COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/max_flow.h @ 757:8680351d0c28

Last change on this file since 757:8680351d0c28 was 757:8680351d0c28, checked in by Alpar Juttner, 17 years ago

resetXxx() changed to setXxx().

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1// -*- C++ -*-
2#ifndef HUGO_MAX_FLOW_H
3#define HUGO_MAX_FLOW_H
4
5#include <vector>
6#include <queue>
7
8#include <hugo/graph_wrapper.h>
9#include <hugo/invalid.h>
10#include <hugo/maps.h>
11
12/// \file
13/// \ingroup galgs
14
15namespace hugo {
16
17  /// \addtogroup galgs
18  /// @{                                                                                                                                       
19  ///Maximum flow algorithms class.
20
21  ///This class provides various algorithms for finding a flow of
22  ///maximum value in a directed graph. The \e source node, the \e
23  ///target node, the \e capacity of the edges and the \e starting \e
24  ///flow value of the edges should be passed to the algorithm through the
25  ///constructor. It is possible to change these quantities using the
26  ///functions \ref setSource, \ref setTarget, \ref setCap and
27  ///\ref setFlow. Before any subsequent runs of any algorithm of
28  ///the class \ref setFlow should be called.
29
30  ///After running an algorithm of the class, the actual flow value
31  ///can be obtained by calling \ref flowValue(). The minimum
32  ///value cut can be written into a \c node map of \c bools by
33  ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes
34  ///the inclusionwise minimum and maximum of the minimum value
35  ///cuts, resp.)                                                                                                                               
36  ///\param Graph The directed graph type the algorithm runs on.
37  ///\param Num The number type of the capacities and the flow values.
38  ///\param CapMap The capacity map type.
39  ///\param FlowMap The flow map type.                                                                                                           
40  ///\author Marton Makai, Jacint Szabo
41  template <typename Graph, typename Num,
42            typename CapMap=typename Graph::template EdgeMap<Num>,
43            typename FlowMap=typename Graph::template EdgeMap<Num> >
44  class MaxFlow {
45  protected:
46    typedef typename Graph::Node Node;
47    typedef typename Graph::NodeIt NodeIt;
48    typedef typename Graph::EdgeIt EdgeIt;
49    typedef typename Graph::OutEdgeIt OutEdgeIt;
50    typedef typename Graph::InEdgeIt InEdgeIt;
51
52    typedef typename std::vector<Node> VecFirst;
53    typedef typename Graph::template NodeMap<Node> NNMap;
54    typedef typename std::vector<Node> VecNode;
55
56    const Graph* g;
57    Node s;
58    Node t;
59    const CapMap* capacity;
60    FlowMap* flow;
61    int n;      //the number of nodes of G
62    typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;   
63    //typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
64    typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
65    typedef typename ResGW::Edge ResGWEdge;
66    typedef typename Graph::template NodeMap<int> ReachedMap;
67
68
69    //level works as a bool map in augmenting path algorithms and is
70    //used by bfs for storing reached information.  In preflow, it
71    //shows the levels of nodes.     
72    ReachedMap level;
73
74    //excess is needed only in preflow
75    typename Graph::template NodeMap<Num> excess;
76
77    // constants used for heuristics
78    static const int H0=20;
79    static const int H1=1;
80
81  public:
82
83    ///Indicates the property of the starting flow.
84
85    ///Indicates the property of the starting flow. The meanings are as follows:
86    ///- \c ZERO_FLOW: constant zero flow
87    ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
88    ///the sum of the out-flows in every node except the \e source and
89    ///the \e target.
90    ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at
91    ///least the sum of the out-flows in every node except the \e source.
92    ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be
93    ///set to the constant zero flow in the beginning of the algorithm in this case.
94    enum FlowEnum{
95      ZERO_FLOW,
96      GEN_FLOW,
97      PRE_FLOW,
98      NO_FLOW
99    };
100
101    enum StatusEnum {
102      AFTER_NOTHING,
103      AFTER_AUGMENTING,
104      AFTER_FAST_AUGMENTING,
105      AFTER_PRE_FLOW_PHASE_1,     
106      AFTER_PRE_FLOW_PHASE_2
107    };
108
109    /// Do not needle this flag only if necessary.
