COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/preflow.h @ 1953:d4f411003580

Last change on this file since 1953:d4f411003580 was 1953:d4f411003580, checked in by Alpar Juttner, 14 years ago

Polish the doc.

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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    ///
112    enum FlowEnum{
113      ///indicates an unspecified edge map. \c flow will be
114      ///set to the constant zero flow in the beginning of
115      ///the algorithm in this case.
116      NO_FLOW,
117      ///constant zero flow
118      ZERO_FLOW,
119      ///any flow, i.e. the sum of the in-flows equals to
120      ///the sum of the out-flows in every node except the \c source and
121      ///the \c target.
122      GEN_FLOW,
123      ///any preflow, i.e. the sum of the in-flows is at
124      ///least the sum of the out-flows in every node except the \c source.
125      PRE_FLOW
126    };
127
128    ///Indicates the state of the preflow algorithm.
129
130    ///Indicates the state of the preflow algorithm.
131    ///
132    enum StatusEnum {
133      ///before running the algorithm or
134      ///at an unspecified state.
135      AFTER_NOTHING,
136      ///right after running \ref phase1()
137      AFTER_PREFLOW_PHASE_1,     
138      ///after running \ref phase2()
139      AFTER_PREFLOW_PHASE_2
140    };
141   
142  protected:
143    FlowEnum flow_prop;
144    StatusEnum status; // Do not needle this flag only if necessary.
145   
146  public:
147    ///The constructor of the class.
148
149    ///The constructor of the class.
150    ///\param _gr The directed graph the algorithm runs on.
151    ///\param _s The source node.
152    ///\param _t The target node.
153    ///\param _cap The capacity of the edges.
154    ///\param _f The flow of the edges.
155    ///\param tol Tolerance class.
156    ///Except the graph, all of these parameters can be reset by
157    ///calling \ref source, \ref target, \ref capacityMap and \ref
158    ///flowMap, resp.
159      Preflow(const Graph& _gr, Node _s, Node _t,
160              const CapacityMap& _cap, FlowMap& _f,
161              const TOL &tol=TOL()) :
162        _g(&_gr), _source(_s), _target(_t), _capacity(&_cap),
163        _flow(&_f), surely(tol),
164        _node_num(countNodes(_gr)), level(_gr), excess(_gr,0),
165        flow_prop(NO_FLOW), status(AFTER_NOTHING) {
166        if ( _source==_target )
167          throw InvalidArgument();
168      }
169   
170    ///Give a reference to the tolerance handler class
171
172    ///Give a reference to the tolerance handler class
173    ///\sa Tolerance
174    TOL &tolerance() { return surely; }
175
176    ///Runs the preflow algorithm. 
177
178    ///Runs the preflow algorithm.
179    ///
180    void run() {
181      phase1(flow_prop);
182      phase2();
183    }
184   
185    ///Runs the preflow algorithm. 
186   
187    ///Runs the preflow algorithm.
188    ///\pre The starting flow map must be
189    /// - a constant zero flow if \c fp is \c ZERO_FLOW,
190    /// - an arbitrary flow if \c fp is \c GEN_FLOW,
191    /// - an arbitrary preflow if \c fp is \c PRE_FLOW,
192    /// - any map if \c fp is NO_FLOW.
193    ///If the starting flow map is a flow or a preflow then
194    ///the algorithm terminates faster.
195    void run(FlowEnum fp) {
196      flow_prop=fp;
197      run();
198    }
199     
200    ///Runs the first phase of the preflow algorithm.
201
202    ///The preflow algorithm consists of two phases, this method runs
203    ///the first phase. After the first phase the maximum flow value
204    ///and a minimum value cut can already be computed, although a
205    ///maximum flow is not yet obtained. So after calling this method
206    ///\ref flowValue returns the value of a maximum flow and \ref
207    ///minCut returns a minimum cut.     
208    ///\warning \ref minMinCut and \ref maxMinCut do not give minimum
209    ///value cuts unless calling \ref phase2. 
