COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/lemon/preflow.h @ 946:c94ef40a22ce

Last change on this file since 946:c94ef40a22ce was 946:c94ef40a22ce, checked in by Mihaly Barasz, 15 years ago

The graph_factory branch (@ 1321) has been merged to trunk.

File size: 21.5 KB
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1/* -*- C++ -*-
2 * src/lemon/preflow.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Combinatorial Optimization Research Group, EGRES).
6 *
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
10 *
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
13 * purpose.
14 *
15 */
16
17#ifndef LEMON_PREFLOW_H
18#define LEMON_PREFLOW_H
19
20#include <vector>
21#include <queue>
22
23#include <lemon/invalid.h>
24#include <lemon/maps.h>
25
26/// \file
27/// \ingroup flowalgs
28/// Implementation of the preflow algorithm.
29
30namespace lemon {
31
32  /// \addtogroup flowalgs
33  /// @{                                                   
34
35  ///%Preflow algorithms class.
36
37  ///This class provides an implementation of the \e preflow \e
38  ///algorithm producing a flow of maximum value in a directed
39  ///graph. The preflow algorithms are the fastest max flow algorithms
40  ///up to now. The \e source node, the \e target node, the \e
41  ///capacity of the edges and the \e starting \e flow value of the
42  ///edges should be passed to the algorithm through the
43  ///constructor. It is possible to change these quantities using the
44  ///functions \ref setSource, \ref setTarget, \ref setCap and \ref
45  ///setFlow.
46  ///
47  ///After running \ref lemon::Preflow::phase1() "phase1()"
48  ///or \ref lemon::Preflow::run() "run()", the maximal flow
49  ///value can be obtained by calling \ref flowValue(). The minimum
50  ///value cut can be written into a <tt>bool</tt> node map by
51  ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes
52  ///the inclusionwise minimum and maximum of the minimum value cuts,
53  ///resp.)
54  ///
55  ///\param Graph The directed graph type the algorithm runs on.
56  ///\param Num The number type of the capacities and the flow values.
57  ///\param CapMap The capacity map type.
58  ///\param FlowMap The flow map type.
59  ///
60  ///\author Jacint Szabo
61  template <typename Graph, typename Num,
62            typename CapMap=typename Graph::template EdgeMap<Num>,
63            typename FlowMap=typename Graph::template EdgeMap<Num> >
64  class Preflow {
65  protected:
66    typedef typename Graph::Node Node;
67    typedef typename Graph::NodeIt NodeIt;
68    typedef typename Graph::EdgeIt EdgeIt;
69    typedef typename Graph::OutEdgeIt OutEdgeIt;
70    typedef typename Graph::InEdgeIt InEdgeIt;
71
72    typedef typename Graph::template NodeMap<Node> NNMap;
73    typedef typename std::vector<Node> VecNode;
74
75    const Graph* g;
76    Node s;
77    Node t;
78    const CapMap* capacity;
79    FlowMap* flow;
80    int n;      //the number of nodes of G
81   
82    typename Graph::template NodeMap<int> level; 
83    typename Graph::template NodeMap<Num> excess;
84
85    // constants used for heuristics
86    static const int H0=20;
87    static const int H1=1;
88
89    public:
90
91    ///Indicates the property of the starting flow map.
92
93    ///Indicates the property of the starting flow map. The meanings are as follows:
94    ///- \c ZERO_FLOW: constant zero flow
95    ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
96    ///the sum of the out-flows in every node except the \e source and
97    ///the \e target.
98    ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at
99    ///least the sum of the out-flows in every node except the \e source.
100    ///- \c NO_FLOW: indicates an unspecified edge map. \c flow will be
101    ///set to the constant zero flow in the beginning of
102    ///the algorithm in this case.
103    ///
104    enum FlowEnum{
105      NO_FLOW,
106      ZERO_FLOW,
107      GEN_FLOW,
108      PRE_FLOW
109    };
110
111    ///Indicates the state of the preflow algorithm.
112
113    ///Indicates the state of the preflow algorithm. The meanings are as follows:
114    ///- \c AFTER_NOTHING: before running the algorithm or at an unspecified state.
115    ///- \c AFTER_PREFLOW_PHASE_1: right after running \c phase1
116    ///- \c AFTER_PREFLOW_PHASE_2: after running \ref phase2()
117    ///
118    enum StatusEnum {
119      AFTER_NOTHING,
120      AFTER_PREFLOW_PHASE_1,     
121      AFTER_PREFLOW_PHASE_2
122    };
123   
124    protected:
125      FlowEnum flow_prop;
126    StatusEnum status; // Do not needle this flag only if necessary.
127   
128  public:
129    ///The constructor of the class.