110    StatusEnum status;
111
112//     int number_of_augmentations;
113
114
115//     template<typename IntMap>
116//     class TrickyReachedMap {
117//     protected:
118//       IntMap* map;
119//       int* number_of_augmentations;
120//     public:
121//       TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) :
122//      map(&_map), number_of_augmentations(&_number_of_augmentations) { }
123//       void set(const Node& n, bool b) {
124//      if (b)
125//        map->set(n, *number_of_augmentations);
126//      else
127//        map->set(n, *number_of_augmentations-1);
128//       }
129//       bool operator[](const Node& n) const {
130//      return (*map)[n]==*number_of_augmentations;
131//       }
132//     };
133   
134    ///Constructor
135
136    ///\todo Document, please.
137    ///
138    MaxFlow(const Graph& _G, Node _s, Node _t,
139            const CapMap& _capacity, FlowMap& _flow) :
140      g(&_G), s(_s), t(_t), capacity(&_capacity),
141      flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0),
142      status(AFTER_NOTHING) { }
143
144    ///Runs a maximum flow algorithm.
145
146    ///Runs a preflow algorithm, which is the fastest maximum flow
147    ///algorithm up-to-date. The default for \c fe is ZERO_FLOW.
148    ///\pre The starting flow must be
149    /// - a constant zero flow if \c fe is \c ZERO_FLOW,
150    /// - an arbitary flow if \c fe is \c GEN_FLOW,
151    /// - an arbitary preflow if \c fe is \c PRE_FLOW,
152    /// - any map if \c fe is NO_FLOW.
153    void run(FlowEnum fe=ZERO_FLOW) {
154      preflow(fe);
155    }
156
157                                                                             
158    ///Runs a preflow algorithm. 
159
160    ///Runs a preflow algorithm. The preflow algorithms provide the
161    ///fastest way to compute a maximum flow in a directed graph.
162    ///\pre The starting flow must be
163    /// - a constant zero flow if \c fe is \c ZERO_FLOW,
164    /// - an arbitary flow if \c fe is \c GEN_FLOW,
165    /// - an arbitary preflow if \c fe is \c PRE_FLOW,
166    /// - any map if \c fe is NO_FLOW.
167    ///
168    ///\todo NO_FLOW should be the default flow.
169    void preflow(FlowEnum fe) {
170      preflowPhase1(fe);
171      preflowPhase2();
172    }
173    // Heuristics:
174    //   2 phase
175    //   gap
176    //   list 'level_list' on the nodes on level i implemented by hand
177    //   stack 'active' on the active nodes on level i                                                                                   
178    //   runs heuristic 'highest label' for H1*n relabels
179    //   runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
180    //   Parameters H0 and H1 are initialized to 20 and 1.
181
182    ///Runs the first phase of the preflow algorithm.
183
184    ///The preflow algorithm consists of two phases, this method runs the
185    ///first phase. After the first phase the maximum flow value and a
186    ///minimum value cut can already be computed, though a maximum flow
187    ///is not yet obtained. So after calling this method \ref flowValue
188    ///and \ref actMinCut gives proper results.
189    ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not
190    ///give minimum value cuts unless calling \ref preflowPhase2.
191    ///\pre The starting flow must be
192    /// - a constant zero flow if \c fe is \c ZERO_FLOW,
193    /// - an arbitary flow if \c fe is \c GEN_FLOW,
194    /// - an arbitary preflow if \c fe is \c PRE_FLOW,
195    /// - any map if \c fe is NO_FLOW.
196    void preflowPhase1(FlowEnum fe)
197    {
198
199      int heur0=(int)(H0*n);  //time while running 'bound decrease'
200      int heur1=(int)(H1*n);  //time while running 'highest label'
201      int heur=heur1;         //starting time interval (#of relabels)
202      int numrelabel=0;
203
204      bool what_heur=1;
205      //It is 0 in case 'bound decrease' and 1 in case 'highest label'
206
207      bool end=false;
208      //Needed for 'bound decrease', true means no active nodes are above bound
209      //b.
210
211      int k=n-2;  //bound on the highest level under n containing a node
212      int b=k;    //bound on the highest level under n of an active node
213
214      VecFirst first(n, INVALID);
215      NNMap next(*g, INVALID); //maybe INVALID is not needed
216
217      NNMap left(*g, INVALID);
218      NNMap right(*g, INVALID);
219      VecNode level_list(n,INVALID);
220      //List of the nodes in level i<n, set to n.
