src/hugo/max_flow.h
author alpar
Mon, 13 Sep 2004 11:24:35 +0000
changeset 835 eb9587f09b42
parent 773 ce9438c5a82d
permissions -rw-r--r--
Remove one remaining range checking.
     1 // -*- C++ -*-
     2 #ifndef HUGO_MAX_FLOW_H
     3 #define HUGO_MAX_FLOW_H
     4 
     5 #include <vector>
     6 #include <queue>
     7 
     8 //#include <hugo/graph_wrapper.h>
     9 #include <hugo/invalid.h>
    10 #include <hugo/maps.h>
    11 
    12 /// \file
    13 /// \ingroup flowalgs
    14 
    15 namespace hugo {
    16 
    17   /// \addtogroup flowalgs
    18   /// @{                                                   
    19 
    20   ///Maximum flow algorithms class.
    21 
    22   ///This class provides various algorithms for finding a flow of
    23   ///maximum value in a directed graph. The \e source node, the \e
    24   ///target node, the \e capacity of the edges and the \e starting \e
    25   ///flow value of the edges should be passed to the algorithm through the
    26   ///constructor. It is possible to change these quantities using the
    27   ///functions \ref setSource, \ref setTarget, \ref setCap and
    28   ///\ref setFlow. Before any subsequent runs of any algorithm of
    29   ///the class \ref setFlow should be called. 
    30   ///
    31   ///After running an algorithm of the class, the actual flow value 
    32   ///can be obtained by calling \ref flowValue(). The minimum
    33   ///value cut can be written into a \c node map of \c bools by
    34   ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes
    35   ///the inclusionwise minimum and maximum of the minimum value
    36   ///cuts, resp.)
    37   ///
    38   ///\param Graph The directed graph type the algorithm runs on.
    39   ///\param Num The number type of the capacities and the flow values.
    40   ///\param CapMap The capacity map type.
    41   ///\param FlowMap The flow map type.
    42   ///
    43   ///\author Marton Makai, Jacint Szabo 
    44   template <typename Graph, typename Num,
    45 	    typename CapMap=typename Graph::template EdgeMap<Num>,
    46             typename FlowMap=typename Graph::template EdgeMap<Num> >
    47   class MaxFlow {
    48   protected:
    49     typedef typename Graph::Node Node;
    50     typedef typename Graph::NodeIt NodeIt;
    51     typedef typename Graph::EdgeIt EdgeIt;
    52     typedef typename Graph::OutEdgeIt OutEdgeIt;
    53     typedef typename Graph::InEdgeIt InEdgeIt;
    54 
    55     typedef typename std::vector<Node> VecFirst;
    56     typedef typename Graph::template NodeMap<Node> NNMap;
    57     typedef typename std::vector<Node> VecNode;
    58 
    59     const Graph* g;
    60     Node s;
    61     Node t;
    62     const CapMap* capacity;
    63     FlowMap* flow;
    64     int n;      //the number of nodes of G
    65     //    typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;   
    66     //typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
    67     //    typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
    68     //    typedef typename ResGW::Edge ResGWEdge;
    69     typedef typename Graph::template NodeMap<int> ReachedMap;
    70 
    71 
    72     //level works as a bool map in augmenting path algorithms and is
    73     //used by bfs for storing reached information.  In preflow, it
    74     //shows the levels of nodes.     
    75     ReachedMap level;
    76 
    77     //excess is needed only in preflow
    78     typename Graph::template NodeMap<Num> excess;
    79 
    80     // constants used for heuristics
    81     static const int H0=20;
    82     static const int H1=1;
    83 
    84   public:
    85 
    86     ///Indicates the property of the starting flow.
    87 
    88     ///Indicates the property of the starting flow. The meanings are as follows:
    89     ///- \c ZERO_FLOW: constant zero flow
    90     ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
    91     ///the sum of the out-flows in every node except the \e source and
    92     ///the \e target.
    93     ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at 
    94     ///least the sum of the out-flows in every node except the \e source.
    95     ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be 
    96     ///set to the constant zero flow in the beginning of the algorithm in this case.
    97     enum FlowEnum{
    98       ZERO_FLOW,
    99       GEN_FLOW,
   100       PRE_FLOW,
   101       NO_FLOW
   102     };
   103 
   104     enum StatusEnum {
   105       AFTER_NOTHING,
   106       AFTER_AUGMENTING,
   107       AFTER_FAST_AUGMENTING, 
   108       AFTER_PRE_FLOW_PHASE_1,      
   109       AFTER_PRE_FLOW_PHASE_2
   110     };
   111 
   112     /// Do not needle this flag only if necessary.
   113     StatusEnum status;
   114 
   115     //     int number_of_augmentations;
   116 
   117 
   118     //     template<typename IntMap>
   119     //     class TrickyReachedMap {
   120     //     protected:
   121     //       IntMap* map;
   122     //       int* number_of_augmentations;
   123     //     public:
   124     //       TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : 
   125     // 	map(&_map), number_of_augmentations(&_number_of_augmentations) { }
   126     //       void set(const Node& n, bool b) {
   127     // 	if (b)
   128     // 	  map->set(n, *number_of_augmentations);
   129     // 	else 
   130     // 	  map->set(n, *number_of_augmentations-1);
   131     //       }
   132     //       bool operator[](const Node& n) const { 
   133     // 	return (*map)[n]==*number_of_augmentations; 
   134     //       }
   135     //     };
   136     
   137     ///Constructor
   138 
   139     ///\todo Document, please.