130
131    ///The constructor of the class.
132    ///\param _G The directed graph the algorithm runs on.
133    ///\param _s The source node.
134    ///\param _t The target node.
135    ///\param _capacity The capacity of the edges.
136    ///\param _flow The flow of the edges.
137    ///Except the graph, all of these parameters can be reset by
138    ///calling \ref setSource, \ref setTarget, \ref setCap and \ref
139    ///setFlow, resp.
140      Preflow(const Graph& _G, Node _s, Node _t,
141              const CapMap& _capacity, FlowMap& _flow) :
142        g(&_G), s(_s), t(_t), capacity(&_capacity),
143        flow(&_flow), n(countNodes(_G)), level(_G), excess(_G,0),
144        flow_prop(NO_FLOW), status(AFTER_NOTHING) { }
145
146
147                                                                             
148    ///Runs the preflow algorithm. 
149
150    ///Runs the preflow algorithm.
151    ///
152    void run() {
153      phase1(flow_prop);
154      phase2();
155    }
156   
157    ///Runs the preflow algorithm. 
158   
159    ///Runs the preflow algorithm.
160    ///\pre The starting flow map must be
161    /// - a constant zero flow if \c fp is \c ZERO_FLOW,
162    /// - an arbitrary flow if \c fp is \c GEN_FLOW,
163    /// - an arbitrary preflow if \c fp is \c PRE_FLOW,
164    /// - any map if \c fp is NO_FLOW.
165    ///If the starting flow map is a flow or a preflow then
166    ///the algorithm terminates faster.
167    void run(FlowEnum fp) {
168      flow_prop=fp;
169      run();
170    }
171     
172    ///Runs the first phase of the preflow algorithm.
173
174    ///The preflow algorithm consists of two phases, this method runs
175    ///the first phase. After the first phase the maximum flow value
176    ///and a minimum value cut can already be computed, though a
177    ///maximum flow is not yet obtained. So after calling this method
178    ///\ref flowValue returns the value of a maximum flow and \ref
179    ///minCut returns a minimum cut.     
180    ///\warning \ref minMinCut and \ref maxMinCut do not give minimum
181    ///value cuts unless calling \ref phase2. 
182    ///\pre The starting flow must be
183    ///- a constant zero flow if \c fp is \c ZERO_FLOW,
184    ///- an arbitary flow if \c fp is \c GEN_FLOW,
185    ///- an arbitary preflow if \c fp is \c PRE_FLOW,
186    ///- any map if \c fp is NO_FLOW.
187    void phase1(FlowEnum fp)
188    {
189      flow_prop=fp;
190      phase1();
191    }
192
193   
194    ///Runs the first phase of the preflow algorithm.
195
196    ///The preflow algorithm consists of two phases, this method runs
197    ///the first phase. After the first phase the maximum flow value
198    ///and a minimum value cut can already be computed, though a
199    ///maximum flow is not yet obtained. So after calling this method
200    ///\ref flowValue returns the value of a maximum flow and \ref
201    ///minCut returns a minimum cut.
202    ///\warning \ref minCut(), \ref minMinCut() and \ref maxMinCut() do not
203    ///give minimum value cuts unless calling \ref phase2().
204    void phase1()
205    {
206      int heur0=(int)(H0*n);  //time while running 'bound decrease'
207      int heur1=(int)(H1*n);  //time while running 'highest label'
208      int heur=heur1;         //starting time interval (#of relabels)
209      int numrelabel=0;
210
211      bool what_heur=1;
212      //It is 0 in case 'bound decrease' and 1 in case 'highest label'
213
214      bool end=false;
215      //Needed for 'bound decrease', true means no active
216      //nodes are above bound b.
217
218      int k=n-2;  //bound on the highest level under n containing a node
219      int b=k;    //bound on the highest level under n of an active node
220
221      VecNode first(n, INVALID);
222      NNMap next(*g, INVALID);
223
224      NNMap left(*g, INVALID);
225      NNMap right(*g, INVALID);
226      VecNode level_list(n,INVALID);
227      //List of the nodes in level i<n, set to n.
228
229      preflowPreproc(first, next, level_list, left, right);
230
231      //Push/relabel on the highest level active nodes.
