COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/preflow.h @ 873:f3a30fda2e49

Last change on this file since 873:f3a30fda2e49 was 851:209c9d53e195, checked in by Alpar Juttner, 20 years ago

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