COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/preflow.h @ 1882:2c3f6c7e01b4

Last change on this file since 1882:2c3f6c7e01b4 was 1875:98698b69a902, checked in by Alpar Juttner, 14 years ago

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1/* -*- C++ -*-
2 * lemon/preflow.h - Part of LEMON, a generic C++ optimization library
3 *
4 * Copyright (C) 2006 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Research Group on Combinatorial Optimization, 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/error.h>
24#include <lemon/invalid.h>
25#include <lemon/tolerance.h>
26#include <lemon/maps.h>
27#include <lemon/graph_utils.h>
28
29/// \file
30/// \ingroup flowalgs
31/// \brief Implementation of the preflow algorithm.
32
33namespace lemon {
34
35  ///\ingroup flowalgs
36  ///\brief %Preflow algorithms class.
37  ///
38  ///This class provides an implementation of the \e preflow \e
39  ///algorithm producing a flow of maximum value in a directed
40  ///graph. The preflow algorithms are the fastest known max flow algorithms
41  ///up to now. The \e source node, the \e target node, the \e
42  ///capacity of the edges and the \e starting \e flow value of the
43  ///edges should be passed to the algorithm through the
44  ///constructor. It is possible to change these quantities using the
45  ///functions \ref source, \ref target, \ref capacityMap and \ref
46  ///flowMap.
47  ///
48  ///After running \ref lemon::Preflow::phase1() "phase1()"
49  ///or \ref lemon::Preflow::run() "run()", the maximal flow
50  ///value can be obtained by calling \ref flowValue(). The minimum
51  ///value cut can be written into a <tt>bool</tt> node map by
52  ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes
53  ///the inclusionwise minimum and maximum of the minimum value cuts,
54  ///resp.)
55  ///
56  ///\param Graph The directed graph type the algorithm runs on.
57  ///\param Num The number type of the capacities and the flow values.
58  ///\param CapacityMap The capacity map type.
59  ///\param FlowMap The flow map type.
60  ///
61  ///\author Jacint Szabo
62  ///\todo Second template parameter is superfluous
63  template <typename Graph, typename Num,
64            typename CapacityMap=typename Graph::template EdgeMap<Num>,
65            typename FlowMap=typename Graph::template EdgeMap<Num>,
66            typename TOL=Tolerance<Num> >
67  class Preflow {
68  protected:
69    typedef typename Graph::Node Node;
70    typedef typename Graph::NodeIt NodeIt;
71    typedef typename Graph::EdgeIt EdgeIt;
72    typedef typename Graph::OutEdgeIt OutEdgeIt;
73    typedef typename Graph::InEdgeIt InEdgeIt;
74
75    typedef typename Graph::template NodeMap<Node> NNMap;
76    typedef typename std::vector<Node> VecNode;
77
78    const Graph* _g;
79    Node _source;
80    Node _target;
81    const CapacityMap* _capacity;
82    FlowMap* _flow;
83
84    TOL surely;
85   
86    int _node_num;      //the number of nodes of G
87   
88    typename Graph::template NodeMap<int> level; 
89    typename Graph::template NodeMap<Num> excess;
90
91    // constants used for heuristics
92    static const int H0=20;
93    static const int H1=1;
94
95  public:
96
97    ///\ref Exception for the case when s=t.
98
99    ///\ref Exception for the case when the source equals the target.
100    class InvalidArgument : public lemon::LogicError {
101    public:
102      virtual const char* exceptionName() const {
103        return "lemon::Preflow::InvalidArgument";
104      }
105    };
106   
107   
108    ///Indicates the property of the starting flow map.
109   
110    ///Indicates the property of the starting flow map.
111    ///The meanings are as follows:
112    ///- \c ZERO_FLOW: constant zero flow
113    ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
114    ///the sum of the out-flows in every node except the \e source and
115    ///the \e target.
116    ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at
117    ///least the sum of the out-flows in every node except the \e source.