210    ///\pre The starting flow must be
211    ///- a constant zero flow if \c fp is \c ZERO_FLOW,
212    ///- an arbitary flow if \c fp is \c GEN_FLOW,
213    ///- an arbitary preflow if \c fp is \c PRE_FLOW,
214    ///- any map if \c fp is NO_FLOW.
215    void phase1(FlowEnum fp)
216    {
217      flow_prop=fp;
218      phase1();
219    }
220
221   
222    ///Runs the first phase of the preflow algorithm.
223
224    ///The preflow algorithm consists of two phases, this method runs
225    ///the first phase. After the first phase the maximum flow value
226    ///and a minimum value cut can already be computed, although a
227    ///maximum flow is not yet obtained. So after calling this method
228    ///\ref flowValue returns the value of a maximum flow and \ref
229    ///minCut returns a minimum cut.
230    ///\warning \ref minMinCut() and \ref maxMinCut() do not
231    ///give minimum value cuts unless calling \ref phase2().
232    void phase1()
233    {
234      int heur0=(int)(H0*_node_num);  //time while running 'bound decrease'
235      int heur1=(int)(H1*_node_num);  //time while running 'highest label'
236      int heur=heur1;         //starting time interval (#of relabels)
237      int numrelabel=0;
238
239      bool what_heur=1;
240      //It is 0 in case 'bound decrease' and 1 in case 'highest label'
241
242      bool end=false;
243      //Needed for 'bound decrease', true means no active
244      //nodes are above bound b.
245
246      int k=_node_num-2;  //bound on the highest level under n containing a node
247      int b=k;    //bound on the highest level under n of an active node
248
249      VecNode first(_node_num, INVALID);
250      NNMap next(*_g, INVALID);
251
252      NNMap left(*_g, INVALID);
253      NNMap right(*_g, INVALID);
254      VecNode level_list(_node_num,INVALID);
255      //List of the nodes in level i<n, set to n.
256
257      preflowPreproc(first, next, level_list, left, right);
258
259      //Push/relabel on the highest level active nodes.
260      while ( true ) {
261        if ( b == 0 ) {
262          if ( !what_heur && !end && k > 0 ) {
263            b=k;
264            end=true;
265          } else break;
266        }
267
268        if ( first[b]==INVALID ) --b;
269        else {
270          end=false;
271          Node w=first[b];
272          first[b]=next[w];
273          int newlevel=push(w, next, first);
274          if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list,
275                                       left, right, b, k, what_heur);
276
277          ++numrelabel;
278          if ( numrelabel >= heur ) {
279            numrelabel=0;
280            if ( what_heur ) {
281              what_heur=0;
282              heur=heur0;
283              end=false;
284            } else {
285              what_heur=1;
286              heur=heur1;
287              b=k;
288            }
289          }
290        }
291      }
292      flow_prop=PRE_FLOW;
293      status=AFTER_PREFLOW_PHASE_1;
294    }
295    // Heuristics:
296    //   2 phase
297    //   gap
298    //   list 'level_list' on the nodes on level i implemented by hand
299    //   stack 'active' on the active nodes on level i     
300    //   runs heuristic 'highest label' for H1*n relabels
301    //   runs heuristic 'bound decrease' for H0*n relabels,
302    //        starts with 'highest label'
303    //   Parameters H0 and H1 are initialized to 20 and 1.
304
305
306    ///Runs the second phase of the preflow algorithm.
307
308    ///The preflow algorithm consists of two phases, this method runs
309    ///the second phase. After calling \ref phase1() and then
310    ///\ref phase2(),
311    /// \ref flowMap() return a maximum flow, \ref flowValue
312    ///returns the value of a maximum flow, \ref minCut returns a
313    ///minimum cut, while the methods \ref minMinCut and \ref
314    ///maxMinCut return the inclusionwise minimum and maximum cuts of
315    ///minimum value, resp.  \pre \ref phase1 must be called before.
