COIN-OR::LEMON - Graph Library

source: lemon-0.x/lemon/preflow.h @ 2033:7bf1f64962c2

Last change on this file since 2033:7bf1f64962c2 was 2033:7bf1f64962c2, checked in by Balazs Dezso, 14 years ago

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[906]1/* -*- C++ -*-
2 *
[1956]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
[1359]7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
[906]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
[921]19#ifndef LEMON_PREFLOW_H
20#define LEMON_PREFLOW_H
[836]21
22#include <vector>
23#include <queue>
24
[1762]25#include <lemon/error.h>
[1993]26#include <lemon/bits/invalid.h>
[1835]27#include <lemon/tolerance.h>
[921]28#include <lemon/maps.h>
[977]29#include <lemon/graph_utils.h>
[836]30
31/// \file
32/// \ingroup flowalgs
[1742]33/// \brief Implementation of the preflow algorithm.
[836]34
[921]35namespace lemon {
[836]36
[1792]37  ///\ingroup flowalgs
38  ///\brief %Preflow algorithms class.
39  ///
[836]40  ///This class provides an implementation of the \e preflow \e
41  ///algorithm producing a flow of maximum value in a directed
[2024]42  ///graph. The preflow algorithms are the fastest known max flow algorithms.
43  ///The \e source node, the \e target node, the \e
[836]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
[1285]47  ///functions \ref source, \ref target, \ref capacityMap and \ref
48  ///flowMap.
[836]49  ///
[921]50  ///After running \ref lemon::Preflow::phase1() "phase1()"
51  ///or \ref lemon::Preflow::run() "run()", the maximal flow
[836]52  ///value can be obtained by calling \ref flowValue(). The minimum
[851]53  ///value cut can be written into a <tt>bool</tt> node map by
54  ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes
[836]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.
[1222]60  ///\param CapacityMap The capacity map type.
[836]61  ///\param FlowMap The flow map type.
[2024]62  ///\param Tolerance The tolerance type.
[836]63  ///
64  ///\author Jacint Szabo
[1227]65  ///\todo Second template parameter is superfluous
[836]66  template <typename Graph, typename Num,
[1222]67            typename CapacityMap=typename Graph::template EdgeMap<Num>,
[1835]68            typename FlowMap=typename Graph::template EdgeMap<Num>,
[2019]69            typename Tolerance=Tolerance<Num> >
[836]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
[1222]81    const Graph* _g;
82    Node _source;
83    Node _target;
84    const CapacityMap* _capacity;
85    FlowMap* _flow;
[1835]86
[2019]87    Tolerance _surely;
[1835]88   
[1222]89    int _node_num;      //the number of nodes of G
[836]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
[1762]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 {
[836]104    public:
[1762]105      virtual const char* exceptionName() const {
106        return "lemon::Preflow::InvalidArgument";
107      }
108    };
109   
110   
[836]111    ///Indicates the property of the starting flow map.
[1762]112   
[1222]113    ///Indicates the property of the starting flow map.
[836]114    ///
115    enum FlowEnum{
[1898]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.
[836]119      NO_FLOW,
[1898]120      ///constant zero flow
[836]121      ZERO_FLOW,
[1898]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.
[836]125      GEN_FLOW,
[1898]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.
[836]128      PRE_FLOW
129    };
130
131    ///Indicates the state of the preflow algorithm.
132
[1222]133    ///Indicates the state of the preflow algorithm.
[836]134    ///
135    enum StatusEnum {
[1898]136      ///before running the algorithm or
137      ///at an unspecified state.
[836]138      AFTER_NOTHING,
[1898]139      ///right after running \ref phase1()
[836]140      AFTER_PREFLOW_PHASE_1,     
[1898]141      ///after running \ref phase2()
[836]142      AFTER_PREFLOW_PHASE_2
143    };
144   
[1762]145  protected:
146    FlowEnum flow_prop;
[836]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.
[1285]153    ///\param _gr The directed graph the algorithm runs on.
[836]154    ///\param _s The source node.
155    ///\param _t The target node.
[1222]156    ///\param _cap The capacity of the edges.
157    ///\param _f The flow of the edges.
[1953]158    ///\param tol Tolerance class.
[836]159    ///Except the graph, all of these parameters can be reset by
[1285]160    ///calling \ref source, \ref target, \ref capacityMap and \ref
161    ///flowMap, resp.