221
222      preflowPreproc(fe, next, first, level_list, left, right);
223      //End of preprocessing
224
225      //Push/relabel on the highest level active nodes.
226      while ( true ) {
227        if ( b == 0 ) {
228          if ( !what_heur && !end && k > 0 ) {
229            b=k;
230            end=true;
231          } else break;
232        }
233
234        if ( !g->valid(first[b]) ) --b;
235        else {
236          end=false;
237          Node w=first[b];
238          first[b]=next[w];
239          int newlevel=push(w, next, first);
240          if ( excess[w] > 0 ) relabel(w, newlevel, next, first, level_list,
241                                       left, right, b, k, what_heur);
242
243          ++numrelabel;
244          if ( numrelabel >= heur ) {
245            numrelabel=0;
246            if ( what_heur ) {
247              what_heur=0;
248              heur=heur0;
249              end=false;
250            } else {
251              what_heur=1;
252              heur=heur1;
253              b=k;
254            }
255          }
256        }
257      }
258
259      status=AFTER_PRE_FLOW_PHASE_1;
260    }
261
262
263    ///Runs the second phase of the preflow algorithm.
264
265    ///The preflow algorithm consists of two phases, this method runs
266    ///the second phase. After calling \ref preflowPhase1 and then
267    ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut,
268    ///\ref minMinCut and \ref maxMinCut give proper results.
269    ///\pre \ref preflowPhase1 must be called before.
270    void preflowPhase2()
271    {
272
273      int k=n-2;  //bound on the highest level under n containing a node
274      int b=k;    //bound on the highest level under n of an active node
275
276   
277      VecFirst first(n, INVALID);
278      NNMap next(*g, INVALID); //maybe INVALID is not needed
279      level.set(s,0);
280      std::queue<Node> bfs_queue;
281      bfs_queue.push(s);
282
283      while (!bfs_queue.empty()) {
284
285        Node v=bfs_queue.front();
286        bfs_queue.pop();
287        int l=level[v]+1;
288
289        InEdgeIt e;
290        for(g->first(e,v); g->valid(e); g->next(e)) {
291          if ( (*capacity)[e] <= (*flow)[e] ) continue;
292          Node u=g->tail(e);
293          if ( level[u] >= n ) {
294            bfs_queue.push(u);
295            level.set(u, l);
296            if ( excess[u] > 0 ) {
297              next.set(u,first[l]);
298              first[l]=u;
299            }
300          }
301        }
302
303        OutEdgeIt f;
304        for(g->first(f,v); g->valid(f); g->next(f)) {
305          if ( 0 >= (*flow)[f] ) continue;
306          Node u=g->head(f);
307          if ( level[u] >= n ) {
308            bfs_queue.push(u);
309            level.set(u, l);
310            if ( excess[u] > 0 ) {
311              next.set(u,first[l]);
312              first[l]=u;
313            }
314          }
315        }
316      }
317      b=n-2;
318
319      while ( true ) {
320
321        if ( b == 0 ) break;
322
323        if ( !g->valid(first[b]) ) --b;
324        else {
325
326          Node w=first[b];
327          first[b]=next[w];
328          int newlevel=push(w,next, first/*active*/);
329
330          //relabel
331          if ( excess[w] > 0 ) {
332            level.set(w,++newlevel);
333            next.set(w,first[newlevel]);
334            first[newlevel]=w;
335            b=newlevel;
336          }
337        }
338      } // while(true)
339
340      status=AFTER_PRE_FLOW_PHASE_2;
341    }
342
343
344    /// Returns the maximum value of a flow.
345
346    /// Returns the maximum value of a flow, by counting the
347    /// over-flow of the target node \ref t.
348    /// It can be called already after running \ref preflowPhase1.
349    Num flowValue() const {
350      Num a=0;
351      for(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e];
352      for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) a-=(*flow)[e];
353      return a;
354      //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan   
355    }
356
357
358    ///Returns a minimum value cut after calling \ref preflowPhase1.
359
360    ///After the first phase of the preflow algorithm the maximum flow
361    ///value and a minimum value cut can already be computed. This
362    ///method can be called after running \ref preflowPhase1 for
363    ///obtaining a minimum value cut.