316    void phase2()
317    {
318
319      int k=_node_num-2;  //bound on the highest level under n containing a node
320      int b=k;    //bound on the highest level under n of an active node
321
322   
323      VecNode first(_node_num, INVALID);
324      NNMap next(*_g, INVALID);
325      level.set(_source,0);
326      std::queue<Node> bfs_queue;
327      bfs_queue.push(_source);
328
329      while ( !bfs_queue.empty() ) {
330
331        Node v=bfs_queue.front();
332        bfs_queue.pop();
333        int l=level[v]+1;
334
335        for(InEdgeIt e(*_g,v); e!=INVALID; ++e) {
336          if ( (*_capacity)[e] <= (*_flow)[e] ) continue;
337          Node u=_g->source(e);
338          if ( level[u] >= _node_num ) {
339            bfs_queue.push(u);
340            level.set(u, l);
341            if ( excess[u] > 0 ) {
342              next.set(u,first[l]);
343              first[l]=u;
344            }
345          }
346        }
347
348        for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) {
349          if ( 0 >= (*_flow)[e] ) continue;
350          Node u=_g->target(e);
351          if ( level[u] >= _node_num ) {
352            bfs_queue.push(u);
353            level.set(u, l);
354            if ( excess[u] > 0 ) {
355              next.set(u,first[l]);
356              first[l]=u;
357            }
358          }
359        }
360      }
361      b=_node_num-2;
362
363      while ( true ) {
364
365        if ( b == 0 ) break;
366        if ( first[b]==INVALID ) --b;
367        else {
368          Node w=first[b];
369          first[b]=next[w];
370          int newlevel=push(w,next, first);
371         
372          //relabel
373          if ( excess[w] > 0 ) {
374            level.set(w,++newlevel);
375            next.set(w,first[newlevel]);
376            first[newlevel]=w;
377            b=newlevel;
378          }
379        }
380      } // while(true)
381      flow_prop=GEN_FLOW;
382      status=AFTER_PREFLOW_PHASE_2;
383    }
384
385    /// Returns the value of the maximum flow.
386
387    /// Returns the value of the maximum flow by returning the excess
388    /// of the target node \c t. This value equals to the value of
389    /// the maximum flow already after running \ref phase1.
390    Num flowValue() const {
391      return excess[_target];
392    }
393
394
395    ///Returns a minimum value cut.
396
397    ///Sets \c M to the characteristic vector of a minimum value
398    ///cut. This method can be called both after running \ref
399    ///phase1 and \ref phase2. It is much faster after
400    ///\ref phase1.  \pre M should be a bool-valued node-map. \pre
401    ///If \ref minCut() is called after \ref phase2() then M should
402    ///be initialized to false.
403    template<typename _CutMap>
404    void minCut(_CutMap& M) const {
405      switch ( status ) {
406        case AFTER_PREFLOW_PHASE_1:
407        for(NodeIt v(*_g); v!=INVALID; ++v) {
408          if (level[v] < _node_num) {
409            M.set(v, false);
410          } else {
411            M.set(v, true);
412          }
413        }
414        break;
415        case AFTER_PREFLOW_PHASE_2:
416        minMinCut(M);
417        break;
418        case AFTER_NOTHING:
419        break;
420      }
421    }
422
423    ///Returns the inclusionwise minimum of the minimum value cuts.
424
425    ///Sets \c M to the characteristic vector of the minimum value cut
426    ///which is inclusionwise minimum. It is computed by processing a
427    ///bfs from the source node \c s in the residual graph.  \pre M
428    ///should be a node map of bools initialized to false.  \pre \ref
429    ///phase2 should already be run.
430    template<typename _CutMap>
431    void minMinCut(_CutMap& M) const {
432
433      std::queue<Node> queue;
434      M.set(_source,true);
435      queue.push(_source);
436     
437      while (!queue.empty()) {
438        Node w=queue.front();
439        queue.pop();
440       
441        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
442          Node v=_g->target(e);
443          if (!M[v] && (*_flow)[e] < (*_capacity)[e] ) {
444            queue.push(v);
445            M.set(v, true);
446          }
447        }
448       
449        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
450          Node v=_g->source(e);
451          if (!M[v] && (*_flow)[e] > 0 ) {
452            queue.push(v);
453            M.set(v, true);
454          }
455        }
456      }
457    }
458   
459    ///Returns the inclusionwise maximum of the minimum value cuts.