232      while ( true ) {
233        if ( b == 0 ) {
234          if ( !what_heur && !end && k > 0 ) {
235            b=k;
236            end=true;
237          } else break;
238        }
239
240        if ( first[b]==INVALID ) --b;
241        else {
242          end=false;
243          Node w=first[b];
244          first[b]=next[w];
245          int newlevel=push(w, next, first);
246          if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list,
247                                       left, right, b, k, what_heur);
248
249          ++numrelabel;
250          if ( numrelabel >= heur ) {
251            numrelabel=0;
252            if ( what_heur ) {
253              what_heur=0;
254              heur=heur0;
255              end=false;
256            } else {
257              what_heur=1;
258              heur=heur1;
259              b=k;
260            }
261          }
262        }
263      }
264      flow_prop=PRE_FLOW;
265      status=AFTER_PREFLOW_PHASE_1;
266    }
267    // Heuristics:
268    //   2 phase
269    //   gap
270    //   list 'level_list' on the nodes on level i implemented by hand
271    //   stack 'active' on the active nodes on level i     
272    //   runs heuristic 'highest label' for H1*n relabels
273    //   runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
274    //   Parameters H0 and H1 are initialized to 20 and 1.
275
276
277    ///Runs the second phase of the preflow algorithm.
278
279    ///The preflow algorithm consists of two phases, this method runs
280    ///the second phase. After calling \ref phase1 and then \ref
281    ///phase2, \ref flow contains a maximum flow, \ref flowValue
282    ///returns the value of a maximum flow, \ref minCut returns a
283    ///minimum cut, while the methods \ref minMinCut and \ref
284    ///maxMinCut return the inclusionwise minimum and maximum cuts of
285    ///minimum value, resp.  \pre \ref phase1 must be called before.
286    void phase2()
287    {
288
289      int k=n-2;  //bound on the highest level under n containing a node
290      int b=k;    //bound on the highest level under n of an active node
291
292   
293      VecNode first(n, INVALID);
294      NNMap next(*g, INVALID);
295      level.set(s,0);
296      std::queue<Node> bfs_queue;
297      bfs_queue.push(s);
298
299      while ( !bfs_queue.empty() ) {
300
301        Node v=bfs_queue.front();
302        bfs_queue.pop();
303        int l=level[v]+1;
304
305        for(InEdgeIt e(*g,v); e!=INVALID; ++e) {
306          if ( (*capacity)[e] <= (*flow)[e] ) continue;
307          Node u=g->tail(e);
308          if ( level[u] >= n ) {
309            bfs_queue.push(u);
310            level.set(u, l);
311            if ( excess[u] > 0 ) {
312              next.set(u,first[l]);
313              first[l]=u;
314            }
315          }
316        }
317
318        for(OutEdgeIt e(*g,v); e!=INVALID; ++e) {
319          if ( 0 >= (*flow)[e] ) continue;
320          Node u=g->head(e);
321          if ( level[u] >= n ) {
322            bfs_queue.push(u);
323            level.set(u, l);
324            if ( excess[u] > 0 ) {
325              next.set(u,first[l]);
326              first[l]=u;
327            }
328          }
329        }
330      }
331      b=n-2;
332
333      while ( true ) {
334
335        if ( b == 0 ) break;
336        if ( first[b]==INVALID ) --b;
337        else {
338          Node w=first[b];
339          first[b]=next[w];
340          int newlevel=push(w,next, first);
341         
342          //relabel
343          if ( excess[w] > 0 ) {
344            level.set(w,++newlevel);
345            next.set(w,first[newlevel]);
346            first[newlevel]=w;
347            b=newlevel;
348          }
349        }
350      } // while(true)
351      flow_prop=GEN_FLOW;
352      status=AFTER_PREFLOW_PHASE_2;
353    }
354
355    /// Returns the value of the maximum flow.
356
357    /// Returns the value of the maximum flow by returning the excess
358    /// of the target node \c t. This value equals to the value of
359    /// the maximum flow already after running \ref phase1.
360    Num flowValue() const {
361      return excess[t];
362    }
363
364
365    ///Returns a minimum value cut.
366
367    ///Sets \c M to the characteristic vector of a minimum value
368    ///cut. This method can be called both after running \ref
369    ///phase1 and \ref phase2. It is much faster after
370    ///\ref phase1.  \pre M should be a bool-valued node-map. \pre
371    ///If \ref minCut() is called after \ref phase2() then M should
372    ///be initialized to false.
