COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/preflow.h @ 836:f8549e3f6c5a

Last change on this file since 836:f8549e3f6c5a was 836:f8549e3f6c5a, checked in by jacint, 16 years ago

preflow last changes

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