COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/preflow.h @ 2376:0ed45a6c74b1

Last change on this file since 2376:0ed45a6c74b1 was 2376:0ed45a6c74b1, checked in by Balazs Dezso, 13 years ago

Reorganization of the modules and groups

File size: 24.5 KB
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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2006
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_PREFLOW_H
20#define LEMON_PREFLOW_H
21
22#include <vector>
23#include <queue>
24
25#include <lemon/error.h>
26#include <lemon/bits/invalid.h>
27#include <lemon/tolerance.h>
28#include <lemon/maps.h>
29#include <lemon/graph_utils.h>
30
31/// \file
32/// \ingroup max_flow
33/// \brief Implementation of the preflow algorithm.
34
35namespace lemon {
36
37  ///\ingroup max_flow
38  ///\brief %Preflow algorithms class.
39  ///
40  ///This class provides an implementation of the \e preflow \e
41  ///algorithm producing a flow of maximum value in a directed
42  ///graph. The preflow algorithms are the fastest known max flow algorithms.
43  ///The \e source node, the \e target node, the \e
44  ///capacity of the edges and the \e starting \e flow value of the
45  ///edges should be passed to the algorithm through the
46  ///constructor. It is possible to change these quantities using the
47  ///functions \ref source, \ref target, \ref capacityMap and \ref
48  ///flowMap.
49  ///
50  ///After running \ref lemon::Preflow::phase1() "phase1()"
51  ///or \ref lemon::Preflow::run() "run()", the maximal flow
52  ///value can be obtained by calling \ref flowValue(). The minimum
53  ///value cut can be written into a <tt>bool</tt> node map by
54  ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes
55  ///the inclusionwise minimum and maximum of the minimum value cuts,
56  ///resp.)
57  ///
58  ///\param Graph The directed graph type the algorithm runs on.
59  ///\param Num The number type of the capacities and the flow values.
60  ///\param CapacityMap The capacity map type.
61  ///\param FlowMap The flow map type.
62  ///\param Tolerance The tolerance type.
63  ///
64  ///\author Jacint Szabo
65  ///\todo Second template parameter is superfluous
66  template <typename Graph, typename Num,
67            typename CapacityMap=typename Graph::template EdgeMap<Num>,
68            typename FlowMap=typename Graph::template EdgeMap<Num>,
69            typename Tolerance=Tolerance<Num> >
70  class Preflow {
71  protected:
72    typedef typename Graph::Node Node;
73    typedef typename Graph::NodeIt NodeIt;
74    typedef typename Graph::EdgeIt EdgeIt;
75    typedef typename Graph::OutEdgeIt OutEdgeIt;
76    typedef typename Graph::InEdgeIt InEdgeIt;
77
78    typedef typename Graph::template NodeMap<Node> NNMap;
79    typedef typename std::vector<Node> VecNode;
80
81    const Graph* _g;
82    Node _source;
83    Node _target;
84    const CapacityMap* _capacity;
85    FlowMap* _flow;
86
87    Tolerance _surely;
88   
89    int _node_num;      //the number of nodes of G
90   
91    typename Graph::template NodeMap<int> level; 
92    typename Graph::template NodeMap<Num> excess;
93
94    // constants used for heuristics
95    static const int H0=20;
96    static const int H1=1;
97
98  public:
99
100    ///\ref Exception for the case when s=t.
101
102    ///\ref Exception for the case when the source equals the target.
103    class InvalidArgument : public lemon::LogicError {
104    public:
105      virtual const char* what() const throw() {
106        return "lemon::Preflow::InvalidArgument";
107      }
108    };
109   
110   
111    ///Indicates the property of the starting flow map.
112   
113    ///Indicates the property of the starting flow map.
114    ///
115    enum FlowEnum{
116      ///indicates an unspecified edge map. \c flow will be
117      ///set to the constant zero flow in the beginning of
118      ///the algorithm in this case.
119      NO_FLOW,
120      ///constant zero flow
121      ZERO_FLOW,
122      ///any flow, i.e. the sum of the in-flows equals to
123      ///the sum of the out-flows in every node except the \c source and
124      ///the \c target.