364    /// \warning Gives proper result only right after calling \ref
365    /// preflowPhase1.
366    /// \todo We have to make some status variable which shows the
367    /// actual state
368    /// of the class. This enables us to determine which methods are valid
369    /// for MinCut computation
370    template<typename _CutMap>
371    void actMinCut(_CutMap& M) const {
372      NodeIt v;
373      switch (status) {
374      case AFTER_PRE_FLOW_PHASE_1:
375        for(g->first(v); g->valid(v); g->next(v)) {
376          if (level[v] < n) {
377            M.set(v, false);
378          } else {
379            M.set(v, true);
380          }
381        }
382        break;
383      case AFTER_PRE_FLOW_PHASE_2:
384      case AFTER_NOTHING:
385      case AFTER_AUGMENTING:
386      case AFTER_FAST_AUGMENTING:
387        minMinCut(M);
388        break;
389      }
390    }
391
392    ///Returns the inclusionwise minimum of the minimum value cuts.
393
394    ///Sets \c M to the characteristic vector of the minimum value cut
395    ///which is inclusionwise minimum. It is computed by processing
396    ///a bfs from the source node \c s in the residual graph.
397    ///\pre M should be a node map of bools initialized to false.
398    ///\pre \c flow must be a maximum flow.
399    template<typename _CutMap>
400    void minMinCut(_CutMap& M) const {
401      std::queue<Node> queue;
402
403      M.set(s,true);
404      queue.push(s);
405
406      while (!queue.empty()) {
407        Node w=queue.front();
408        queue.pop();
409
410        OutEdgeIt e;
411        for(g->first(e,w) ; g->valid(e); g->next(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        InEdgeIt f;
420        for(g->first(f,w) ; g->valid(f); g->next(f)) {
421          Node v=g->tail(f);
422          if (!M[v] && (*flow)[f] > 0 ) {
423            queue.push(v);
424            M.set(v, true);
425          }
426        }
427      }
428    }
429
430    ///Returns the inclusionwise maximum of the minimum value cuts.
431
432    ///Sets \c M to the characteristic vector of the minimum value cut
433    ///which is inclusionwise maximum. It is computed by processing a
434    ///backward bfs from the target node \c t in the residual graph.
435    ///\pre M should be a node map of bools initialized to false.
436    ///\pre \c flow must be a maximum flow.
437    template<typename _CutMap>
438    void maxMinCut(_CutMap& M) const {
439
440      NodeIt v;
441      for(g->first(v) ; g->valid(v); g->next(v)) {
442        M.set(v, true);
443      }
444
445      std::queue<Node> queue;
446
447      M.set(t,false);
448      queue.push(t);
449
450      while (!queue.empty()) {
451        Node w=queue.front();
452        queue.pop();
453
454        InEdgeIt e;
455        for(g->first(e,w) ; g->valid(e); g->next(e)) {
456          Node v=g->tail(e);
457          if (M[v] && (*flow)[e] < (*capacity)[e] ) {
458            queue.push(v);
459            M.set(v, false);
460          }
461        }
462
463        OutEdgeIt f;
464        for(g->first(f,w) ; g->valid(f); g->next(f)) {
465          Node v=g->head(f);
466          if (M[v] && (*flow)[f] > 0 ) {
467            queue.push(v);
468            M.set(v, false);
469          }
470        }
471      }
472    }
473
474    ///Returns a minimum value cut.
475
476    ///Sets \c M to the characteristic vector of a minimum value cut.
477    ///\pre M should be a node map of bools initialized to false.
478    ///\pre \c flow must be a maximum flow.   
479    template<typename CutMap>
480    void minCut(CutMap& M) const { minMinCut(M); }
481
482    ///Sets the source node to \c _s.
483
484    ///Sets the source node to \c _s.
485    ///
486    void setSource(Node _s) { s=_s; status=AFTER_NOTHING; }
487
488    ///Sets the target node to \c _t.
489
490    ///Sets the target node to \c _t.
491    ///
492    void setTarget(Node _t) { t=_t; status=AFTER_NOTHING; }
493
494    /// Sets the edge map of the capacities to _cap.
495
496    /// Sets the edge map of the capacities to _cap.