460
461    ///Sets \c M to the characteristic vector of the minimum value cut
462    ///which is inclusionwise maximum. It is computed by processing a
463    ///backward bfs from the target node \c t in the residual graph.
464    ///\pre \ref phase2() or run() should already be run.
465    template<typename _CutMap>
466    void maxMinCut(_CutMap& M) const {
467
468      for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true);
469
470      std::queue<Node> queue;
471
472      M.set(_target,false);
473      queue.push(_target);
474
475      while (!queue.empty()) {
476        Node w=queue.front();
477        queue.pop();
478
479        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
480          Node v=_g->source(e);
481          if (M[v] && (*_flow)[e] < (*_capacity)[e] ) {
482            queue.push(v);
483            M.set(v, false);
484          }
485        }
486
487        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
488          Node v=_g->target(e);
489          if (M[v] && (*_flow)[e] > 0 ) {
490            queue.push(v);
491            M.set(v, false);
492          }
493        }
494      }
495    }
496
497    ///Sets the source node to \c _s.
498
499    ///Sets the source node to \c _s.
500    ///
501    void source(Node _s) {
502      _source=_s;
503      if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
504      status=AFTER_NOTHING;
505    }
506
507    ///Returns the source node.
508
509    ///Returns the source node.
510    ///
511    Node source() const {
512      return _source;
513    }
514
515    ///Sets the target node to \c _t.
516
517    ///Sets the target node to \c _t.
518    ///
519    void target(Node _t) {
520      _target=_t;
521      if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
522      status=AFTER_NOTHING;
523    }
524
525    ///Returns the target node.
526
527    ///Returns the target node.
528    ///
529    Node target() const {
530      return _target;
531    }
532
533    /// Sets the edge map of the capacities to _cap.
534
535    /// Sets the edge map of the capacities to _cap.
536    ///
537    void capacityMap(const CapacityMap& _cap) {
538      _capacity=&_cap;
539      status=AFTER_NOTHING;
540    }
541    /// Returns a reference to capacity map.
542
543    /// Returns a reference to capacity map.
544    ///
545    const CapacityMap &capacityMap() const {
546      return *_capacity;
547    }
548
549    /// Sets the edge map of the flows to _flow.
550
551    /// Sets the edge map of the flows to _flow.
552    ///
553    void flowMap(FlowMap& _f) {
554      _flow=&_f;
555      flow_prop=NO_FLOW;
556      status=AFTER_NOTHING;
557    }
558     
559    /// Returns a reference to flow map.
560
561    /// Returns a reference to flow map.
562    ///
563    const FlowMap &flowMap() const {
564      return *_flow;
565    }
566
567  private:
568
569    int push(Node w, NNMap& next, VecNode& first) {
570
571      int lev=level[w];
572      Num exc=excess[w];
573      int newlevel=_node_num;       //bound on the next level of w
574
575      for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
576        if ( (*_flow)[e] >= (*_capacity)[e] ) continue;
577        Node v=_g->target(e);
578
579        if( lev > level[v] ) { //Push is allowed now
580         
581          if ( excess[v]<=0 && v!=_target && v!=_source ) {
582            next.set(v,first[level[v]]);
583            first[level[v]]=v;
584          }
585
586          Num cap=(*_capacity)[e];
587          Num flo=(*_flow)[e];
588          Num remcap=cap-flo;
589         
590          if ( remcap >= exc ) { //A nonsaturating push.
591           
592            _flow->set(e, flo+exc);
593            excess.set(v, excess[v]+exc);
594            exc=0;
595            break;
596
597          } else { //A saturating push.