[2033]162    Preflow(const Graph& _gr, Node _s, Node _t,
163            const CapacityMap& _cap, FlowMap& _f,
164            const Tolerance &_sr=Tolerance()) :
[1222]165        _g(&_gr), _source(_s), _target(_t), _capacity(&_cap),
[2019]166        _flow(&_f), _surely(_sr),
[1835]167        _node_num(countNodes(_gr)), level(_gr), excess(_gr,0),
[1762]168        flow_prop(NO_FLOW), status(AFTER_NOTHING) {
169        if ( _source==_target )
170          throw InvalidArgument();
[2033]171    }
[1762]172   
[1898]173    ///Give a reference to the tolerance handler class
[836]174
[1898]175    ///Give a reference to the tolerance handler class
176    ///\sa Tolerance
[2019]177    Tolerance &tolerance() { return _surely; }
[1898]178
[836]179    ///Runs the preflow algorithm. 
180
[851]181    ///Runs the preflow algorithm.
182    ///
[836]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
[920]205    ///The preflow algorithm consists of two phases, this method runs
206    ///the first phase. After the first phase the maximum flow value
[1285]207    ///and a minimum value cut can already be computed, although a
[920]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.
[836]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
[920]227    ///The preflow algorithm consists of two phases, this method runs
228    ///the first phase. After the first phase the maximum flow value
[1285]229    ///and a minimum value cut can already be computed, although a
[920]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.
[1786]233    ///\warning \ref minMinCut() and \ref maxMinCut() do not
[911]234    ///give minimum value cuts unless calling \ref phase2().
[836]235    void phase1()
236    {
[1222]237      int heur0=(int)(H0*_node_num);  //time while running 'bound decrease'
238      int heur1=(int)(H1*_node_num);  //time while running 'highest label'
[836]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
[1222]249      int k=_node_num-2;  //bound on the highest level under n containing a node
[2024]250      int b=k;    //bound on the highest level under n containing an active node
[836]251
[1222]252      VecNode first(_node_num, INVALID);
253      NNMap next(*_g, INVALID);
[836]254
[1222]255      NNMap left(*_g, INVALID);
256      NNMap right(*_g, INVALID);
257      VecNode level_list(_node_num,INVALID);
[836]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);
[2024]277          if ( _surely.positive(excess[w]) ) relabel(w, newlevel, first, next, level_list,
[836]278                                       left, right, b, k, what_heur);
279
280          ++numrelabel;
281          if ( numrelabel >= heur ) {
282            numrelabel=0;
283            if ( what_heur ) {
284              what_heur=0;
285              heur=heur0;
286              end=false;
287            } else {
288              what_heur=1;
289              heur=heur1;
290              b=k;
291            }
292          }
293        }
294      }
295      flow_prop=PRE_FLOW;
296      status=AFTER_PREFLOW_PHASE_1;
297    }
298    // Heuristics:
299    //   2 phase
300    //   gap
301    //   list 'level_list' on the nodes on level i implemented by hand
302    //   stack 'active' on the active nodes on level i     
303    //   runs heuristic 'highest label' for H1*n relabels
[1222]304    //   runs heuristic 'bound decrease' for H0*n relabels,
305    //        starts with 'highest label'
[836]306    //   Parameters H0 and H1 are initialized to 20 and 1.
307
308
309    ///Runs the second phase of the preflow algorithm.
310
311    ///The preflow algorithm consists of two phases, this method runs
[1631]312    ///the second phase. After calling \ref phase1() and then
313    ///\ref phase2(),
314    /// \ref flowMap() return a maximum flow, \ref flowValue
[920]315    ///returns the value of a maximum flow, \ref minCut returns a
316    ///minimum cut, while the methods \ref minMinCut and \ref
317    ///maxMinCut return the inclusionwise minimum and maximum cuts of
318    ///minimum value, resp.  \pre \ref phase1 must be called before.