125      GEN_FLOW,
126      ///any preflow, i.e. the sum of the in-flows is at
127      ///least the sum of the out-flows in every node except the \c source.
128      PRE_FLOW
129    };
130
131    ///Indicates the state of the preflow algorithm.
132
133    ///Indicates the state of the preflow algorithm.
134    ///
135    enum StatusEnum {
136      ///before running the algorithm or
137      ///at an unspecified state.
138      AFTER_NOTHING,
139      ///right after running \ref phase1()
140      AFTER_PREFLOW_PHASE_1,     
141      ///after running \ref phase2()
142      AFTER_PREFLOW_PHASE_2
143    };
144   
145  protected:
146    FlowEnum flow_prop;
147    StatusEnum status; // Do not needle this flag only if necessary.
148   
149  public:
150    ///The constructor of the class.
151
152    ///The constructor of the class.
153    ///\param _gr The directed graph the algorithm runs on.
154    ///\param _s The source node.
155    ///\param _t The target node.
156    ///\param _cap The capacity of the edges.
157    ///\param _f The flow of the edges.
158    ///\param _sr Tolerance class.
159    ///Except the graph, all of these parameters can be reset by
160    ///calling \ref source, \ref target, \ref capacityMap and \ref
161    ///flowMap, resp.
162    Preflow(const Graph& _gr, Node _s, Node _t,
163            const CapacityMap& _cap, FlowMap& _f,
164            const Tolerance &_sr=Tolerance()) :
165        _g(&_gr), _source(_s), _target(_t), _capacity(&_cap),
166        _flow(&_f), _surely(_sr),
167        _node_num(countNodes(_gr)), level(_gr), excess(_gr,0),
168        flow_prop(NO_FLOW), status(AFTER_NOTHING) {
169        if ( _source==_target )
170          throw InvalidArgument();
171    }
172   
173    ///Give a reference to the tolerance handler class
174
175    ///Give a reference to the tolerance handler class
176    ///\sa Tolerance
177    Tolerance &tolerance() { return _surely; }
178
179    ///Runs the preflow algorithm. 
180
181    ///Runs the preflow algorithm.
182    ///
183    void run() {
184      phase1(flow_prop);
185      phase2();
186    }
187   
188    ///Runs the preflow algorithm. 
189   
190    ///Runs the preflow algorithm.
191    ///\pre The starting flow map must be
192    /// - a constant zero flow if \c fp is \c ZERO_FLOW,
193    /// - an arbitrary flow if \c fp is \c GEN_FLOW,
194    /// - an arbitrary preflow if \c fp is \c PRE_FLOW,
195    /// - any map if \c fp is NO_FLOW.
196    ///If the starting flow map is a flow or a preflow then
197    ///the algorithm terminates faster.
198    void run(FlowEnum fp) {
199      flow_prop=fp;
200      run();
201    }
202     
203    ///Runs the first phase of the preflow algorithm.
204
205    ///The preflow algorithm consists of two phases, this method runs
206    ///the first phase. After the first phase the maximum flow value
207    ///and a minimum value cut can already be computed, although a
208    ///maximum flow is not yet obtained. So after calling this method
209    ///\ref flowValue returns the value of a maximum flow and \ref
210    ///minCut returns a minimum cut.     
211    ///\warning \ref minMinCut and \ref maxMinCut do not give minimum
212    ///value cuts unless calling \ref phase2. 
213    ///\pre The starting flow must be
214    ///- a constant zero flow if \c fp is \c ZERO_FLOW,
215    ///- an arbitary flow if \c fp is \c GEN_FLOW,
216    ///- an arbitary preflow if \c fp is \c PRE_FLOW,
217    ///- any map if \c fp is NO_FLOW.
218    void phase1(FlowEnum fp)
219    {
220      flow_prop=fp;
221      phase1();
222    }
223
224   
225    ///Runs the first phase of the preflow algorithm.