118    ///- \c NO_FLOW: indicates an unspecified edge map. \c flow will be
119    ///set to the constant zero flow in the beginning of
120    ///the algorithm in this case.
121    ///
122    enum FlowEnum{
123      NO_FLOW,
124      ZERO_FLOW,
125      GEN_FLOW,
126      PRE_FLOW
127    };
128
129    ///Indicates the state of the preflow algorithm.
130
131    ///Indicates the state of the preflow algorithm.
132    ///The meanings are as follows:
133    ///- \c AFTER_NOTHING: before running the algorithm or
134    ///  at an unspecified state.
135    ///- \c AFTER_PREFLOW_PHASE_1: right after running \c phase1
136    ///- \c AFTER_PREFLOW_PHASE_2: after running \ref phase2()
137    ///
138    enum StatusEnum {
139      AFTER_NOTHING,
140      AFTER_PREFLOW_PHASE_1,     
141      AFTER_PREFLOW_PHASE_2
142    };
143   
144  protected:
145    FlowEnum flow_prop;
146    StatusEnum status; // Do not needle this flag only if necessary.
147   
148  public:
149    ///The constructor of the class.
150
151    ///The constructor of the class.
152    ///\param _gr The directed graph the algorithm runs on.
153    ///\param _s The source node.
154    ///\param _t The target node.
155    ///\param _cap The capacity of the edges.
156    ///\param _f The flow of the edges.
157    ///Except the graph, all of these parameters can be reset by
158    ///calling \ref source, \ref target, \ref capacityMap and \ref
159    ///flowMap, resp.
160      Preflow(const Graph& _gr, Node _s, Node _t,
161              const CapacityMap& _cap, FlowMap& _f,
162              const TOL &tol=TOL()) :
163        _g(&_gr), _source(_s), _target(_t), _capacity(&_cap),
164        _flow(&_f), surely(tol),
165        _node_num(countNodes(_gr)), level(_gr), excess(_gr,0),
166        flow_prop(NO_FLOW), status(AFTER_NOTHING) {
167        if ( _source==_target )
168          throw InvalidArgument();
169      }
170   
171
172                                                                             
173    ///Runs the preflow algorithm. 
174
175    ///Runs the preflow algorithm.
176    ///
177    void run() {
178      phase1(flow_prop);
179      phase2();
180    }
181   
182    ///Runs the preflow algorithm. 
183   
184    ///Runs the preflow algorithm.
185    ///\pre The starting flow map must be
186    /// - a constant zero flow if \c fp is \c ZERO_FLOW,
187    /// - an arbitrary flow if \c fp is \c GEN_FLOW,
188    /// - an arbitrary preflow if \c fp is \c PRE_FLOW,
189    /// - any map if \c fp is NO_FLOW.
190    ///If the starting flow map is a flow or a preflow then
191    ///the algorithm terminates faster.
192    void run(FlowEnum fp) {
193      flow_prop=fp;
194      run();
195    }
196     
197    ///Runs the first phase of the preflow algorithm.
198
199    ///The preflow algorithm consists of two phases, this method runs
200    ///the first phase. After the first phase the maximum flow value
201    ///and a minimum value cut can already be computed, although a
202    ///maximum flow is not yet obtained. So after calling this method
203    ///\ref flowValue returns the value of a maximum flow and \ref
204    ///minCut returns a minimum cut.     
205    ///\warning \ref minMinCut and \ref maxMinCut do not give minimum
206    ///value cuts unless calling \ref phase2. 
207    ///\pre The starting flow must be
208    ///- a constant zero flow if \c fp is \c ZERO_FLOW,
209    ///- an arbitary flow if \c fp is \c GEN_FLOW,
210    ///- an arbitary preflow if \c fp is \c PRE_FLOW,
211    ///- any map if \c fp is NO_FLOW.
212    void phase1(FlowEnum fp)
213    {
214      flow_prop=fp;
215      phase1();
216    }
217
218   
219    ///Runs the first phase of the preflow algorithm.