[836]319    void phase2()
320    {
321
[1222]322      int k=_node_num-2;  //bound on the highest level under n containing a node
[836]323      int b=k;    //bound on the highest level under n of an active node
324
325   
[1222]326      VecNode first(_node_num, INVALID);
327      NNMap next(*_g, INVALID);
328      level.set(_source,0);
[836]329      std::queue<Node> bfs_queue;
[1222]330      bfs_queue.push(_source);
[836]331
332      while ( !bfs_queue.empty() ) {
333
334        Node v=bfs_queue.front();
335        bfs_queue.pop();
336        int l=level[v]+1;
337
[1222]338        for(InEdgeIt e(*_g,v); e!=INVALID; ++e) {
[2024]339          if ( !_surely.less((*_flow)[e], (*_capacity)[e]) ) continue;
[1222]340          Node u=_g->source(e);
341          if ( level[u] >= _node_num ) {
[836]342            bfs_queue.push(u);
343            level.set(u, l);
[2024]344            if ( _surely.positive(excess[u]) ) {
[836]345              next.set(u,first[l]);
346              first[l]=u;
347            }
348          }
349        }
350
[1222]351        for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) {
[2024]352          if ( !_surely.positive((*_flow)[e]) ) continue;
[1222]353          Node u=_g->target(e);
354          if ( level[u] >= _node_num ) {
[836]355            bfs_queue.push(u);
356            level.set(u, l);
[2024]357            if ( _surely.positive(excess[u]) ) {
[836]358              next.set(u,first[l]);
359              first[l]=u;
360            }
361          }
362        }
363      }
[1222]364      b=_node_num-2;
[836]365
366      while ( true ) {
367
368        if ( b == 0 ) break;
369        if ( first[b]==INVALID ) --b;
370        else {
371          Node w=first[b];
372          first[b]=next[w];
373          int newlevel=push(w,next, first);
374         
375          //relabel
[2024]376          if ( _surely.positive(excess[w]) ) {
[836]377            level.set(w,++newlevel);
378            next.set(w,first[newlevel]);
379            first[newlevel]=w;
380            b=newlevel;
381          }
382        }
383      } // while(true)
384      flow_prop=GEN_FLOW;
385      status=AFTER_PREFLOW_PHASE_2;
386    }
387
388    /// Returns the value of the maximum flow.
389
390    /// Returns the value of the maximum flow by returning the excess
[911]391    /// of the target node \c t. This value equals to the value of
[836]392    /// the maximum flow already after running \ref phase1.
393    Num flowValue() const {
[1222]394      return excess[_target];
[836]395    }
396
397
398    ///Returns a minimum value cut.
399
400    ///Sets \c M to the characteristic vector of a minimum value
401    ///cut. This method can be called both after running \ref
402    ///phase1 and \ref phase2. It is much faster after
[849]403    ///\ref phase1.  \pre M should be a bool-valued node-map. \pre
[911]404    ///If \ref minCut() is called after \ref phase2() then M should
[836]405    ///be initialized to false.
406    template<typename _CutMap>
407    void minCut(_CutMap& M) const {
408      switch ( status ) {
409        case AFTER_PREFLOW_PHASE_1:
[1222]410        for(NodeIt v(*_g); v!=INVALID; ++v) {
411          if (level[v] < _node_num) {
[836]412            M.set(v, false);
413          } else {
414            M.set(v, true);
415          }
416        }
417        break;
418        case AFTER_PREFLOW_PHASE_2:
419        minMinCut(M);
420        break;
421        case AFTER_NOTHING:
422        break;
423      }
424    }
425
426    ///Returns the inclusionwise minimum of the minimum value cuts.
427
428    ///Sets \c M to the characteristic vector of the minimum value cut
429    ///which is inclusionwise minimum. It is computed by processing a
430    ///bfs from the source node \c s in the residual graph.  \pre M
431    ///should be a node map of bools initialized to false.  \pre \ref
432    ///phase2 should already be run.
433    template<typename _CutMap>
434    void minMinCut(_CutMap& M) const {
435
436      std::queue<Node> queue;
[1222]437      M.set(_source,true);
[1227]438      queue.push(_source);
[836]439     
440      while (!queue.empty()) {
441        Node w=queue.front();
442        queue.pop();
443       
[1222]444        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
445          Node v=_g->target(e);
[2024]446          if (!M[v] && _surely.less((*_flow)[e] , (*_capacity)[e]) ) {
[836]447            queue.push(v);
448            M.set(v, true);
449          }
450        }
451       
[1222]452        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
453          Node v=_g->source(e);
[2024]454          if (!M[v] && _surely.positive((*_flow)[e]) ) {
[836]455            queue.push(v);
456            M.set(v, true);
457          }
458        }
459      }
460    }
461   
462    ///Returns the inclusionwise maximum of the minimum value cuts.
463
464    ///Sets \c M to the characteristic vector of the minimum value cut
465    ///which is inclusionwise maximum. It is computed by processing a
466    ///backward bfs from the target node \c t in the residual graph.
[911]467    ///\pre \ref phase2() or run() should already be run.