226
227    ///The preflow algorithm consists of two phases, this method runs
228    ///the first phase. After the first phase the maximum flow value
229    ///and a minimum value cut can already be computed, although a
230    ///maximum flow is not yet obtained. So after calling this method
231    ///\ref flowValue returns the value of a maximum flow and \ref
232    ///minCut returns a minimum cut.
233    ///\warning \ref minMinCut() and \ref maxMinCut() do not
234    ///give minimum value cuts unless calling \ref phase2().
235    void phase1()
236    {
237      int heur0=(int)(H0*_node_num);  //time while running 'bound decrease'
238      int heur1=(int)(H1*_node_num);  //time while running 'highest label'
239      int heur=heur1;         //starting time interval (#of relabels)
240      int numrelabel=0;
241
242      bool what_heur=1;
243      //It is 0 in case 'bound decrease' and 1 in case 'highest label'
244
245      bool end=false;
246      //Needed for 'bound decrease', true means no active
247      //nodes are above bound b.
248
249      int k=_node_num-2;  //bound on the highest level under n containing a node
250      int b=k;    //bound on the highest level under n containing an active node
251
252      VecNode first(_node_num, INVALID);
253      NNMap next(*_g, INVALID);
254
255      NNMap left(*_g, INVALID);
256      NNMap right(*_g, INVALID);
257      VecNode level_list(_node_num,INVALID);
258      //List of the nodes in level i<n, set to n.
259
260      preflowPreproc(first, next, level_list, left, right);
261
262      //Push/relabel on the highest level active nodes.
263      while ( true ) {
264        if ( b == 0 ) {
265          if ( !what_heur && !end && k > 0 ) {
266            b=k;
267            end=true;
268          } else break;
269        }
270
271        if ( first[b]==INVALID ) --b;
272        else {
273          end=false;
274          Node w=first[b];
275          first[b]=next[w];
276          int newlevel=push(w, next, first);
277          if ( excess[w] != 0 ) {
278            relabel(w, newlevel, first, next, level_list,
279                    left, right, b, k, what_heur);
280          }
281
282          ++numrelabel;
283          if ( numrelabel >= heur ) {
284            numrelabel=0;
285            if ( what_heur ) {
286              what_heur=0;
287              heur=heur0;
288              end=false;
289            } else {
290              what_heur=1;
291              heur=heur1;
292              b=k;
293            }
294          }
295        }
296      }
297      flow_prop=PRE_FLOW;
298      status=AFTER_PREFLOW_PHASE_1;
299    }
300    // Heuristics:
301    //   2 phase
302    //   gap
303    //   list 'level_list' on the nodes on level i implemented by hand
304    //   stack 'active' on the active nodes on level i     
305    //   runs heuristic 'highest label' for H1*n relabels
306    //   runs heuristic 'bound decrease' for H0*n relabels,
307    //        starts with 'highest label'
308    //   Parameters H0 and H1 are initialized to 20 and 1.
309
310
311    ///Runs the second phase of the preflow algorithm.
312
313    ///The preflow algorithm consists of two phases, this method runs
314    ///the second phase. After calling \ref phase1() and then
315    ///\ref phase2(),
316    /// \ref flowMap() return a maximum flow, \ref flowValue
317    ///returns the value of a maximum flow, \ref minCut returns a
318    ///minimum cut, while the methods \ref minMinCut and \ref
319    ///maxMinCut return the inclusionwise minimum and maximum cuts of
320    ///minimum value, resp.  \pre \ref phase1 must be called before.
321    ///
322    /// \todo The inexact computation can cause positive excess on a set of
323    /// unpushable nodes. We may have to watch the empty level in this case
324    /// due to avoid the terrible long running time.