497    ///
498    void setCap(const CapMap& _cap)
499    { capacity=&_cap; status=AFTER_NOTHING; }
500
501    /// Sets the edge map of the flows to _flow.
502
503    /// Sets the edge map of the flows to _flow.
504    ///
505    void setFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; }
506
507
508  private:
509
510    int push(Node w, NNMap& next, VecFirst& first) {
511
512      int lev=level[w];
513      Num exc=excess[w];
514      int newlevel=n;       //bound on the next level of w
515
516      OutEdgeIt e;
517      for(g->first(e,w); g->valid(e); g->next(e)) {
518
519        if ( (*flow)[e] >= (*capacity)[e] ) continue;
520        Node v=g->head(e);
521
522        if( lev > level[v] ) { //Push is allowed now
523
524          if ( excess[v]<=0 && v!=t && v!=s ) {
525            next.set(v,first[level[v]]);
526            first[level[v]]=v;
527          }
528
529          Num cap=(*capacity)[e];
530          Num flo=(*flow)[e];
531          Num remcap=cap-flo;
532
533          if ( remcap >= exc ) { //A nonsaturating push.
534
535            flow->set(e, flo+exc);
536            excess.set(v, excess[v]+exc);
537            exc=0;
538            break;
539
540          } else { //A saturating push.
541            flow->set(e, cap);
542            excess.set(v, excess[v]+remcap);
543            exc-=remcap;
544          }
545        } else if ( newlevel > level[v] ) newlevel = level[v];
546      } //for out edges wv
547
548      if ( exc > 0 ) {
549        InEdgeIt e;
550        for(g->first(e,w); g->valid(e); g->next(e)) {
551
552          if( (*flow)[e] <= 0 ) continue;
553          Node v=g->tail(e);
554
555          if( lev > level[v] ) { //Push is allowed now
556
557            if ( excess[v]<=0 && v!=t && v!=s ) {
558              next.set(v,first[level[v]]);
559              first[level[v]]=v;
560            }
561
562            Num flo=(*flow)[e];
563
564            if ( flo >= exc ) { //A nonsaturating push.
565
566              flow->set(e, flo-exc);
567              excess.set(v, excess[v]+exc);
568              exc=0;
569              break;
570            } else {  //A saturating push.
571
572              excess.set(v, excess[v]+flo);
573              exc-=flo;
574              flow->set(e,0);
575            }
576          } else if ( newlevel > level[v] ) newlevel = level[v];
577        } //for in edges vw
578
579      } // if w still has excess after the out edge for cycle
580
581      excess.set(w, exc);
582
583      return newlevel;
584    }
585
586
587
588    void preflowPreproc(FlowEnum fe, NNMap& next, VecFirst& first,
589                        VecNode& level_list, NNMap& left, NNMap& right)
590    {
591      switch (fe) { //setting excess
592        case NO_FLOW:
593        {
594          EdgeIt e;
595          for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0);
596         
597          NodeIt v;
598          for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
599          break;
600        }
601        case ZERO_FLOW:
602        {
603          NodeIt v;
604          for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
605          break;
606        }
607        case GEN_FLOW:
608        {
609          NodeIt v;
610          for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
611
612          Num exc=0;
613          InEdgeIt e;
614          for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e];
615          OutEdgeIt f;
616          for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f];
617          excess.set(t,exc);
618          break;
619        }
620        default: break;
621      }
622
623      NodeIt v;
624      for(g->first(v); g->valid(v); g->next(v)) level.set(v,n);
625      //setting each node to level n
626     
627      std::queue<Node> bfs_queue;
628
629
630      switch (fe) {
631      case NO_FLOW:   //flow is already set to const zero
632      case ZERO_FLOW:
633        {
634          //Reverse_bfs from t, to find the starting level.
635          level.set(t,0);
636          bfs_queue.push(t);
637
638          while (!bfs_queue.empty()) {
639
640            Node v=bfs_queue.front();
641            bfs_queue.pop();
642            int l=level[v]+1;
643
644            InEdgeIt e;
645            for(g->first(e,v); g->valid(e); g->next(e)) {
646              Node w=g->tail(e);
647              if ( level[w] == n && w != s ) {
648                bfs_queue.push(w);
649                Node z=level_list[l];
650                if ( g->valid(z) ) left.set(z,w);
651                right.set(w,z);
652                level_list[l]=w;
653                level.set(w, l);
654              }
655            }
656          }
657
658          //the starting flow
659          OutEdgeIt e;
660          for(g->first(e,s); g->valid(e); g->next(e))
661            {
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                  {
668                    next.set(w,first[level[w]]);
669                    first[level[w]]=w;
670                  }
671                flow->set(e, c);
672                excess.set(w, excess[w]+c);
673              }
674            }
675          break;
676        }
677
678      case GEN_FLOW:
679        {
680          //Reverse_bfs from t in the residual graph,
681          //to find the starting level.