[836]468    template<typename _CutMap>
469    void maxMinCut(_CutMap& M) const {
470
[1222]471      for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true);
[836]472
473      std::queue<Node> queue;
474
[1222]475      M.set(_target,false);
476      queue.push(_target);
[836]477
478      while (!queue.empty()) {
479        Node w=queue.front();
480        queue.pop();
481
[1222]482        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
483          Node v=_g->source(e);
[2024]484          if (M[v] && _surely.less((*_flow)[e], (*_capacity)[e]) ) {
[836]485            queue.push(v);
486            M.set(v, false);
487          }
488        }
489
[1222]490        for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
491          Node v=_g->target(e);
[2024]492          if (M[v] && _surely.positive((*_flow)[e]) ) {
[836]493            queue.push(v);
494            M.set(v, false);
495          }
496        }
497      }
498    }
499
500    ///Sets the source node to \c _s.
501
502    ///Sets the source node to \c _s.
503    ///
[1222]504    void source(Node _s) {
505      _source=_s;
[836]506      if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
507      status=AFTER_NOTHING;
508    }
509
[1222]510    ///Returns the source node.
511
512    ///Returns the source node.
513    ///
514    Node source() const {
515      return _source;
516    }
517
[836]518    ///Sets the target node to \c _t.
519
520    ///Sets the target node to \c _t.
521    ///
[1222]522    void target(Node _t) {
523      _target=_t;
[836]524      if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
525      status=AFTER_NOTHING;
526    }
527
[1222]528    ///Returns the target node.
529
530    ///Returns the target node.
531    ///
532    Node target() const {
533      return _target;
534    }
535
[836]536    /// Sets the edge map of the capacities to _cap.
537
538    /// Sets the edge map of the capacities to _cap.
539    ///
[1222]540    void capacityMap(const CapacityMap& _cap) {
541      _capacity=&_cap;
[836]542      status=AFTER_NOTHING;
543    }
[1285]544    /// Returns a reference to capacity map.
[1222]545
[1285]546    /// Returns a reference to capacity map.
[1222]547    ///
548    const CapacityMap &capacityMap() const {
549      return *_capacity;
550    }
[836]551
552    /// Sets the edge map of the flows to _flow.
553
554    /// Sets the edge map of the flows to _flow.
555    ///
[1222]556    void flowMap(FlowMap& _f) {
557      _flow=&_f;
[836]558      flow_prop=NO_FLOW;
559      status=AFTER_NOTHING;
560    }
[1222]561     
[1285]562    /// Returns a reference to flow map.
[836]563
[1285]564    /// Returns a reference to flow map.
[1222]565    ///
566    const FlowMap &flowMap() const {
567      return *_flow;
568    }
[836]569
570  private:
571
572    int push(Node w, NNMap& next, VecNode& first) {
573
574      int lev=level[w];
575      Num exc=excess[w];
[1222]576      int newlevel=_node_num;       //bound on the next level of w
[836]577
[1222]578      for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
[2024]579        if ( !_surely.less((*_flow)[e], (*_capacity)[e]) ) continue;
[1222]580        Node v=_g->target(e);
[2024]581       
[836]582        if( lev > level[v] ) { //Push is allowed now
583         
[2024]584          if ( !_surely.positive(excess[v]) && v!=_target && v!=_source ) {
[836]585            next.set(v,first[level[v]]);
586            first[level[v]]=v;
587          }
588
[1222]589          Num cap=(*_capacity)[e];
590          Num flo=(*_flow)[e];
[836]591          Num remcap=cap-flo;
592         
[2024]593          if ( ! _surely.less(remcap, exc) ) { //A nonsaturating push.
[836]594           
[1222]595            _flow->set(e, flo+exc);
[836]596            excess.set(v, excess[v]+exc);
597            exc=0;
598            break;
599
600          } else { //A saturating push.
[1222]601            _flow->set(e, cap);
[836]602            excess.set(v, excess[v]+remcap);
603            exc-=remcap;
604          }
605        } else if ( newlevel > level[v] ) newlevel = level[v];
606      } //for out edges wv
607
[2024]608      if ( _surely.positive(exc) ) {
[1222]609        for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) {
[836]610         
[2024]611          if ( !_surely.positive((*_flow)[e]) ) continue;
[1222]612          Node v=_g->source(e);
[2024]613         
[836]614          if( lev > level[v] ) { //Push is allowed now
615
[2024]616            if ( !_surely.positive(excess[v]) && v!=_target && v!=_source ) {
[836]617              next.set(v,first[level[v]]);
618              first[level[v]]=v;
619            }
620
[1222]621            Num flo=(*_flow)[e];
[836]622
[2024]623            if ( !_surely.less(flo, exc) ) { //A nonsaturating push.
