COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/preflow.h @ 2476:059dcdda37c5

Last change on this file since 2476:059dcdda37c5 was 2473:9ffff9051a4b, checked in by Peter Kovacs, 12 years ago

Small improvement in documentation.

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1/* -*- C++ -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library
4 *
5 * Copyright (C) 2003-2007
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 Tol 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 Tol=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    Tol _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 Tol 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 Tol &_sr=Tol()) :
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    Tol &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    ///\warning A real flow map (i.e. not \ref lemon::NullMap "NullMap")
214    ///is needed for this phase.
215    ///\pre The starting flow must be
216    ///- a constant zero flow if \c fp is \c ZERO_FLOW,
217    ///- an arbitary flow if \c fp is \c GEN_FLOW,
218    ///- an arbitary preflow if \c fp is \c PRE_FLOW,
219    ///- any map if \c fp is NO_FLOW.
220    void phase1(FlowEnum fp)
221    {
222      flow_prop=fp;
223      phase1();
224    }
225
226   
227    ///Runs the first phase of the preflow algorithm.
228
229    ///The preflow algorithm consists of two phases, this method runs
230    ///the first phase. After the first phase the maximum flow value
231    ///and a minimum value cut can already be computed, although a
232    ///maximum flow is not yet obtained. So after calling this method
233    ///\ref flowValue returns the value of a maximum flow and \ref
234    ///minCut returns a minimum cut.
235    ///\warning \ref minMinCut() and \ref maxMinCut() do not
236    ///give minimum value cuts unless calling \ref phase2().
237    ///\warning A real flow map (i.e. not \ref lemon::NullMap "NullMap")
238    ///is needed for this phase.
239    void phase1()
240    {
241      int heur0=int(H0*_node_num);  //time while running 'bound decrease'
242      int heur1=int(H1*_node_num);  //time while running 'highest label'
243      int heur=heur1;         //starting time interval (#of relabels)
244      int numrelabel=0;
245
246      bool what_heur=1;
247      //It is 0 in case 'bound decrease' and 1 in case 'highest label'
248
249      bool end=false;
250      //Needed for 'bound decrease', true means no active
251      //nodes are above bound b.
252
253      int k=_node_num-2;  //bound on the highest level under n containing a node
254      int b=k;    //bound on the highest level under n containing an active node
255
256      VecNode first(_node_num, INVALID);
257      NNMap next(*_g, INVALID);
258
259      NNMap left(*_g, INVALID);
260      NNMap right(*_g, INVALID);
261      VecNode level_list(_node_num,INVALID);
262      //List of the nodes in level i<n, set to n.
263
264      preflowPreproc(first, next, level_list, left, right);
265
266      //Push/relabel on the highest level active nodes.
267      while ( true ) {
268        if ( b == 0 ) {
269          if ( !what_heur && !end && k > 0 ) {
270            b=k;
271            end=true;
272          } else break;
273        }
274
275        if ( first[b]==INVALID ) --b;
276        else {
277          end=false;
278          Node w=first[b];
279          first[b]=next[w];
280          int newlevel=push(w, next, first);
281          if ( excess[w] != 0 ) {
282            relabel(w, newlevel, first, next, level_list,
283                    left, right, b, k, what_heur);
284          }
285
286          ++numrelabel;
287          if ( numrelabel >= heur ) {
288            numrelabel=0;
289            if ( what_heur ) {
290              what_heur=0;
291              heur=heur0;
292              end=false;
293            } else {
294              what_heur=1;
295              heur=heur1;
296              b=k;
297            }
298          }
299        }
300      }
301      flow_prop=PRE_FLOW;
302      status=AFTER_PREFLOW_PHASE_1;
303    }
304    // Heuristics:
305    //   2 phase
306    //   gap
307    //   list 'level_list' on the nodes on level i implemented by hand
308    //   stack 'active' on the active nodes on level i     
309    //   runs heuristic 'highest label' for H1*n relabels
310    //   runs heuristic 'bound decrease' for H0*n relabels,
311    //        starts with 'highest label'
312    //   Parameters H0 and H1 are initialized to 20 and 1.
313
314
315    ///Runs the second phase of the preflow algorithm.