373    template<typename _CutMap>
374    void minCut(_CutMap& M) const {
375      switch ( status ) {
376        case AFTER_PREFLOW_PHASE_1:
377        for(NodeIt v(*g); v!=INVALID; ++v) {
378          if (level[v] < n) {
379            M.set(v, false);
380          } else {
381            M.set(v, true);
382          }
383        }
384        break;
385        case AFTER_PREFLOW_PHASE_2:
386        minMinCut(M);
387        break;
388        case AFTER_NOTHING:
389        break;
390      }
391    }
392
393    ///Returns the inclusionwise minimum of the minimum value cuts.
394
395    ///Sets \c M to the characteristic vector of the minimum value cut
396    ///which is inclusionwise minimum. It is computed by processing a
397    ///bfs from the source node \c s in the residual graph.  \pre M
398    ///should be a node map of bools initialized to false.  \pre \ref
399    ///phase2 should already be run.
400    template<typename _CutMap>
401    void minMinCut(_CutMap& M) const {
402
403      std::queue<Node> queue;
404      M.set(s,true);
405      queue.push(s);
406     
407      while (!queue.empty()) {
408        Node w=queue.front();
409        queue.pop();
410       
411        for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
412          Node v=g->head(e);
413          if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
414            queue.push(v);
415            M.set(v, true);
416          }
417        }
418       
419        for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
420          Node v=g->tail(e);
421          if (!M[v] && (*flow)[e] > 0 ) {
422            queue.push(v);
423            M.set(v, true);
424          }
425        }
426      }
427    }
428   
429    ///Returns the inclusionwise maximum of the minimum value cuts.
430
431    ///Sets \c M to the characteristic vector of the minimum value cut
432    ///which is inclusionwise maximum. It is computed by processing a
433    ///backward bfs from the target node \c t in the residual graph.
434    ///\pre \ref phase2() or run() should already be run.
435    template<typename _CutMap>
436    void maxMinCut(_CutMap& M) const {
437
438      for(NodeIt v(*g) ; v!=INVALID; ++v) M.set(v, true);
439
440      std::queue<Node> queue;
441
442      M.set(t,false);
443      queue.push(t);
444
445      while (!queue.empty()) {
446        Node w=queue.front();
447        queue.pop();
448
449        for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
450          Node v=g->tail(e);
451          if (M[v] && (*flow)[e] < (*capacity)[e] ) {
452            queue.push(v);
453            M.set(v, false);
454          }
455        }
456
457        for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
458          Node v=g->head(e);
459          if (M[v] && (*flow)[e] > 0 ) {
460            queue.push(v);
461            M.set(v, false);
462          }
463        }
464      }
465    }
466
467    ///Sets the source node to \c _s.
468
469    ///Sets the source node to \c _s.
470    ///
471    void setSource(Node _s) {
472      s=_s;
473      if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
474      status=AFTER_NOTHING;
475    }
476
477    ///Sets the target node to \c _t.
478
479    ///Sets the target node to \c _t.
480    ///
481    void setTarget(Node _t) {
482      t=_t;
483      if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
484      status=AFTER_NOTHING;
485    }
486
487    /// Sets the edge map of the capacities to _cap.
488
489    /// Sets the edge map of the capacities to _cap.
490    ///
491    void setCap(const CapMap& _cap) {
492      capacity=&_cap;
493      status=AFTER_NOTHING;
494    }
495
496    /// Sets the edge map of the flows to _flow.
497
498    /// Sets the edge map of the flows to _flow.
499    ///
500    void setFlow(FlowMap& _flow) {
501      flow=&_flow;
502      flow_prop=NO_FLOW;
503      status=AFTER_NOTHING;
504    }
505
506
507  private:
508
509    int push(Node w, NNMap& next, VecNode& first) {
510
511      int lev=level[w];
512      Num exc=excess[w];
513      int newlevel=n;       //bound on the next level of w
514
515      for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
516        if ( (*flow)[e] >= (*capacity)[e] ) continue;
517        Node v=g->head(e);
518
519        if( lev > level[v] ) { //Push is allowed now
520         
521          if ( excess[v]<=0 && v!=t && v!=s ) {
522            next.set(v,first[level[v]]);
523            first[level[v]]=v;
524          }
525
526          Num cap=(*capacity)[e];
527          Num flo=(*flow)[e];
528          Num remcap=cap-flo;
529         
530          if ( remcap >= exc ) { //A nonsaturating push.
531           
532            flow->set(e, flo+exc);
533            excess.set(v, excess[v]+exc);
534            exc=0;
535            break;
536
537          } else { //A saturating push.