[836]624
[1222]625              _flow->set(e, flo-exc);
[836]626              excess.set(v, excess[v]+exc);
627              exc=0;
628              break;
629            } else {  //A saturating push.
630
631              excess.set(v, excess[v]+flo);
632              exc-=flo;
[1222]633              _flow->set(e,0);
[836]634            }
635          } else if ( newlevel > level[v] ) newlevel = level[v];
636        } //for in edges vw
637
638      } // if w still has excess after the out edge for cycle
639
640      excess.set(w, exc);
641     
642      return newlevel;
643    }
644   
645   
646   
647    void preflowPreproc(VecNode& first, NNMap& next,
648                        VecNode& level_list, NNMap& left, NNMap& right)
649    {
[1222]650      for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num);
[836]651      std::queue<Node> bfs_queue;
652     
653      if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) {
654        //Reverse_bfs from t in the residual graph,
655        //to find the starting level.
[1222]656        level.set(_target,0);
657        bfs_queue.push(_target);
[836]658       
659        while ( !bfs_queue.empty() ) {
660         
661          Node v=bfs_queue.front();
662          bfs_queue.pop();
663          int l=level[v]+1;
664         
[1222]665          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
[2024]666            if ( !_surely.less((*_flow)[e],(*_capacity)[e]) ) continue;
[1222]667            Node w=_g->source(e);
668            if ( level[w] == _node_num && w != _source ) {
[836]669              bfs_queue.push(w);
670              Node z=level_list[l];
671              if ( z!=INVALID ) left.set(z,w);
672              right.set(w,z);
673              level_list[l]=w;
674              level.set(w, l);
675            }
676          }
677         
[1222]678          for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
[2024]679            if ( !_surely.positive((*_flow)[e]) ) continue;
[1222]680            Node w=_g->target(e);
681            if ( level[w] == _node_num && w != _source ) {
[836]682              bfs_queue.push(w);
683              Node z=level_list[l];
684              if ( z!=INVALID ) left.set(z,w);
685              right.set(w,z);
686              level_list[l]=w;
687              level.set(w, l);
688            }
689          }
690        } //while
691      } //if
692
693
694      switch (flow_prop) {
695        case NO_FLOW: 
[1222]696        for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0);
[836]697        case ZERO_FLOW:
[1222]698        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
[836]699       
700        //Reverse_bfs from t, to find the starting level.
[1222]701        level.set(_target,0);
702        bfs_queue.push(_target);
[836]703       
704        while ( !bfs_queue.empty() ) {
705         
706          Node v=bfs_queue.front();
707          bfs_queue.pop();
708          int l=level[v]+1;
709         
[1222]710          for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) {
711            Node w=_g->source(e);
712            if ( level[w] == _node_num && w != _source ) {
[836]713              bfs_queue.push(w);
714              Node z=level_list[l];
715              if ( z!=INVALID ) left.set(z,w);
716              right.set(w,z);
717              level_list[l]=w;
718              level.set(w, l);
719            }
720          }
721        }
722       
723        //the starting flow
[1222]724        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
725          Num c=(*_capacity)[e];
[2024]726          if ( !_surely.positive(c) ) continue;
[1222]727          Node w=_g->target(e);
728          if ( level[w] < _node_num ) {
[2024]729            if ( !_surely.positive(excess[w]) && w!=_target ) { //putting into the stack
[836]730              next.set(w,first[level[w]]);
731              first[level[w]]=w;
732            }
[1222]733            _flow->set(e, c);
[836]734            excess.set(w, excess[w]+c);
735          }
736        }
737        break;
738
739        case GEN_FLOW:
[1222]740        for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0);
[836]741        {
742          Num exc=0;
[1222]743          for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e];
744          for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e];
745          excess.set(_target,exc);
[836]746        }
747
748        //the starting flow
[1222]749        for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e)  {
750          Num rem=(*_capacity)[e]-(*_flow)[e];
[2024]751          if ( !_surely.positive(rem) ) continue;
[1222]752          Node w=_g->target(e);
753          if ( level[w] < _node_num ) {
[2024]754            if ( !_surely.positive(excess[w]) && w!=_target ) { //putting into the stack