220
221    ///The preflow algorithm consists of two phases, this method runs
222    ///the first phase. After the first phase the maximum flow value
223    ///and a minimum value cut can already be computed, although a
224    ///maximum flow is not yet obtained. So after calling this method
225    ///\ref flowValue returns the value of a maximum flow and \ref
226    ///minCut returns a minimum cut.
227    ///\warning \ref minMinCut() and \ref maxMinCut() do not
228    ///give minimum value cuts unless calling \ref phase2().
229    void phase1()
230    {
231      int heur0=(int)(H0*_node_num);  //time while running 'bound decrease'
232      int heur1=(int)(H1*_node_num);  //time while running 'highest label'
233      int heur=heur1;         //starting time interval (#of relabels)
234      int numrelabel=0;
235
236      bool what_heur=1;
237      //It is 0 in case 'bound decrease' and 1 in case 'highest label'
238
239      bool end=false;
240      //Needed for 'bound decrease', true means no active
241      //nodes are above bound b.
242
243      int k=_node_num-2;  //bound on the highest level under n containing a node
244      int b=k;    //bound on the highest level under n of an active node
245
246      VecNode first(_node_num, INVALID);
247      NNMap next(*_g, INVALID);
248
249      NNMap left(*_g, INVALID);
250      NNMap right(*_g, INVALID);
251      VecNode level_list(_node_num,INVALID);
252      //List of the nodes in level i<n, set to n.
253
254      preflowPreproc(first, next, level_list, left, right);
255
256      //Push/relabel on the highest level active nodes.
257      while ( true ) {
258        if ( b == 0 ) {
259          if ( !what_heur && !end && k > 0 ) {
260            b=k;
261            end=true;
262          } else break;
263        }
264
265        if ( first[b]==INVALID ) --b;
266        else {
267          end=false;
268          Node w=first[b];
269          first[b]=next[w];
270          int newlevel=push(w, next, first);
271          if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list,
272                                       left, right, b, k, what_heur);
273
274          ++numrelabel;
275          if ( numrelabel >= heur ) {
276            numrelabel=0;
277            if ( what_heur ) {
278              what_heur=0;
279              heur=heur0;
280              end=false;
281            } else {
282              what_heur=1;
283              heur=heur1;
284              b=k;
285            }
286          }
287        }
288      }
289      flow_prop=PRE_FLOW;
290      status=AFTER_PREFLOW_PHASE_1;
291    }
292    // Heuristics:
293    //   2 phase
294    //   gap
295    //   list 'level_list' on the nodes on level i implemented by hand
296    //   stack 'active' on the active nodes on level i     
297    //   runs heuristic 'highest label' for H1*n relabels
298    //   runs heuristic 'bound decrease' for H0*n relabels,
299    //        starts with 'highest label'
300    //   Parameters H0 and H1 are initialized to 20 and 1.
301
302
303    ///Runs the second phase of the preflow algorithm.
304
305    ///The preflow algorithm consists of two phases, this method runs
306    ///the second phase. After calling \ref phase1() and then
307    ///\ref phase2(),
308    /// \ref flowMap() return a maximum flow, \ref flowValue
309    ///returns the value of a maximum flow, \ref minCut returns a
310    ///minimum cut, while the methods \ref minMinCut and \ref
311    ///maxMinCut return the inclusionwise minimum and maximum cuts of
312    ///minimum value, resp.  \pre \ref phase1 must be called before.