325    void phase2()
326    {
327
328      int k=_node_num-2;  //bound on the highest level under n containing a node
329      int b=k;    //bound on the highest level under n of an active node
330
331   
332      VecNode first(_node_num, INVALID);
333      NNMap next(*_g, INVALID);
334      level.set(_source,0);
335      std::queue<Node> bfs_queue;
336      bfs_queue.push(_source);
337
338      while ( !bfs_queue.empty() ) {
339
340        Node v=bfs_queue.front();
341        bfs_queue.pop();
342        int l=level[v]+1;
343
344        for(InEdgeIt e(*_g,v); e!=INVALID; ++e) {
345          if ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue;
346          Node u=_g->source(e);
347          if ( level[u] >= _node_num ) {
348            bfs_queue.push(u);
349            level.set(u, l);
350            if ( excess[u] != 0 ) {
351              next.set(u,first[l]);
352              first[l]=u;
353            }
354          }
355        }
356
357        for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) {
358          if ( !_surely.positive((*_flow)[e]) ) continue;
359          Node u=_g->target(e);
360          if ( level[u] >= _node_num ) {
361            bfs_queue.push(u);
362            level.set(u, l);
363            if ( excess[u] != 0 ) {
364              next.set(u,first[l]);
365              first[l]=u;
366            }
367          }
368        }
369      }
370      b=_node_num-2;
371
372      while ( true ) {
373
374        if ( b == 0 ) break;
375        if ( first[b]==INVALID ) --b;
376        else {
377          Node w=first[b];
378          first[b]=next[w];
379          int newlevel=push(w,next, first);
380         
381          if ( newlevel == _node_num) {
382            excess.set(w, 0);
383            level.set(w,_node_num);
384          }
385          //relabel
386          if ( excess[w] != 0 ) {
387            level.set(w,++newlevel);
388            next.set(w,first[newlevel]);
389            first[newlevel]=w;
390            b=newlevel;
391          }
392        }
393      } // while(true)
394      flow_prop=GEN_FLOW;
395      status=AFTER_PREFLOW_PHASE_2;
396    }
397
398    /// Returns the value of the maximum flow.
399
400    /// Returns the value of the maximum flow by returning the excess
401    /// of the target node \c t. This value equals to the value of
402    /// the maximum flow already after running \ref phase1.
403    Num flowValue() const {
404      return excess[_target];
405    }
406
407
408    ///Returns a minimum value cut.
409
410    ///Sets \c M to the characteristic vector of a minimum value
411    ///cut. This method can be called both after running \ref
412    ///phase1 and \ref phase2. It is much faster after
413    ///\ref phase1.  \pre M should be a bool-valued node-map. \pre
414    ///If \ref minCut() is called after \ref phase2() then M should
415    ///be initialized to false.
416    template<typename _CutMap>
417    void minCut(_CutMap& M) const {
418      switch ( status ) {
419        case AFTER_PREFLOW_PHASE_1:
420        for(NodeIt v(*_g); v!=INVALID; ++v) {
421          if (level[v] < _node_num) {
422            M.set(v, false);
423          } else {
424            M.set(v, true);
425          }
426        }
427        break;
428        case AFTER_PREFLOW_PHASE_2:
429        minMinCut(M);
430        break;
431        case AFTER_NOTHING:
432        break;
433      }
434    }
435
436    ///Returns the inclusionwise minimum of the minimum value cuts.
437
438    ///Sets \c M to the characteristic vector of the minimum value cut
439    ///which is inclusionwise minimum. It is computed by processing a
440    ///bfs from the source node \c s in the residual graph.  \pre M
441    ///should be a node map of bools initialized to false.  \pre \ref
442    ///phase2 should already be run.
443    template<typename _CutMap>
444    void minMinCut(_CutMap& M) const {
445
446      std::queue<Node> queue;
447      M.set(_source,true);
448      queue.push(_source);
449     
450      while (!queue.empty()) {
451        Node w=queue.front();
452        queue.pop();
453       
454        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
455          Node v=_g->target(e);
456          if (!M[v] && _surely.positive((*_capacity)[e] -(*_flow)[e]) ) {
457            queue.push(v);
458            M.set(v, true);
459          }
460        }
461       
462        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
463          Node v=_g->source(e);
464          if (!M[v] && _surely.positive((*_flow)[e]) ) {
465            queue.push(v);
466            M.set(v, true);
467          }
468        }
469      }
470    }
471   
472    ///Returns the inclusionwise maximum of the minimum value cuts.