[836]755              next.set(w,first[level[w]]);
756              first[level[w]]=w;
757            }   
[1222]758            _flow->set(e, (*_capacity)[e]);
[836]759            excess.set(w, excess[w]+rem);
760          }
761        }
762       
[1222]763        for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) {
[2024]764          if ( !_surely.positive((*_flow)[e]) ) continue;
[1222]765          Node w=_g->source(e);
766          if ( level[w] < _node_num ) {
[2024]767            if ( !_surely.positive(excess[w]) && w!=_target ) {
[836]768              next.set(w,first[level[w]]);
769              first[level[w]]=w;
770            } 
[1222]771            excess.set(w, excess[w]+(*_flow)[e]);
772            _flow->set(e, 0);
[836]773          }
774        }
775        break;
776
777        case PRE_FLOW: 
778        //the starting flow
[1222]779        for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
780          Num rem=(*_capacity)[e]-(*_flow)[e];
[2024]781          if ( !_surely.positive(rem) ) continue;
[1222]782          Node w=_g->target(e);
783          if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]);
[836]784        }
785       
[1222]786        for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) {
[2024]787          if ( !_surely.positive((*_flow)[e]) ) continue;
[1222]788          Node w=_g->source(e);
789          if ( level[w] < _node_num ) _flow->set(e, 0);
[836]790        }
791       
792        //computing the excess
[1222]793        for(NodeIt w(*_g); w!=INVALID; ++w) {
[836]794          Num exc=0;
[1222]795          for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e];
796          for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e];
[836]797          excess.set(w,exc);
798         
799          //putting the active nodes into the stack
800          int lev=level[w];
[2024]801            if ( _surely.positive(exc) && lev < _node_num && Node(w) != _target ) {
[836]802              next.set(w,first[lev]);
803              first[lev]=w;
804            }
805        }
806        break;
807      } //switch
808    } //preflowPreproc
809
810
811    void relabel(Node w, int newlevel, VecNode& first, NNMap& next,
812                 VecNode& level_list, NNMap& left,
813                 NNMap& right, int& b, int& k, bool what_heur )
814    {
815
816      int lev=level[w];
817
818      Node right_n=right[w];
819      Node left_n=left[w];
820
821      //unlacing starts
822      if ( right_n!=INVALID ) {
823        if ( left_n!=INVALID ) {
824          right.set(left_n, right_n);
825          left.set(right_n, left_n);
826        } else {
827          level_list[lev]=right_n;
828          left.set(right_n, INVALID);
829        }
830      } else {
831        if ( left_n!=INVALID ) {
832          right.set(left_n, INVALID);
833        } else {
834          level_list[lev]=INVALID;
835        }
836      }
837      //unlacing ends
838
839      if ( level_list[lev]==INVALID ) {
840
841        //gapping starts
842        for (int i=lev; i!=k ; ) {
843          Node v=level_list[++i];
844          while ( v!=INVALID ) {
[1222]845            level.set(v,_node_num);
[836]846            v=right[v];
847          }
848          level_list[i]=INVALID;
849          if ( !what_heur ) first[i]=INVALID;
850        }
851
[1222]852        level.set(w,_node_num);
[836]853        b=lev-1;
854        k=b;
855        //gapping ends
856
857      } else {
858
[1222]859        if ( newlevel == _node_num ) level.set(w,_node_num);
[836]860        else {
861          level.set(w,++newlevel);
862          next.set(w,first[newlevel]);
863          first[newlevel]=w;
864          if ( what_heur ) b=newlevel;
865          if ( k < newlevel ) ++k;      //now k=newlevel
866          Node z=level_list[newlevel];
867          if ( z!=INVALID ) left.set(z,w);
868          right.set(w,z);
869          left.set(w,INVALID);
870          level_list[newlevel]=w;
871        }
872      }
873    } //relabel
874
875  };
[1227]876
[1792]877  ///\ingroup flowalgs
878  ///\brief Function type interface for Preflow algorithm.
879  ///
[1227]880  ///Function type interface for Preflow algorithm.
881  ///\sa Preflow
882  template<class GR, class CM, class FM>
883  Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g,
884                            typename GR::Node source,
885                            typename GR::Node target,
886                            const CM &cap,
887                            FM &flow
888                            )
889  {
890    return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow);
891  }
892
[921]893} //namespace lemon
[836]894
[921]895#endif //LEMON_PREFLOW_H
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