316
317    ///The preflow algorithm consists of two phases, this method runs
318    ///the second phase. After calling \ref phase1() and then
319    ///\ref phase2(),
320    /// \ref flowMap() return a maximum flow, \ref flowValue
321    ///returns the value of a maximum flow, \ref minCut returns a
322    ///minimum cut, while the methods \ref minMinCut and \ref
323    ///maxMinCut return the inclusionwise minimum and maximum cuts of
324    ///minimum value, resp.  \pre \ref phase1 must be called before.
325    ///
326    /// \todo The inexact computation can cause positive excess on a set of
327    /// unpushable nodes. We may have to watch the empty level in this case
328    /// due to avoid the terrible long running time.
329    void phase2()
330    {
331
332      int k=_node_num-2;  //bound on the highest level under n containing a node
333      int b=k;    //bound on the highest level under n of an active node
334
335   
336      VecNode first(_node_num, INVALID);
337      NNMap next(*_g, INVALID);
338      level.set(_source,0);
339      std::queue<Node> bfs_queue;
340      bfs_queue.push(_source);
341
342      while ( !bfs_queue.empty() ) {
343
344        Node v=bfs_queue.front();
345        bfs_queue.pop();
346        int l=level[v]+1;
347
348        for(InEdgeIt e(*_g,v); e!=INVALID; ++e) {
349          if ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue;
350          Node u=_g->source(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        for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) {
362          if ( !_surely.positive((*_flow)[e]) ) continue;
363          Node u=_g->target(e);
364          if ( level[u] >= _node_num ) {
365            bfs_queue.push(u);
366            level.set(u, l);
367            if ( excess[u] != 0 ) {
368              next.set(u,first[l]);
369              first[l]=u;
370            }
371          }
372        }
373      }
374      b=_node_num-2;
375
376      while ( true ) {
377
378        if ( b == 0 ) break;
379        if ( first[b]==INVALID ) --b;
380        else {
381          Node w=first[b];
382          first[b]=next[w];
383          int newlevel=push(w,next, first);
384         
385          if ( newlevel == _node_num) {
386            excess.set(w, 0);
387            level.set(w,_node_num);
388          }
389          //relabel
390          if ( excess[w] != 0 ) {
391            level.set(w,++newlevel);
392            next.set(w,first[newlevel]);
393            first[newlevel]=w;
394            b=newlevel;
395          }
396        }
397      } // while(true)
398      flow_prop=GEN_FLOW;
399      status=AFTER_PREFLOW_PHASE_2;
400    }
401
402    /// Returns the value of the maximum flow.
403
404    /// Returns the value of the maximum flow by returning the excess
405    /// of the target node \c t. This value equals to the value of
406    /// the maximum flow already after running \ref phase1.
407    Num flowValue() const {
408      return excess[_target];
409    }
410
411
412    ///Returns a minimum value cut.
413
414    ///Sets \c M to the characteristic vector of a minimum value
415    ///cut. This method can be called both after running \ref
416    ///phase1 and \ref phase2. It is much faster after
417    ///\ref phase1.  \pre M should be a bool-valued node-map. \pre
418    ///If \ref minCut() is called after \ref phase2() then M should
419    ///be initialized to false.
420    template<typename _CutMap>
421    void minCut(_CutMap& M) const {
422      switch ( status ) {
423        case AFTER_PREFLOW_PHASE_1:
424        for(NodeIt v(*_g); v!=INVALID; ++v) {
425          if (level[v] < _node_num) {
426            M.set(v, false);
427          } else {
428            M.set(v, true);
429          }
430        }
431        break;
432        case AFTER_PREFLOW_PHASE_2:
433        minMinCut(M);
434        break;
435        case AFTER_NOTHING:
436        break;
437      }
438    }
439
440    ///Returns the inclusionwise minimum of the minimum value cuts.
441
442    ///Sets \c M to the characteristic vector of the minimum value cut
443    ///which is inclusionwise minimum. It is computed by processing a
444    ///bfs from the source node \c s in the residual graph.  \pre M
445    ///should be a node map of bools initialized to false.  \pre \ref
446    ///phase2 should already be run.