598            _flow->set(e, cap);
599            excess.set(v, excess[v]+remcap);
600            exc-=remcap;
601          }
602        } else if ( newlevel > level[v] ) newlevel = level[v];
603      } //for out edges wv
604
605      if ( exc > 0 ) {
606        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
607         
608          if( (*_flow)[e] <= 0 ) continue;
609          Node v=_g->source(e);
610
611          if( lev > level[v] ) { //Push is allowed now
612
613            if ( excess[v]<=0 && v!=_target && v!=_source ) {
614              next.set(v,first[level[v]]);
615              first[level[v]]=v;
616            }
617
618            Num flo=(*_flow)[e];
619
620            if ( flo >= exc ) { //A nonsaturating push.
621
622              _flow->set(e, flo-exc);
623              excess.set(v, excess[v]+exc);
624              exc=0;
625              break;
626            } else {  //A saturating push.
627
628              excess.set(v, excess[v]+flo);
629              exc-=flo;
630              _flow->set(e,0);
631            }
632          } else if ( newlevel > level[v] ) newlevel = level[v];
633        } //for in edges vw
634
635      } // if w still has excess after the out edge for cycle
636
637      excess.set(w, exc);
638     
639      return newlevel;
640    }
641   
642   
643   
644    void preflowPreproc(VecNode& first, NNMap& next,
645                        VecNode& level_list, NNMap& left, NNMap& right)
646    {
647      for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num);
648      std::queue<Node> bfs_queue;
649     
650      if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) {
651        //Reverse_bfs from t in the residual graph,
652        //to find the starting level.
653        level.set(_target,0);
654        bfs_queue.push(_target);
655       
656        while ( !bfs_queue.empty() ) {
657         
658          Node v=bfs_queue.front();
659          bfs_queue.pop();
660          int l=level[v]+1;
661         
662          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
663            if ( (*_capacity)[e] <= (*_flow)[e] ) continue;
664            Node w=_g->source(e);
665            if ( level[w] == _node_num && w != _source ) {
666              bfs_queue.push(w);
667              Node z=level_list[l];
668              if ( z!=INVALID ) left.set(z,w);
669              right.set(w,z);
670              level_list[l]=w;
671              level.set(w, l);
672            }
673          }
674         
675          for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
676            if ( 0 >= (*_flow)[e] ) continue;
677            Node w=_g->target(e);
678            if ( level[w] == _node_num && w != _source ) {
679              bfs_queue.push(w);
680              Node z=level_list[l];
681              if ( z!=INVALID ) left.set(z,w);
682              right.set(w,z);
683              level_list[l]=w;
684              level.set(w, l);
685            }
686          }
687        } //while
688      } //if
689
690
691      switch (flow_prop) {
692        case NO_FLOW: 
693        for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0);
694        case ZERO_FLOW:
695        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
696       
697        //Reverse_bfs from t, to find the starting level.
698        level.set(_target,0);
699        bfs_queue.push(_target);
700       
701        while ( !bfs_queue.empty() ) {
702         
703          Node v=bfs_queue.front();
704          bfs_queue.pop();
705          int l=level[v]+1;
706         
707          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
708            Node w=_g->source(e);
709            if ( level[w] == _node_num && w != _source ) {
710              bfs_queue.push(w);
711              Node z=level_list[l];
712              if ( z!=INVALID ) 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        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
722          Num c=(*_capacity)[e];
723          if ( c <= 0 ) continue;
724          Node w=_g->target(e);
725          if ( level[w] < _node_num ) {
726            if ( excess[w] <= 0 && w!=_target ) { //putting into the stack
727              next.set(w,first[level[w]]);
728              first[level[w]]=w;
729            }
730            _flow->set(e, c);
731            excess.set(w, excess[w]+c);
732          }
733        }
734        break;
735
736        case GEN_FLOW:
737        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
738        {
739          Num exc=0;
740          for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e];
741          for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e];
742          excess.set(_target,exc);
743        }
744
745        //the starting flow