682          level.set(t,0);
683          bfs_queue.push(t);
684
685          while (!bfs_queue.empty()) {
686
687            Node v=bfs_queue.front();
688            bfs_queue.pop();
689            int l=level[v]+1;
690
691            InEdgeIt e;
692            for(g->first(e,v); g->valid(e); g->next(e)) {
693              if ( (*capacity)[e] <= (*flow)[e] ) continue;
694              Node w=g->tail(e);
695              if ( level[w] == n && w != s ) {
696                bfs_queue.push(w);
697                Node z=level_list[l];
698                if ( g->valid(z) ) left.set(z,w);
699                right.set(w,z);
700                level_list[l]=w;
701                level.set(w, l);
702              }
703            }
704
705            OutEdgeIt f;
706            for(g->first(f,v); g->valid(f); g->next(f)) {
707              if ( 0 >= (*flow)[f] ) continue;
708              Node w=g->head(f);
709              if ( level[w] == n && w != s ) {
710                bfs_queue.push(w);
711                Node z=level_list[l];
712                if ( g->valid(z) ) left.set(z,w);
713                right.set(w,z);
714                level_list[l]=w;
715                level.set(w, l);
716              }
717            }
718          }
719
720          //the starting flow
721          OutEdgeIt e;
722          for(g->first(e,s); g->valid(e); g->next(e))
723            {
724              Num rem=(*capacity)[e]-(*flow)[e];
725              if ( rem <= 0 ) continue;
726              Node w=g->head(e);
727              if ( level[w] < n ) {
728                if ( excess[w] <= 0 && w!=t ) //putting into the stack
729                  {
730                    next.set(w,first[level[w]]);
731                    first[level[w]]=w;
732                  }   
733                flow->set(e, (*capacity)[e]);
734                excess.set(w, excess[w]+rem);
735              }
736            }
737
738          InEdgeIt f;
739          for(g->first(f,s); g->valid(f); g->next(f))
740            {
741              if ( (*flow)[f] <= 0 ) continue;
742              Node w=g->tail(f);
743              if ( level[w] < n ) {
744                if ( excess[w] <= 0 && w!=t )
745                  {
746                    next.set(w,first[level[w]]);
747                    first[level[w]]=w;
748                  } 
749                excess.set(w, excess[w]+(*flow)[f]);
750                flow->set(f, 0);
751              }
752            }
753          break;
754        } //case GEN_FLOW
755   
756      case PRE_FLOW:
757        {
758          //Reverse_bfs from t in the residual graph,
759          //to find the starting level.