447    template<typename _CutMap>
448    void minMinCut(_CutMap& M) const {
449
450      std::queue<Node> queue;
451      M.set(_source,true);
452      queue.push(_source);
453     
454      while (!queue.empty()) {
455        Node w=queue.front();
456        queue.pop();
457       
458        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
459          Node v=_g->target(e);
460          if (!M[v] && _surely.positive((*_capacity)[e] -(*_flow)[e]) ) {
461            queue.push(v);
462            M.set(v, true);
463          }
464        }
465       
466        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
467          Node v=_g->source(e);
468          if (!M[v] && _surely.positive((*_flow)[e]) ) {
469            queue.push(v);
470            M.set(v, true);
471          }
472        }
473      }
474    }
475   
476    ///Returns the inclusionwise maximum of the minimum value cuts.
477
478    ///Sets \c M to the characteristic vector of the minimum value cut
479    ///which is inclusionwise maximum. It is computed by processing a
480    ///backward bfs from the target node \c t in the residual graph.
481    ///\pre \ref phase2() or run() should already be run.
482    template<typename _CutMap>
483    void maxMinCut(_CutMap& M) const {
484
485      for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true);
486
487      std::queue<Node> queue;
488
489      M.set(_target,false);
490      queue.push(_target);
491
492      while (!queue.empty()) {
493        Node w=queue.front();
494        queue.pop();
495
496        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
497          Node v=_g->source(e);
498          if (M[v] && _surely.positive((*_capacity)[e] - (*_flow)[e]) ) {
499            queue.push(v);
500            M.set(v, false);
501          }
502        }
503
504        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
505          Node v=_g->target(e);
506          if (M[v] && _surely.positive((*_flow)[e]) ) {
507            queue.push(v);
508            M.set(v, false);
509          }
510        }
511      }
512    }
513
514    ///Sets the source node to \c _s.
515
516    ///Sets the source node to \c _s.
517    ///
518    void source(Node _s) {
519      _source=_s;
520      if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
521      status=AFTER_NOTHING;
522    }
523
524    ///Returns the source node.
525
526    ///Returns the source node.
527    ///
528    Node source() const {
529      return _source;
530    }
531
532    ///Sets the target node to \c _t.
533
534    ///Sets the target node to \c _t.
535    ///
536    void target(Node _t) {
537      _target=_t;
538      if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
539      status=AFTER_NOTHING;
540    }
541
542    ///Returns the target node.
543
544    ///Returns the target node.
545    ///
546    Node target() const {
547      return _target;
548    }
549
550    /// Sets the edge map of the capacities to _cap.
551
552    /// Sets the edge map of the capacities to _cap.
553    ///
554    void capacityMap(const CapacityMap& _cap) {
555      _capacity=&_cap;
556      status=AFTER_NOTHING;
557    }
558    /// Returns a reference to capacity map.
559
560    /// Returns a reference to capacity map.
561    ///
562    const CapacityMap &capacityMap() const {
563      return *_capacity;
564    }
565
566    /// Sets the edge map of the flows to _flow.
567
568    /// Sets the edge map of the flows to _flow.
569    ///
570    void flowMap(FlowMap& _f) {
571      _flow=&_f;
572      flow_prop=NO_FLOW;
573      status=AFTER_NOTHING;
574    }
575     
576    /// Returns a reference to flow map.
577
578    /// Returns a reference to flow map.
579    ///
580    const FlowMap &flowMap() const {
581      return *_flow;
582    }
583
584  private:
585
586    int push(Node w, NNMap& next, VecNode& first) {
587
588      int lev=level[w];
589      Num exc=excess[w];
590      int newlevel=_node_num;       //bound on the next level of w
591
592      for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
593        if ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue;
594        Node v=_g->target(e);
595       
596        if( lev > level[v] ) { //Push is allowed now
597         
598          if ( excess[v] == 0 && v!=_target && v!=_source ) {
599            next.set(v,first[level[v]]);
600            first[level[v]]=v;
601          }
602
603          Num cap=(*_capacity)[e];
604          Num flo=(*_flow)[e];
605          Num remcap=cap-flo;
606         
607          if ( ! _surely.less(remcap, exc) ) { //A nonsaturating push.
608           
609            _flow->set(e, flo+exc);
610            excess.set(v, excess[v]+exc);
611            exc=0;
612            break;
613
614          } else { //A saturating push.