746        for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e)  {
747          Num rem=(*_capacity)[e]-(*_flow)[e];
748          if ( rem <= 0 ) continue;
749          Node w=_g->target(e);
750          if ( level[w] < _node_num ) {
751            if ( excess[w] <= 0 && w!=_target ) { //putting into the stack
752              next.set(w,first[level[w]]);
753              first[level[w]]=w;
754            }   
755            _flow->set(e, (*_capacity)[e]);
756            excess.set(w, excess[w]+rem);
757          }
758        }
759       
760        for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) {
761          if ( (*_flow)[e] <= 0 ) continue;
762          Node w=_g->source(e);
763          if ( level[w] < _node_num ) {
764            if ( excess[w] <= 0 && w!=_target ) {
765              next.set(w,first[level[w]]);
766              first[level[w]]=w;
767            } 
768            excess.set(w, excess[w]+(*_flow)[e]);
769            _flow->set(e, 0);
770          }
771        }
772        break;
773
774        case PRE_FLOW: 
775        //the starting flow
776        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
777          Num rem=(*_capacity)[e]-(*_flow)[e];
778          if ( rem <= 0 ) continue;
779          Node w=_g->target(e);
780          if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]);
781        }
782       
783        for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
784          if ( (*_flow)[e] <= 0 ) continue;
785          Node w=_g->source(e);
786          if ( level[w] < _node_num ) _flow->set(e, 0);
787        }
788       
789        //computing the excess
790        for(NodeIt w(*_g); w!=INVALID; ++w) {
791          Num exc=0;
792          for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e];
793          for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e];
794          excess.set(w,exc);
795         
796          //putting the active nodes into the stack
797          int lev=level[w];
798            if ( exc > 0 && lev < _node_num && Node(w) != _target ) {
799              next.set(w,first[lev]);
800              first[lev]=w;
801            }
802        }
803        break;
804      } //switch
805    } //preflowPreproc
806
807
808    void relabel(Node w, int newlevel, VecNode& first, NNMap& next,
809                 VecNode& level_list, NNMap& left,
810                 NNMap& right, int& b, int& k, bool what_heur )
811    {
812
813      int lev=level[w];
814
815      Node right_n=right[w];
816      Node left_n=left[w];
817
818      //unlacing starts
819      if ( right_n!=INVALID ) {
820        if ( left_n!=INVALID ) {
821          right.set(left_n, right_n);
822          left.set(right_n, left_n);
823        } else {
824          level_list[lev]=right_n;
825          left.set(right_n, INVALID);
826        }
827      } else {
828        if ( left_n!=INVALID ) {
829          right.set(left_n, INVALID);
830        } else {
831          level_list[lev]=INVALID;
832        }
833      }
834      //unlacing ends
835
836      if ( level_list[lev]==INVALID ) {
837
838        //gapping starts
839        for (int i=lev; i!=k ; ) {
840          Node v=level_list[++i];
841          while ( v!=INVALID ) {
842            level.set(v,_node_num);
843            v=right[v];
844          }
845          level_list[i]=INVALID;
846          if ( !what_heur ) first[i]=INVALID;
847        }
848
849        level.set(w,_node_num);
850        b=lev-1;
851        k=b;
852        //gapping ends
853
854      } else {
855
856        if ( newlevel == _node_num ) level.set(w,_node_num);
857        else {
858          level.set(w,++newlevel);
859          next.set(w,first[newlevel]);
860          first[newlevel]=w;
861          if ( what_heur ) b=newlevel;
862          if ( k < newlevel ) ++k;      //now k=newlevel
863          Node z=level_list[newlevel];
864          if ( z!=INVALID ) left.set(z,w);
865          right.set(w,z);
866          left.set(w,INVALID);
867          level_list[newlevel]=w;
868        }
869      }
870    } //relabel
871
872  };
873
874  ///\ingroup flowalgs
875  ///\brief Function type interface for Preflow algorithm.
876  ///
877  ///Function type interface for Preflow algorithm.
878  ///\sa Preflow
879  template<class GR, class CM, class FM>
880  Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g,
881                            typename GR::Node source,
882                            typename GR::Node target,
883                            const CM &cap,
884                            FM &flow
885                            )
886  {
887    return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow);
888  }
889
890} //namespace lemon
891
892#endif //LEMON_PREFLOW_H
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