map.
490    ///
491    /// Returns a const reference to the flow map.
492    ///
493    /// \pre \ref run() must be called before using this function.
494    const FlowMap& flowMap() const {
495      return flow;
496    }
497
498    /// \brief Returns a const reference to the potential map (the dual
499    /// solution).
500    ///
501    /// Returns a const reference to the potential map (the dual
502    /// solution).
503    ///
504    /// \pre \ref run() must be called before using this function.
505    const PotentialMap& potentialMap() const {
506      return potential;
507    }
508
509    /// \brief Returns the total cost of the found flow.
510    ///
511    /// Returns the total cost of the found flow. The complexity of the
512    /// function is \f$ O(e) \f$.
513    ///
514    /// \pre \ref run() must be called before using this function.
515    Cost totalCost() const {
516      Cost c = 0;
517      for (EdgeIt e(graph); e != INVALID; ++e)
518        c += flow[e] * cost[e];
519      return c;
520    }
521
522    /// \brief Runs the algorithm.
523    ///
524    /// Runs the algorithm.
525    ///
526    /// \return \c true if a feasible flow can be found.
527    bool run() {
528      return init() && start();
529    }
530
531  protected:
532
533    /// \brief Initializes the algorithm.
534    bool init() {
535      if (!valid_supply) return false;
536
537      // Initalizing Dijkstra class
538      updater.potentialMap(potential);
539      dijkstra.distMap(updater).predMap(pred);
540
541#ifdef WITH_SCALING
542      // Initilaizing delta value
543      Supply max_sup = 0, max_dem = 0;
544      for (NodeIt n(graph); n != INVALID; ++n) {
545        if (supply[n] >  max_sup) max_sup =  supply[n];
546        if (supply[n] < -max_dem) max_dem = -supply[n];
547      }
548      if (max_dem < max_sup) max_sup = max_dem;
549      for ( delta = 1; SCALING_FACTOR * delta < max_sup;
550            delta *= SCALING_FACTOR ) ;
551#endif
552      return true;
553    }
554
555#ifdef WITH_SCALING
556    /// \brief Executes the capacity scaling version of the successive
557    /// shortest path algorithm.
558    bool start() {
559      typedef typename DeltaResGraph::EdgeIt DeltaResEdgeIt;
560      typedef typename DeltaResGraph::Edge DeltaResEdge;
561#ifdef _DEBUG_ITER_
562      int dijk_num = 0;
563#endif
564
565      // Processing capacity scaling phases
566      ResNode s, t;
567      for ( ; delta >= 1; delta = delta < SCALING_FACTOR && delta > 1 ?
568                                  1 : delta / SCALING_FACTOR )
569      {
570        // Saturating edges not satisfying the optimality condition
571        Capacity r;
572        for (DeltaResEdgeIt e(dres_graph); e != INVALID; ++e) {
573          if (red_cost[e] < 0) {
574            res_graph.augment(e, r = res_graph.rescap(e));
575            imbalance[dres_graph.target(e)] += r;
576            imbalance[dres_graph.source(e)] -= r;
577          }
578        }
579
580        // Finding excess nodes
581        excess_nodes.clear();
582        deficit_nodes.clear();
583        for (ResNodeIt n(res_graph); n != INVALID; ++n) {
584          if (imbalance[n] >=  delta) excess_nodes.push_back(n);
585          if (imbalance[n] <= -delta) deficit_nodes.push_back(n);
586        }
587        next_node = 0;
588
589        // Finding shortest paths
590        while (next_node < excess_nodes.size()) {
591          // Checking deficit nodes
592          if (delta > 1) {
593            bool delta_def = false;
594            for (int i = 0; i < deficit_nodes.size(); ++i) {
595              if (imbalance[deficit_nodes[i]] <= -delta) {
596                delta_def = true;
597                break;
598              }
599            }
600            if (!delta_def) break;
601          }
602
603          // Running Dijkstra
604          s = excess_nodes[next_node];
605          updater.init();
606          dijkstra.init();
607          dijkstra.addSource(s);
608#ifdef _DEBUG_ITER_
609          ++dijk_num;
610#endif
611          if ((t = dijkstra.start(delta_deficit)) == INVALID) {
612            if (delta > 1) {
613              ++next_node;
614              continue;
615            }
616            return false;
617          }
618
619          // Updating node potentials
620          updater.update();
621
622          // Augment along a shortest path from s to t
623          Capacity d = imbalance[s] < -imbalance[t] ?
624            imbalance[s] : -imbalance[t];
625          ResNode u = t;
626          ResEdge e;
627          if (d > delta) {
628            while ((e = pred[u]) != INVALID) {
629              if (res_graph.rescap(e) < d) d = res_graph.rescap(e);
630              u = dres_graph.source(e);
631            }
632          }
633          u = t;
634          while ((e = pred[u]) != INVALID) {
635            res_graph.augment(e, d);
636            u = dres_graph.source(e);
637          }
638          imbalance[s] -= d;
639          imbalance[t] += d;
640          if (imbalance[s] < delta) ++next_node;
641        }
642      }
643#ifdef _DEBUG_ITER_
644      std::cout << "Cost Scaling algorithm finished with running Dijkstra algorithm "
645        << dijk_num << " times." << std::endl;
646#endif
647
648      // Handling nonzero lower bounds
649      if (lower) {
650        for (EdgeIt e(graph); e != INVALID; ++e)
651          flow[e] += (*lower)[e];
652      }
653      return true;
654    }
655
656#else //WITHOUT_CAPACITY_SCALING
657    /// \brief Executes the successive shortest path algorithm without
658    /// capacity scaling.
659    bool start() {
660      // Finding excess nodes
661      for (ResNodeIt n(res_graph); n != INVALID; ++n) {
662        if (imbalance[n] > 0) excess_nodes.push_back(n);
663      }
664      if (excess_nodes.size() == 0) return true;
665      next_node = 0;
666
667      // Finding shortest paths
668      ResNode s, t;
669      while ( imbalance[excess_nodes[next_node]] > 0 ||
670              ++next_node < excess_nodes.size() )
671      {
672        // Running Dijkstra
673        s = excess_nodes[next_node];
674        updater.init();
675        dijkstra.init();
676        dijkstra.addSource(s);
677        if ((t = dijkstra.start(has_deficit)) == INVALID)
678          return false;
679
680        // Updating node potentials
681        updater.update();
682
683        // Augmenting along a shortest path from s to t
684        Capacity delta = imbalance[s] < -imbalance[t] ?
685          imbalance[s] : -imbalance[t];
686        ResNode u = t;
687        ResEdge e;
688        while ((e = pred[u]) != INVALID) {
689          if (res_graph.rescap(e) < delta) delta = res_graph.rescap(e);
690          u = res_graph.source(e);
691        }
692        u = t;
693        while ((e = pred[u]) != INVALID) {
694          res_graph.augment(e, delta);
695          u = res_graph.source(e);
696        }
697        imbalance[s] -= delta;
698        imbalance[t] += delta;
699      }
700
701      // Handling nonzero lower bounds
702      if (lower) {
703        for (EdgeIt e(graph); e != INVALID; ++e)
704          flow[e] += (*lower)[e];
705      }
706      return true;
707    }
708#endif
709
710  }; //class CapacityScaling
711
712  ///@}
713
714} //namespace lemon
715
716#endif //LEMON_CAPACITY_SCALING_H
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