615            _flow->set(e, cap);
616            excess.set(v, excess[v]+remcap);
617            exc-=remcap;
618          }
619        } else if ( newlevel > level[v] ) newlevel = level[v];
620      } //for out edges wv
621
622      if ( exc != 0 ) {
623        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
624         
625          if ( !_surely.positive((*_flow)[e]) ) continue;
626          Node v=_g->source(e);
627         
628          if( lev > level[v] ) { //Push is allowed now
629
630            if ( excess[v] == 0 && v!=_target && v!=_source ) {
631              next.set(v,first[level[v]]);
632              first[level[v]]=v;
633            }
634
635            Num flo=(*_flow)[e];
636
637            if ( !_surely.less(flo, exc) ) { //A nonsaturating push.
638
639              _flow->set(e, flo-exc);
640              excess.set(v, excess[v]+exc);
641              exc=0;
642              break;
643            } else {  //A saturating push.
644
645              excess.set(v, excess[v]+flo);
646              exc-=flo;
647              _flow->set(e,0);
648            }
649          } else if ( newlevel > level[v] ) newlevel = level[v];
650        } //for in edges vw
651
652      } // if w still has excess after the out edge for cycle
653
654      excess.set(w, exc);
655     
656      return newlevel;
657    }
658   
659   
660   
661    void preflowPreproc(VecNode& first, NNMap& next,
662                        VecNode& level_list, NNMap& left, NNMap& right)
663    {
664      for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num);
665      std::queue<Node> bfs_queue;
666     
667      if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) {
668        //Reverse_bfs from t in the residual graph,
669        //to find the starting level.
670        level.set(_target,0);
671        bfs_queue.push(_target);
672       
673        while ( !bfs_queue.empty() ) {
674         
675          Node v=bfs_queue.front();
676          bfs_queue.pop();
677          int l=level[v]+1;
678         
679          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
680            if ( !_surely.positive((*_capacity)[e] - (*_flow)[e] )) continue;
681            Node w=_g->source(e);
682            if ( level[w] == _node_num && w != _source ) {
683              bfs_queue.push(w);
684              Node z=level_list[l];
685              if ( z!=INVALID ) left.set(z,w);
686              right.set(w,z);
687              level_list[l]=w;
688              level.set(w, l);
689            }
690          }
691         
692          for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
693            if ( !_surely.positive((*_flow)[e]) ) continue;
694            Node w=_g->target(e);
695            if ( level[w] == _node_num && w != _source ) {
696              bfs_queue.push(w);
697              Node z=level_list[l];
698              if ( z!=INVALID ) left.set(z,w);
699              right.set(w,z);
700              level_list[l]=w;
701              level.set(w, l);
702            }
703          }
704        } //while
705      } //if
706
707
708      switch (flow_prop) {
709        case NO_FLOW: 
710        for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0);
711        case ZERO_FLOW:
712        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
713       
714        //Reverse_bfs from t, to find the starting level.
715        level.set(_target,0);
716        bfs_queue.push(_target);
717       
718        while ( !bfs_queue.empty() ) {
719         
720          Node v=bfs_queue.front();
721          bfs_queue.pop();
722          int l=level[v]+1;
723         
724          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
725            Node w=_g->source(e);
726            if ( level[w] == _node_num && w != _source ) {
727              bfs_queue.push(w);
728              Node z=level_list[l];
729              if ( z!=INVALID ) left.set(z,w);
730              right.set(w,z);
731              level_list[l]=w;
732              level.set(w, l);
733            }
734          }
735        }
736       
737        //the starting flow
738        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
739          Num c=(*_capacity)[e];
740          if ( !_surely.positive(c) ) continue;
741          Node w=_g->target(e);
742          if ( level[w] < _node_num ) {
743            if ( excess[w] == 0 && w!=_target ) { //putting into the stack
744              next.set(w,first[level[w]]);
745              first[level[w]]=w;
746            }
747            _flow->set(e, c);
748            excess.set(w, excess[w]+c);
749          }
750        }
751        break;
752
753        case GEN_FLOW:
754        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
755        {
756          Num exc=0;
757          for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e];
758          for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e];
759          if (!_surely.positive(exc)) {
760            exc = 0;
761          }