313    void phase2()
314    {
315
316      int k=_node_num-2;  //bound on the highest level under n containing a node
317      int b=k;    //bound on the highest level under n of an active node
318
319   
320      VecNode first(_node_num, INVALID);
321      NNMap next(*_g, INVALID);
322      level.set(_source,0);
323      std::queue<Node> bfs_queue;
324      bfs_queue.push(_source);
325
326      while ( !bfs_queue.empty() ) {
327
328        Node v=bfs_queue.front();
329        bfs_queue.pop();
330        int l=level[v]+1;
331
332        for(InEdgeIt e(*_g,v); e!=INVALID; ++e) {
333          if ( (*_capacity)[e] <= (*_flow)[e] ) continue;
334          Node u=_g->source(e);
335          if ( level[u] >= _node_num ) {
336            bfs_queue.push(u);
337            level.set(u, l);
338            if ( excess[u] > 0 ) {
339              next.set(u,first[l]);
340              first[l]=u;
341            }
342          }
343        }
344
345        for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) {
346          if ( 0 >= (*_flow)[e] ) continue;
347          Node u=_g->target(e);
348          if ( level[u] >= _node_num ) {
349            bfs_queue.push(u);
350            level.set(u, l);
351            if ( excess[u] > 0 ) {
352              next.set(u,first[l]);
353              first[l]=u;
354            }
355          }
356        }
357      }
358      b=_node_num-2;
359
360      while ( true ) {
361
362        if ( b == 0 ) break;
363        if ( first[b]==INVALID ) --b;
364        else {
365          Node w=first[b];
366          first[b]=next[w];
367          int newlevel=push(w,next, first);
368         
369          //relabel
370          if ( excess[w] > 0 ) {
371            level.set(w,++newlevel);
372            next.set(w,first[newlevel]);
373            first[newlevel]=w;
374            b=newlevel;
375          }
376        }
377      } // while(true)
378      flow_prop=GEN_FLOW;
379      status=AFTER_PREFLOW_PHASE_2;
380    }
381
382    /// Returns the value of the maximum flow.
383
384    /// Returns the value of the maximum flow by returning the excess
385    /// of the target node \c t. This value equals to the value of
386    /// the maximum flow already after running \ref phase1.
387    Num flowValue() const {
388      return excess[_target];
389    }
390
391
392    ///Returns a minimum value cut.
393
394    ///Sets \c M to the characteristic vector of a minimum value
395    ///cut. This method can be called both after running \ref
396    ///phase1 and \ref phase2. It is much faster after
397    ///\ref phase1.  \pre M should be a bool-valued node-map. \pre
398    ///If \ref minCut() is called after \ref phase2() then M should
399    ///be initialized to false.
400    template<typename _CutMap>
401    void minCut(_CutMap& M) const {
402      switch ( status ) {
403        case AFTER_PREFLOW_PHASE_1:
404        for(NodeIt v(*_g); v!=INVALID; ++v) {
405          if (level[v] < _node_num) {
406            M.set(v, false);
407          } else {
408            M.set(v, true);
409          }
410        }
411        break;
412        case AFTER_PREFLOW_PHASE_2:
413        minMinCut(M);
414        break;
415        case AFTER_NOTHING:
416        break;
417      }
418    }
419
420    ///Returns the inclusionwise minimum of the minimum value cuts.
421
422    ///Sets \c M to the characteristic vector of the minimum value cut
423    ///which is inclusionwise minimum. It is computed by processing a
424    ///bfs from the source node \c s in the residual graph.  \pre M
425    ///should be a node map of bools initialized to false.  \pre \ref
426    ///phase2 should already be run.
427    template<typename _CutMap>
428    void minMinCut(_CutMap& M) const {
429
430      std::queue<Node> queue;
431      M.set(_source,true);
432      queue.push(_source);
433     
434      while (!queue.empty()) {
435        Node w=queue.front();
436        queue.pop();
437       
438        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
439          Node v=_g->target(e);
440          if (!M[v] && (*_flow)[e] < (*_capacity)[e] ) {
441            queue.push(v);
442            M.set(v, true);
443          }
444        }
445       
446        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
447          Node v=_g->source(e);
448          if (!M[v] && (*_flow)[e] > 0 ) {
449            queue.push(v);
450            M.set(v, true);
451          }
452        }
453      }
454    }
455   
456    ///Returns the inclusionwise maximum of the minimum value cuts.
457
458    ///Sets \c M to the characteristic vector of the minimum value cut
459    ///which is inclusionwise maximum. It is computed by processing a
460    ///backward bfs from the target node \c t in the residual graph.