473
474    ///Sets \c M to the characteristic vector of the minimum value cut
475    ///which is inclusionwise maximum. It is computed by processing a
476    ///backward bfs from the target node \c t in the residual graph.
477    ///\pre \ref phase2() or run() should already be run.
478    template<typename _CutMap>
479    void maxMinCut(_CutMap& M) const {
480
481      for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true);
482
483      std::queue<Node> queue;
484
485      M.set(_target,false);
486      queue.push(_target);
487
488      while (!queue.empty()) {
489        Node w=queue.front();
490        queue.pop();
491
492        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
493          Node v=_g->source(e);
494          if (M[v] && _surely.positive((*_capacity)[e] - (*_flow)[e]) ) {
495            queue.push(v);
496            M.set(v, false);
497          }
498        }
499
500        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
501          Node v=_g->target(e);
502          if (M[v] && _surely.positive((*_flow)[e]) ) {
503            queue.push(v);
504            M.set(v, false);
505          }
506        }
507      }
508    }
509
510    ///Sets the source node to \c _s.
511
512    ///Sets the source node to \c _s.
513    ///
514    void source(Node _s) {
515      _source=_s;
516      if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
517      status=AFTER_NOTHING;
518    }
519
520    ///Returns the source node.
521
522    ///Returns the source node.
523    ///
524    Node source() const {
525      return _source;
526    }
527
528    ///Sets the target node to \c _t.
529
530    ///Sets the target node to \c _t.
531    ///
532    void target(Node _t) {
533      _target=_t;
534      if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
535      status=AFTER_NOTHING;
536    }
537
538    ///Returns the target node.
539
540    ///Returns the target node.
541    ///
542    Node target() const {
543      return _target;
544    }
545
546    /// Sets the edge map of the capacities to _cap.
547
548    /// Sets the edge map of the capacities to _cap.
549    ///
550    void capacityMap(const CapacityMap& _cap) {
551      _capacity=&_cap;
552      status=AFTER_NOTHING;
553    }
554    /// Returns a reference to capacity map.
555
556    /// Returns a reference to capacity map.
557    ///
558    const CapacityMap &capacityMap() const {
559      return *_capacity;
560    }
561
562    /// Sets the edge map of the flows to _flow.
563
564    /// Sets the edge map of the flows to _flow.
565    ///
566    void flowMap(FlowMap& _f) {
567      _flow=&_f;
568      flow_prop=NO_FLOW;
569      status=AFTER_NOTHING;
570    }
571     
572    /// Returns a reference to flow map.
573
574    /// Returns a reference to flow map.
575    ///
576    const FlowMap &flowMap() const {
577      return *_flow;
578    }
579
580  private:
581
582    int push(Node w, NNMap& next, VecNode& first) {
583
584      int lev=level[w];
585      Num exc=excess[w];
586      int newlevel=_node_num;       //bound on the next level of w
587
588      for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
589        if ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue;
590        Node v=_g->target(e);
591       
592        if( lev > level[v] ) { //Push is allowed now
593         
594          if ( excess[v] == 0 && v!=_target && v!=_source ) {
595            next.set(v,first[level[v]]);
596            first[level[v]]=v;
597          }
598
599          Num cap=(*_capacity)[e];
600          Num flo=(*_flow)[e];
601          Num remcap=cap-flo;
602         
603          if ( ! _surely.less(remcap, exc) ) { //A nonsaturating push.
604           
605            _flow->set(e, flo+exc);
606            excess.set(v, excess[v]+exc);
607            exc=0;
608            break;
609
610          } else { //A saturating push.