762          excess.set(_target,exc);
763        }
764
765        //the starting flow
766        for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e)  {
767          Num rem=(*_capacity)[e]-(*_flow)[e];
768          if ( !_surely.positive(rem) ) continue;
769          Node w=_g->target(e);
770          if ( level[w] < _node_num ) {
771            if ( excess[w] == 0 && w!=_target ) { //putting into the stack
772              next.set(w,first[level[w]]);
773              first[level[w]]=w;
774            }   
775            _flow->set(e, (*_capacity)[e]);
776            excess.set(w, excess[w]+rem);
777          }
778        }
779       
780        for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) {
781          if ( !_surely.positive((*_flow)[e]) ) continue;
782          Node w=_g->source(e);
783          if ( level[w] < _node_num ) {
784            if ( excess[w] == 0 && w!=_target ) {
785              next.set(w,first[level[w]]);
786              first[level[w]]=w;
787            } 
788            excess.set(w, excess[w]+(*_flow)[e]);
789            _flow->set(e, 0);
790          }
791        }
792        break;
793
794        case PRE_FLOW: 
795        //the starting flow
796        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
797          Num rem=(*_capacity)[e]-(*_flow)[e];
798          if ( !_surely.positive(rem) ) continue;
799          Node w=_g->target(e);
800          if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]);
801        }
802       
803        for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
804          if ( !_surely.positive((*_flow)[e]) ) continue;
805          Node w=_g->source(e);
806          if ( level[w] < _node_num ) _flow->set(e, 0);
807        }
808       
809        //computing the excess
810        for(NodeIt w(*_g); w!=INVALID; ++w) {
811          Num exc=0;
812          for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e];
813          for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e];
814          if (!_surely.positive(exc)) {
815            exc = 0;
816          }
817          excess.set(w,exc);
818         
819          //putting the active nodes into the stack
820          int lev=level[w];
821            if ( exc != 0 && lev < _node_num && Node(w) != _target ) {
822              next.set(w,first[lev]);
823              first[lev]=w;
824            }
825        }
826        break;
827      } //switch
828    } //preflowPreproc
829
830
831    void relabel(Node w, int newlevel, VecNode& first, NNMap& next,
832                 VecNode& level_list, NNMap& left,
833                 NNMap& right, int& b, int& k, bool what_heur )
834    {
835
836      int lev=level[w];
837
838      Node right_n=right[w];
839      Node left_n=left[w];
840
841      //unlacing starts
842      if ( right_n!=INVALID ) {
843        if ( left_n!=INVALID ) {
844          right.set(left_n, right_n);
845          left.set(right_n, left_n);
846        } else {
847          level_list[lev]=right_n;
848          left.set(right_n, INVALID);
849        }
850      } else {
851        if ( left_n!=INVALID ) {
852          right.set(left_n, INVALID);
853        } else {
854          level_list[lev]=INVALID;
855        }
856      }
857      //unlacing ends
858
859      if ( level_list[lev]==INVALID ) {
860
861        //gapping starts
862        for (int i=lev; i!=k ; ) {
863          Node v=level_list[++i];
864          while ( v!=INVALID ) {
865            level.set(v,_node_num);
866            v=right[v];
867          }
868          level_list[i]=INVALID;
869          if ( !what_heur ) first[i]=INVALID;
870        }
871
872        level.set(w,_node_num);
873        b=lev-1;
874        k=b;
875        //gapping ends
876
877      } else {
878
879        if ( newlevel == _node_num ) level.set(w,_node_num);
880        else {
881          level.set(w,++newlevel);
882          next.set(w,first[newlevel]);
883          first[newlevel]=w;
884          if ( what_heur ) b=newlevel;
885          if ( k < newlevel ) ++k;      //now k=newlevel
886          Node z=level_list[newlevel];
887          if ( z!=INVALID ) left.set(z,w);
888          right.set(w,z);
889          left.set(w,INVALID);
890          level_list[newlevel]=w;
891        }
892      }
893    } //relabel
894
895  };
896
897  ///\ingroup max_flow
898  ///\brief Function type interface for Preflow algorithm.
899  ///
900  ///Function type interface for Preflow algorithm.
901  ///\sa Preflow
902  template<class GR, class CM, class FM>
903  Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g,
904                            typename GR::Node source,
905                            typename GR::Node target,
906                            const CM &cap,
907                            FM &flow
908                            )
909  {
910    return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow);
911  }
912
913} //namespace lemon
914
915#endif //LEMON_PREFLOW_H
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