461    ///\pre \ref phase2() or run() should already be run.
462    template<typename _CutMap>
463    void maxMinCut(_CutMap& M) const {
464
465      for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true);
466
467      std::queue<Node> queue;
468
469      M.set(_target,false);
470      queue.push(_target);
471
472      while (!queue.empty()) {
473        Node w=queue.front();
474        queue.pop();
475
476        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
477          Node v=_g->source(e);
478          if (M[v] && (*_flow)[e] < (*_capacity)[e] ) {
479            queue.push(v);
480            M.set(v, false);
481          }
482        }
483
484        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
485          Node v=_g->target(e);
486          if (M[v] && (*_flow)[e] > 0 ) {
487            queue.push(v);
488            M.set(v, false);
489          }
490        }
491      }
492    }
493
494    ///Sets the source node to \c _s.
495
496    ///Sets the source node to \c _s.
497    ///
498    void source(Node _s) {
499      _source=_s;
500      if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
501      status=AFTER_NOTHING;
502    }
503
504    ///Returns the source node.
505
506    ///Returns the source node.
507    ///
508    Node source() const {
509      return _source;
510    }
511
512    ///Sets the target node to \c _t.
513
514    ///Sets the target node to \c _t.
515    ///
516    void target(Node _t) {
517      _target=_t;
518      if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
519      status=AFTER_NOTHING;
520    }
521
522    ///Returns the target node.
523
524    ///Returns the target node.
525    ///
526    Node target() const {
527      return _target;
528    }
529
530    /// Sets the edge map of the capacities to _cap.
531
532    /// Sets the edge map of the capacities to _cap.
533    ///
534    void capacityMap(const CapacityMap& _cap) {
535      _capacity=&_cap;
536      status=AFTER_NOTHING;
537    }
538    /// Returns a reference to capacity map.
539
540    /// Returns a reference to capacity map.
541    ///
542    const CapacityMap &capacityMap() const {
543      return *_capacity;
544    }
545
546    /// Sets the edge map of the flows to _flow.
547
548    /// Sets the edge map of the flows to _flow.
549    ///
550    void flowMap(FlowMap& _f) {
551      _flow=&_f;
552      flow_prop=NO_FLOW;
553      status=AFTER_NOTHING;
554    }
555     
556    /// Returns a reference to flow map.
557
558    /// Returns a reference to flow map.
559    ///
560    const FlowMap &flowMap() const {
561      return *_flow;
562    }
563
564  private:
565
566    int push(Node w, NNMap& next, VecNode& first) {
567
568      int lev=level[w];
569      Num exc=excess[w];
570      int newlevel=_node_num;       //bound on the next level of w
571
572      for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
573        if ( (*_flow)[e] >= (*_capacity)[e] ) continue;
574        Node v=_g->target(e);
575
576        if( lev > level[v] ) { //Push is allowed now
577         
578          if ( excess[v]<=0 && v!=_target && v!=_source ) {
579            next.set(v,first[level[v]]);
580            first[level[v]]=v;
581          }
582
583          Num cap=(*_capacity)[e];
584          Num flo=(*_flow)[e];
585          Num remcap=cap-flo;
586         
587          if ( remcap >= exc ) { //A nonsaturating push.
588           
589            _flow->set(e, flo+exc);
590            excess.set(v, excess[v]+exc);
591            exc=0;
592            break;
593
594          } else { //A saturating push.
595            _flow->set(e, cap);
596            excess.set(v, excess[v]+remcap);
597            exc-=remcap;
598          }
599        } else if ( newlevel > level[v] ) newlevel = level[v];
600      } //for out edges wv
601
602      if ( exc > 0 ) {
603        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
604         
605          if( (*_flow)[e] <= 0 ) continue;
606          Node v=_g->source(e);
607
608          if( lev > level[v] ) { //Push is allowed now
609
610            if ( excess[v]<=0 && v!=_target && v!=_source ) {
611              next.set(v,first[level[v]]);
612              first[level[v]]=v;
613            }
614
615            Num flo=(*_flow)[e];
616
617            if ( flo >= exc ) { //A nonsaturating push.