611            _flow->set(e, cap);
612            excess.set(v, excess[v]+remcap);
613            exc-=remcap;
614          }
615        } else if ( newlevel > level[v] ) newlevel = level[v];
616      } //for out edges wv
617
618      if ( exc != 0 ) {
619        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
620         
621          if ( !_surely.positive((*_flow)[e]) ) continue;
622          Node v=_g->source(e);
623         
624          if( lev > level[v] ) { //Push is allowed now
625
626            if ( excess[v] == 0 && v!=_target && v!=_source ) {
627              next.set(v,first[level[v]]);
628              first[level[v]]=v;
629            }
630
631            Num flo=(*_flow)[e];
632
633            if ( !_surely.less(flo, exc) ) { //A nonsaturating push.
634
635              _flow->set(e, flo-exc);
636              excess.set(v, excess[v]+exc);
637              exc=0;
638              break;
639            } else {  //A saturating push.
640
641              excess.set(v, excess[v]+flo);
642              exc-=flo;
643              _flow->set(e,0);
644            }
645          } else if ( newlevel > level[v] ) newlevel = level[v];
646        } //for in edges vw
647
648      } // if w still has excess after the out edge for cycle
649
650      excess.set(w, exc);
651     
652      return newlevel;
653    }
654   
655   
656   
657    void preflowPreproc(VecNode& first, NNMap& next,
658                        VecNode& level_list, NNMap& left, NNMap& right)
659    {
660      for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num);
661      std::queue<Node> bfs_queue;
662     
663      if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) {
664        //Reverse_bfs from t in the residual graph,
665        //to find the starting level.
666        level.set(_target,0);
667        bfs_queue.push(_target);
668       
669        while ( !bfs_queue.empty() ) {
670         
671          Node v=bfs_queue.front();
672          bfs_queue.pop();
673          int l=level[v]+1;
674         
675          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
676            if ( !_surely.positive((*_capacity)[e] - (*_flow)[e] )) continue;
677            Node w=_g->source(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         
688          for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
689            if ( !_surely.positive((*_flow)[e]) ) continue;
690            Node w=_g->target(e);
691            if ( level[w] == _node_num && w != _source ) {
692              bfs_queue.push(w);
693              Node z=level_list[l];
694              if ( z!=INVALID ) left.set(z,w);
695              right.set(w,z);
696              level_list[l]=w;
697              level.set(w, l);
698            }
699          }
700        } //while
701      } //if
702
703
704      switch (flow_prop) {
705        case NO_FLOW: 
706        for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0);
707        case ZERO_FLOW:
708        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
709       
710        //Reverse_bfs from t, to find the starting level.
711        level.set(_target,0);
712        bfs_queue.push(_target);
713       
714        while ( !bfs_queue.empty() ) {
715         
716          Node v=bfs_queue.front();
717          bfs_queue.pop();
718          int l=level[v]+1;
719         
720          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
721            Node w=_g->source(e);
722            if ( level[w] == _node_num && w != _source ) {
723              bfs_queue.push(w);
724              Node z=level_list[l];
725              if ( z!=INVALID ) left.set(z,w);
726              right.set(w,z);
727              level_list[l]=w;
728              level.set(w, l);
729            }
730          }
731        }
732       
733        //the starting flow
734        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
735          Num c=(*_capacity)[e];
736          if ( !_surely.positive(c) ) continue;
737          Node w=_g->target(e);
738          if ( level[w] < _node_num ) {
739            if ( excess[w] == 0 && w!=_target ) { //putting into the stack
740              next.set(w,first[level[w]]);
741              first[level[w]]=w;
742            }
743            _flow->set(e, c);
744            excess.set(w, excess[w]+c);
745          }
746        }
747        break;
748
749        case GEN_FLOW:
750        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
751        {
752          Num exc=0;
753          for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e];
754          for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e];
755          if (!_surely.positive(exc)) {
756            exc = 0;
757          }
758          excess.set(_target,exc);
759        }
760
761        //the starting flow
762        for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e)  {