538            flow->set(e, cap);
539            excess.set(v, excess[v]+remcap);
540            exc-=remcap;
541          }
542        } else if ( newlevel > level[v] ) newlevel = level[v];
543      } //for out edges wv
544
545      if ( exc > 0 ) {
546        for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
547         
548          if( (*flow)[e] <= 0 ) continue;
549          Node v=g->tail(e);
550
551          if( lev > level[v] ) { //Push is allowed now
552
553            if ( excess[v]<=0 && v!=t && v!=s ) {
554              next.set(v,first[level[v]]);
555              first[level[v]]=v;
556            }
557
558            Num flo=(*flow)[e];
559
560            if ( flo >= exc ) { //A nonsaturating push.
561
562              flow->set(e, flo-exc);
563              excess.set(v, excess[v]+exc);
564              exc=0;
565              break;
566            } else {  //A saturating push.
567
568              excess.set(v, excess[v]+flo);
569              exc-=flo;
570              flow->set(e,0);
571            }
572          } else if ( newlevel > level[v] ) newlevel = level[v];
573        } //for in edges vw
574
575      } // if w still has excess after the out edge for cycle
576
577      excess.set(w, exc);
578     
579      return newlevel;
580    }
581   
582   
583   
584    void preflowPreproc(VecNode& first, NNMap& next,
585                        VecNode& level_list, NNMap& left, NNMap& right)
586    {
587      for(NodeIt v(*g); v!=INVALID; ++v) level.set(v,n);
588      std::queue<Node> bfs_queue;
589     
590      if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) {
591        //Reverse_bfs from t in the residual graph,
592        //to find the starting level.
593        level.set(t,0);
594        bfs_queue.push(t);
595       
596        while ( !bfs_queue.empty() ) {
597         
598          Node v=bfs_queue.front();
599          bfs_queue.pop();
600          int l=level[v]+1;
601         
602          for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) {
603            if ( (*capacity)[e] <= (*flow)[e] ) continue;
604            Node w=g->tail(e);
605            if ( level[w] == n && w != s ) {
606              bfs_queue.push(w);
607              Node z=level_list[l];
608              if ( z!=INVALID ) left.set(z,w);
609              right.set(w,z);
610              level_list[l]=w;
611              level.set(w, l);
612            }
613          }
614         
615          for(OutEdgeIt e(*g,v) ; e!=INVALID; ++e) {
616            if ( 0 >= (*flow)[e] ) continue;
617            Node w=g->head(e);
618            if ( level[w] == n && w != s ) {
619              bfs_queue.push(w);
620              Node z=level_list[l];
621              if ( z!=INVALID ) left.set(z,w);
622              right.set(w,z);
623              level_list[l]=w;
624              level.set(w, l);
625            }
626          }
627        } //while
628      } //if
629
630
631      switch (flow_prop) {
632        case NO_FLOW: 
633        for(EdgeIt e(*g); e!=INVALID; ++e) flow->set(e,0);
634        case ZERO_FLOW:
635        for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
636       
637        //Reverse_bfs from t, to find the starting level.
638        level.set(t,0);
639        bfs_queue.push(t);
640       
641        while ( !bfs_queue.empty() ) {
642         
643          Node v=bfs_queue.front();
644          bfs_queue.pop();
645          int l=level[v]+1;
646         
647          for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) {
648            Node w=g->tail(e);
649            if ( level[w] == n && w != s ) {
650              bfs_queue.push(w);
651              Node z=level_list[l];
652              if ( z!=INVALID ) left.set(z,w);
653              right.set(w,z);
654              level_list[l]=w;
655              level.set(w, l);
656            }
657          }
658        }
659       
660        //the starting flow
661        for(OutEdgeIt e(*g,s) ; e!=INVALID; ++e) {
662          Num c=(*capacity)[e];
663          if ( c <= 0 ) continue;
664          Node w=g->head(e);
665          if ( level[w] < n ) {
666            if ( excess[w] <= 0 && w!=t ) { //putting into the stack
667              next.set(w,first[level[w]]);
668              first[level[w]]=w;
669            }
670            flow->set(e, c);
671            excess.set(w, excess[w]+c);
672          }
673        }