618
619              _flow->set(e, flo-exc);
620              excess.set(v, excess[v]+exc);
621              exc=0;
622              break;
623            } else {  //A saturating push.
624
625              excess.set(v, excess[v]+flo);
626              exc-=flo;
627              _flow->set(e,0);
628            }
629          } else if ( newlevel > level[v] ) newlevel = level[v];
630        } //for in edges vw
631
632      } // if w still has excess after the out edge for cycle
633
634      excess.set(w, exc);
635     
636      return newlevel;
637    }
638   
639   
640   
641    void preflowPreproc(VecNode& first, NNMap& next,
642                        VecNode& level_list, NNMap& left, NNMap& right)
643    {
644      for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num);
645      std::queue<Node> bfs_queue;
646     
647      if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) {
648        //Reverse_bfs from t in the residual graph,
649        //to find the starting level.
650        level.set(_target,0);
651        bfs_queue.push(_target);
652       
653        while ( !bfs_queue.empty() ) {
654         
655          Node v=bfs_queue.front();
656          bfs_queue.pop();
657          int l=level[v]+1;
658         
659          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
660            if ( (*_capacity)[e] <= (*_flow)[e] ) continue;
661            Node w=_g->source(e);
662            if ( level[w] == _node_num && w != _source ) {
663              bfs_queue.push(w);
664              Node z=level_list[l];
665              if ( z!=INVALID ) left.set(z,w);
666              right.set(w,z);
667              level_list[l]=w;
668              level.set(w, l);
669            }
670          }
671         
672          for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
673            if ( 0 >= (*_flow)[e] ) continue;
674            Node w=_g->target(e);
675            if ( level[w] == _node_num && w != _source ) {
676              bfs_queue.push(w);
677              Node z=level_list[l];
678              if ( z!=INVALID ) left.set(z,w);
679              right.set(w,z);
680              level_list[l]=w;
681              level.set(w, l);
682            }
683          }
684        } //while
685      } //if
686
687
688      switch (flow_prop) {
689        case NO_FLOW: 
690        for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0);
691        case ZERO_FLOW:
692        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
693       
694        //Reverse_bfs from t, to find the starting level.
695        level.set(_target,0);
696        bfs_queue.push(_target);
697       
698        while ( !bfs_queue.empty() ) {
699         
700          Node v=bfs_queue.front();
701          bfs_queue.pop();
702          int l=level[v]+1;
703         
704          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
705            Node w=_g->source(e);
706            if ( level[w] == _node_num && w != _source ) {
707              bfs_queue.push(w);
708              Node z=level_list[l];
709              if ( z!=INVALID ) left.set(z,w);
710              right.set(w,z);
711              level_list[l]=w;
712              level.set(w, l);
713            }
714          }
715        }
716       
717        //the starting flow
718        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
719          Num c=(*_capacity)[e];
720          if ( c <= 0 ) continue;
721          Node w=_g->target(e);
722          if ( level[w] < _node_num ) {
723            if ( excess[w] <= 0 && w!=_target ) { //putting into the stack
724              next.set(w,first[level[w]]);
725              first[level[w]]=w;
726            }
727            _flow->set(e, c);
728            excess.set(w, excess[w]+c);
729          }
730        }
731        break;
732
733        case GEN_FLOW:
734        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
735        {
736          Num exc=0;
737          for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e];
738          for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e];
739          excess.set(_target,exc);
740        }
741
742        //the starting flow
743        for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e)  {
744          Num rem=(*_capacity)[e]-(*_flow)[e];
745          if ( rem <= 0 ) continue;
746          Node w=_g->target(e);
747          if ( level[w] < _node_num ) {
748            if ( excess[w] <= 0 && w!=_target ) { //putting into the stack