763          Num rem=(*_capacity)[e]-(*_flow)[e];
764          if ( !_surely.positive(rem) ) continue;
765          Node w=_g->target(e);
766          if ( level[w] < _node_num ) {
767            if ( excess[w] == 0 && w!=_target ) { //putting into the stack
768              next.set(w,first[level[w]]);
769              first[level[w]]=w;
770            }   
771            _flow->set(e, (*_capacity)[e]);
772            excess.set(w, excess[w]+rem);
773          }
774        }
775       
776        for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) {
777          if ( !_surely.positive((*_flow)[e]) ) continue;
778          Node w=_g->source(e);
779          if ( level[w] < _node_num ) {
780            if ( excess[w] == 0 && w!=_target ) {
781              next.set(w,first[level[w]]);
782              first[level[w]]=w;
783            } 
784            excess.set(w, excess[w]+(*_flow)[e]);
785            _flow->set(e, 0);
786          }
787        }
788        break;
789
790        case PRE_FLOW: 
791        //the starting flow
792        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
793          Num rem=(*_capacity)[e]-(*_flow)[e];
794          if ( !_surely.positive(rem) ) continue;
795          Node w=_g->target(e);
796          if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]);
797        }
798       
799        for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
800          if ( !_surely.positive((*_flow)[e]) ) continue;
801          Node w=_g->source(e);
802          if ( level[w] < _node_num ) _flow->set(e, 0);
803        }
804       
805        //computing the excess
806        for(NodeIt w(*_g); w!=INVALID; ++w) {
807          Num exc=0;
808          for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e];
809          for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e];
810          if (!_surely.positive(exc)) {
811            exc = 0;
812          }
813          excess.set(w,exc);
814         
815          //putting the active nodes into the stack
816          int lev=level[w];
817            if ( exc != 0 && lev < _node_num && Node(w) != _target ) {
818              next.set(w,first[lev]);
819              first[lev]=w;
820            }
821        }
822        break;
823      } //switch
824    } //preflowPreproc
825
826
827    void relabel(Node w, int newlevel, VecNode& first, NNMap& next,
828                 VecNode& level_list, NNMap& left,
829                 NNMap& right, int& b, int& k, bool what_heur )
830    {
831
832      int lev=level[w];
833
834      Node right_n=right[w];
835      Node left_n=left[w];
836
837      //unlacing starts
838      if ( right_n!=INVALID ) {
839        if ( left_n!=INVALID ) {
840          right.set(left_n, right_n);
841          left.set(right_n, left_n);
842        } else {
843          level_list[lev]=right_n;
844          left.set(right_n, INVALID);
845        }
846      } else {
847        if ( left_n!=INVALID ) {
848          right.set(left_n, INVALID);
849        } else {
850          level_list[lev]=INVALID;
851        }
852      }
853      //unlacing ends
854
855      if ( level_list[lev]==INVALID ) {
856
857        //gapping starts
858        for (int i=lev; i!=k ; ) {
859          Node v=level_list[++i];
860          while ( v!=INVALID ) {
861            level.set(v,_node_num);
862            v=right[v];
863          }
864          level_list[i]=INVALID;
865          if ( !what_heur ) first[i]=INVALID;
866        }
867
868        level.set(w,_node_num);
869        b=lev-1;
870        k=b;
871        //gapping ends
872
873      } else {
874
875        if ( newlevel == _node_num ) level.set(w,_node_num);
876        else {
877          level.set(w,++newlevel);
878          next.set(w,first[newlevel]);
879          first[newlevel]=w;
880          if ( what_heur ) b=newlevel;
881          if ( k < newlevel ) ++k;      //now k=newlevel
882          Node z=level_list[newlevel];
883          if ( z!=INVALID ) left.set(z,w);
884          right.set(w,z);
885          left.set(w,INVALID);
886          level_list[newlevel]=w;
887        }
888      }
889    } //relabel
890
891  };
892
893  ///\ingroup max_flow
894  ///\brief Function type interface for Preflow algorithm.
895  ///
896  ///Function type interface for Preflow algorithm.
897  ///\sa Preflow
898  template<class GR, class CM, class FM>
899  Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g,
900                            typename GR::Node source,
901                            typename GR::Node target,
902                            const CM &cap,
903                            FM &flow
904                            )
905  {
906    return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow);
907  }
908
909} //namespace lemon
910
911#endif //LEMON_PREFLOW_H
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