760          level.set(t,0);
761          bfs_queue.push(t);
762
763          while (!bfs_queue.empty()) {
764
765            Node v=bfs_queue.front();
766            bfs_queue.pop();
767            int l=level[v]+1;
768
769            InEdgeIt e;
770            for(g->first(e,v); g->valid(e); g->next(e)) {
771              if ( (*capacity)[e] <= (*flow)[e] ) continue;
772              Node w=g->tail(e);
773              if ( level[w] == n && w != s ) {
774                bfs_queue.push(w);
775                Node z=level_list[l];
776                if ( g->valid(z) ) left.set(z,w);
777                right.set(w,z);
778                level_list[l]=w;
779                level.set(w, l);
780              }
781            }
782
783            OutEdgeIt f;
784            for(g->first(f,v); g->valid(f); g->next(f)) {
785              if ( 0 >= (*flow)[f] ) continue;
786              Node w=g->head(f);
787              if ( level[w] == n && w != s ) {
788                bfs_queue.push(w);
789                Node z=level_list[l];
790                if ( g->valid(z) ) left.set(z,w);
791                right.set(w,z);
792                level_list[l]=w;
793                level.set(w, l);
794              }
795            }
796          }
797
798
799          //the starting flow
800          OutEdgeIt e;
801          for(g->first(e,s); g->valid(e); g->next(e))
802            {
803              Num rem=(*capacity)[e]-(*flow)[e];
804              if ( rem <= 0 ) continue;
805              Node w=g->head(e);
806              if ( level[w] < n ) {
807                flow->set(e, (*capacity)[e]);
808                excess.set(w, excess[w]+rem);
809              }
810            }
811
812          InEdgeIt f;
813          for(g->first(f,s); g->valid(f); g->next(f))
814            {
815              if ( (*flow)[f] <= 0 ) continue;
816              Node w=g->tail(f);
817              if ( level[w] < n ) {
818                excess.set(w, excess[w]+(*flow)[f]);
819                flow->set(f, 0);
820              }
821            }
822         
823          NodeIt w; //computing the excess
824          for(g->first(w); g->valid(w); g->next(w)) {
825            Num exc=0;
826
827            InEdgeIt e;
828            for(g->first(e,w); g->valid(e); g->next(e)) exc+=(*flow)[e];
829            OutEdgeIt f;
830            for(g->first(f,w); g->valid(f); g->next(f)) exc-=(*flow)[f];
831
832            excess.set(w,exc);
833
834            //putting the active nodes into the stack
835            int lev=level[w];
836            if ( exc > 0 && lev < n && w != t )
837              {
838                next.set(w,first[lev]);
839                first[lev]=w;
840              }
841          }
842          break;
843        } //case PRE_FLOW
844      }
845    } //preflowPreproc
846
847
848    void relabel(Node w, int newlevel, NNMap& next, VecFirst& first,
849                 VecNode& level_list, NNMap& left,
850                 NNMap& right, int& b, int& k, bool what_heur )
851    {
852
853      Num lev=level[w];
854
855      Node right_n=right[w];
856      Node left_n=left[w];
857
858      //unlacing starts
859      if ( g->valid(right_n) ) {
860        if ( g->valid(left_n) ) {
861          right.set(left_n, right_n);
862          left.set(right_n, left_n);
863        } else {
864          level_list[lev]=right_n;
865          left.set(right_n, INVALID);
866        }
867      } else {
868        if ( g->valid(left_n) ) {
869          right.set(left_n, INVALID);
870        } else {
871          level_list[lev]=INVALID;
872        }
873      }
874      //unlacing ends
875
876      if ( !g->valid(level_list[lev]) ) {
877
878        //gapping starts
879        for (int i=lev; i!=k ; ) {
880          Node v=level_list[++i];
881          while ( g->valid(v) ) {
882            level.set(v,n);
883            v=right[v];
884          }
885          level_list[i]=INVALID;
886          if ( !what_heur ) first[i]=INVALID;
887        }
888
889        level.set(w,n);
890        b=lev-1;
891        k=b;
892        //gapping ends
893
894      } else {
895
896        if ( newlevel == n ) level.set(w,n);
897        else {
898          level.set(w,++newlevel);
899          next.set(w,first[newlevel]);
900          first[newlevel]=w;
901          if ( what_heur ) b=newlevel;
902          if ( k < newlevel ) ++k;      //now k=newlevel
903          Node z=level_list[newlevel];
904          if ( g->valid(z) ) left.set(z,w);
905          right.set(w,z);
906          left.set(w,INVALID);
907          level_list[newlevel]=w;
908        }
909      }
910    } //relabel
911
912    void printexcess() {////
913      std::cout << "Excesses:" <<std::endl;
914
915      NodeIt v;
916      for(g->first(v); g->valid(v); g->next(v)) {
917        std::cout << 1+(g->id(v)) << ":" << excess[v]<<std::endl;
918      }
919    }
920
921 void printlevel() {////
922      std::cout << "Levels:" <<std::endl;
923
924      NodeIt v;
925      for(g->first(v); g->valid(v); g->next(v)) {
926        std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl;
927      }
928    }
929
930void printactive() {////
931      std::cout << "Levels:" <<std::endl;
932
933      NodeIt v;
934      for(g->first(v); g->valid(v); g->next(v)) {
935        std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl;
936      }
937    }
938
939
940  };  //class MaxFlow
941} //namespace hugo
942
943#endif //HUGO_MAX_FLOW_H
944
945
946
947
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