749              next.set(w,first[level[w]]);
750              first[level[w]]=w;
751            }   
752            _flow->set(e, (*_capacity)[e]);
753            excess.set(w, excess[w]+rem);
754          }
755        }
756       
757        for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) {
758          if ( (*_flow)[e] <= 0 ) continue;
759          Node w=_g->source(e);
760          if ( level[w] < _node_num ) {
761            if ( excess[w] <= 0 && w!=_target ) {
762              next.set(w,first[level[w]]);
763              first[level[w]]=w;
764            } 
765            excess.set(w, excess[w]+(*_flow)[e]);
766            _flow->set(e, 0);
767          }
768        }
769        break;
770
771        case PRE_FLOW: 
772        //the starting flow
773        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
774          Num rem=(*_capacity)[e]-(*_flow)[e];
775          if ( rem <= 0 ) continue;
776          Node w=_g->target(e);
777          if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]);
778        }
779       
780        for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
781          if ( (*_flow)[e] <= 0 ) continue;
782          Node w=_g->source(e);
783          if ( level[w] < _node_num ) _flow->set(e, 0);
784        }
785       
786        //computing the excess
787        for(NodeIt w(*_g); w!=INVALID; ++w) {
788          Num exc=0;
789          for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e];
790          for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e];
791          excess.set(w,exc);
792         
793          //putting the active nodes into the stack
794          int lev=level[w];
795            if ( exc > 0 && lev < _node_num && Node(w) != _target ) {
796              next.set(w,first[lev]);
797              first[lev]=w;
798            }
799        }
800        break;
801      } //switch
802    } //preflowPreproc
803
804
805    void relabel(Node w, int newlevel, VecNode& first, NNMap& next,
806                 VecNode& level_list, NNMap& left,
807                 NNMap& right, int& b, int& k, bool what_heur )
808    {
809
810      int lev=level[w];
811
812      Node right_n=right[w];
813      Node left_n=left[w];
814
815      //unlacing starts
816      if ( right_n!=INVALID ) {
817        if ( left_n!=INVALID ) {
818          right.set(left_n, right_n);
819          left.set(right_n, left_n);
820        } else {
821          level_list[lev]=right_n;
822          left.set(right_n, INVALID);
823        }
824      } else {
825        if ( left_n!=INVALID ) {
826          right.set(left_n, INVALID);
827        } else {
828          level_list[lev]=INVALID;
829        }
830      }
831      //unlacing ends
832
833      if ( level_list[lev]==INVALID ) {
834
835        //gapping starts
836        for (int i=lev; i!=k ; ) {
837          Node v=level_list[++i];
838          while ( v!=INVALID ) {
839            level.set(v,_node_num);
840            v=right[v];
841          }
842          level_list[i]=INVALID;
843          if ( !what_heur ) first[i]=INVALID;
844        }
845
846        level.set(w,_node_num);
847        b=lev-1;
848        k=b;
849        //gapping ends
850
851      } else {
852
853        if ( newlevel == _node_num ) level.set(w,_node_num);
854        else {
855          level.set(w,++newlevel);
856          next.set(w,first[newlevel]);
857          first[newlevel]=w;
858          if ( what_heur ) b=newlevel;
859          if ( k < newlevel ) ++k;      //now k=newlevel
860          Node z=level_list[newlevel];
861          if ( z!=INVALID ) left.set(z,w);
862          right.set(w,z);
863          left.set(w,INVALID);
864          level_list[newlevel]=w;
865        }
866      }
867    } //relabel
868
869  };
870
871  ///\ingroup flowalgs
872  ///\brief Function type interface for Preflow algorithm.
873  ///
874  ///Function type interface for Preflow algorithm.
875  ///\sa Preflow
876  template<class GR, class CM, class FM>
877  Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g,
878                            typename GR::Node source,
879                            typename GR::Node target,
880                            const CM &cap,
881                            FM &flow
882                            )
883  {
884    return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow);
885  }
886
887} //namespace lemon
888
889#endif //LEMON_PREFLOW_H
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