674        break;
675
676        case GEN_FLOW:
677        for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
678        {
679          Num exc=0;
680          for(InEdgeIt e(*g,t) ; e!=INVALID; ++e) exc+=(*flow)[e];
681          for(OutEdgeIt e(*g,t) ; e!=INVALID; ++e) exc-=(*flow)[e];
682          excess.set(t,exc);
683        }
684
685        //the starting flow
686        for(OutEdgeIt e(*g,s); e!=INVALID; ++e) {
687          Num rem=(*capacity)[e]-(*flow)[e];
688          if ( rem <= 0 ) continue;
689          Node w=g->head(e);
690          if ( level[w] < n ) {
691            if ( excess[w] <= 0 && w!=t ) { //putting into the stack
692              next.set(w,first[level[w]]);
693              first[level[w]]=w;
694            }   
695            flow->set(e, (*capacity)[e]);
696            excess.set(w, excess[w]+rem);
697          }
698        }
699       
700        for(InEdgeIt e(*g,s); e!=INVALID; ++e) {
701          if ( (*flow)[e] <= 0 ) continue;
702          Node w=g->tail(e);
703          if ( level[w] < n ) {
704            if ( excess[w] <= 0 && w!=t ) {
705              next.set(w,first[level[w]]);
706              first[level[w]]=w;
707            } 
708            excess.set(w, excess[w]+(*flow)[e]);
709            flow->set(e, 0);
710          }
711        }
712        break;
713
714        case PRE_FLOW: 
715        //the starting flow
716        for(OutEdgeIt e(*g,s) ; e!=INVALID; ++e) {
717          Num rem=(*capacity)[e]-(*flow)[e];
718          if ( rem <= 0 ) continue;
719          Node w=g->head(e);
720          if ( level[w] < n ) flow->set(e, (*capacity)[e]);
721        }
722       
723        for(InEdgeIt e(*g,s) ; e!=INVALID; ++e) {
724          if ( (*flow)[e] <= 0 ) continue;
725          Node w=g->tail(e);
726          if ( level[w] < n ) flow->set(e, 0);
727        }
728       
729        //computing the excess
730        for(NodeIt w(*g); w!=INVALID; ++w) {
731          Num exc=0;
732          for(InEdgeIt e(*g,w); e!=INVALID; ++e) exc+=(*flow)[e];
733          for(OutEdgeIt e(*g,w); e!=INVALID; ++e) exc-=(*flow)[e];
734          excess.set(w,exc);
735         
736          //putting the active nodes into the stack
737          int lev=level[w];
738            if ( exc > 0 && lev < n && Node(w) != t ) {
739              next.set(w,first[lev]);
740              first[lev]=w;
741            }
742        }
743        break;
744      } //switch
745    } //preflowPreproc
746
747
748    void relabel(Node w, int newlevel, VecNode& first, NNMap& next,
749                 VecNode& level_list, NNMap& left,
750                 NNMap& right, int& b, int& k, bool what_heur )
751    {
752
753      int lev=level[w];
754
755      Node right_n=right[w];
756      Node left_n=left[w];
757
758      //unlacing starts
759      if ( right_n!=INVALID ) {
760        if ( left_n!=INVALID ) {
761          right.set(left_n, right_n);
762          left.set(right_n, left_n);
763        } else {
764          level_list[lev]=right_n;
765          left.set(right_n, INVALID);
766        }
767      } else {
768        if ( left_n!=INVALID ) {
769          right.set(left_n, INVALID);
770        } else {
771          level_list[lev]=INVALID;
772        }
773      }
774      //unlacing ends
775
776      if ( level_list[lev]==INVALID ) {
777
778        //gapping starts
779        for (int i=lev; i!=k ; ) {
780          Node v=level_list[++i];
781          while ( v!=INVALID ) {
782            level.set(v,n);
783            v=right[v];
784          }
785          level_list[i]=INVALID;
786          if ( !what_heur ) first[i]=INVALID;
787        }
788
789        level.set(w,n);
790        b=lev-1;
791        k=b;
792        //gapping ends
793
794      } else {
795
796        if ( newlevel == n ) level.set(w,n);
797        else {
798          level.set(w,++newlevel);
799          next.set(w,first[newlevel]);
800          first[newlevel]=w;
801          if ( what_heur ) b=newlevel;
802          if ( k < newlevel ) ++k;      //now k=newlevel
803          Node z=level_list[newlevel];
804          if ( z!=INVALID ) left.set(z,w);
805          right.set(w,z);
806          left.set(w,INVALID);
807          level_list[newlevel]=w;
808        }
809      }
810    } //relabel
811
812  };
813} //namespace lemon
814
815#endif //LEMON_PREFLOW_H
816
817
818
819
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