   140     ///
   141     MaxFlow(const Graph& _G, Node _s, Node _t,
   142 	    const CapMap& _capacity, FlowMap& _flow) :
   143       g(&_G), s(_s), t(_t), capacity(&_capacity),
   144       flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0), 
   145       status(AFTER_NOTHING) { }
   146 
   147     ///Runs a maximum flow algorithm.
   148 
   149     ///Runs a preflow algorithm, which is the fastest maximum flow
   150     ///algorithm up-to-date. The default for \c fe is ZERO_FLOW.
   151     ///\pre The starting flow must be
   152     /// - a constant zero flow if \c fe is \c ZERO_FLOW,
   153     /// - an arbitary flow if \c fe is \c GEN_FLOW,
   154     /// - an arbitary preflow if \c fe is \c PRE_FLOW,
   155     /// - any map if \c fe is NO_FLOW.
   156     void run(FlowEnum fe=ZERO_FLOW) {
   157       preflow(fe);
   158     }
   159 
   160                                                                               
   161     ///Runs a preflow algorithm.  
   162 
   163     ///Runs a preflow algorithm. The preflow algorithms provide the
   164     ///fastest way to compute a maximum flow in a directed graph.
   165     ///\pre The starting flow must be
   166     /// - a constant zero flow if \c fe is \c ZERO_FLOW,
   167     /// - an arbitary flow if \c fe is \c GEN_FLOW,
   168     /// - an arbitary preflow if \c fe is \c PRE_FLOW,
   169     /// - any map if \c fe is NO_FLOW.
   170     ///
   171     ///\todo NO_FLOW should be the default flow.
   172     void preflow(FlowEnum fe) {
   173       preflowPhase1(fe);
   174       preflowPhase2();
   175     }
   176     // Heuristics:
   177     //   2 phase
   178     //   gap
   179     //   list 'level_list' on the nodes on level i implemented by hand
   180     //   stack 'active' on the active nodes on level i                                                                                    
   181     //   runs heuristic 'highest label' for H1*n relabels
   182     //   runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
   183     //   Parameters H0 and H1 are initialized to 20 and 1.
   184 
   185     ///Runs the first phase of the preflow algorithm.
   186 
   187     ///The preflow algorithm consists of two phases, this method runs the
   188     ///first phase. After the first phase the maximum flow value and a
   189     ///minimum value cut can already be computed, though a maximum flow
   190     ///is not yet obtained. So after calling this method \ref flowValue
   191     ///and \ref actMinCut gives proper results.
   192     ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not
   193     ///give minimum value cuts unless calling \ref preflowPhase2.
   194     ///\pre The starting flow must be
   195     /// - a constant zero flow if \c fe is \c ZERO_FLOW,
   196     /// - an arbitary flow if \c fe is \c GEN_FLOW,
   197     /// - an arbitary preflow if \c fe is \c PRE_FLOW,
   198     /// - any map if \c fe is NO_FLOW.
   199     void preflowPhase1(FlowEnum fe)
   200     {
   201 
   202       int heur0=(int)(H0*n);  //time while running 'bound decrease'
   203       int heur1=(int)(H1*n);  //time while running 'highest label'
   204       int heur=heur1;         //starting time interval (#of relabels)
   205       int numrelabel=0;
   206 
   207       bool what_heur=1;
   208       //It is 0 in case 'bound decrease' and 1 in case 'highest label'
   209 
   210       bool end=false;
   211       //Needed for 'bound decrease', true means no active nodes are above bound
   212       //b.
   213 
   214       int k=n-2;  //bound on the highest level under n containing a node
   215       int b=k;    //bound on the highest level under n of an active node
   216 
   217       VecFirst first(n, INVALID);
   218       NNMap next(*g, INVALID); //maybe INVALID is not needed
   219 
   220       NNMap left(*g, INVALID);
   221       NNMap right(*g, INVALID);
   222       VecNode level_list(n,INVALID);
   223       //List of the nodes in level i<n, set to n.
   224 
   225       preflowPreproc(fe, next, first, level_list, left, right);
   226       //End of preprocessing
   227 
   228       //Push/relabel on the highest level active nodes.
   229       while ( true ) {
   230 	if ( b == 0 ) {
   231 	  if ( !what_heur && !end && k > 0 ) {
   232 	    b=k;
   233 	    end=true;
   234 	  } else break;
   235 	}
   236 
   237 	if ( first[b]==INVALID ) --b;
   238 	else {
   239 	  end=false;
   240 	  Node w=first[b];
   241 	  first[b]=next[w];
   242 	  int newlevel=push(w, next, first);
   243 	  if ( excess[w] > 0 ) relabel(w, newlevel, next, first, level_list,
   244 				       left, right, b, k, what_heur);
   245 
   246 	  ++numrelabel;
   247 	  if ( numrelabel >= heur ) {
   248 	    numrelabel=0;
   249 	    if ( what_heur ) {
   250 	      what_heur=0;
   251 	      heur=heur0;
   252 	      end=false;
   253 	    } else {
   254 	      what_heur=1;
   255 	      heur=heur1;
   256 	      b=k;
   257 	    }
   258 	  }
   259 	}
   260       }
   261 
   262       status=AFTER_PRE_FLOW_PHASE_1;
   263     }
   264 
   265 
   266     ///Runs the second phase of the preflow algorithm.
   267 
   268     ///The preflow algorithm consists of two phases, this method runs
   269     ///the second phase. After calling \ref preflowPhase1 and then
   270     ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut,
   271     ///\ref minMinCut and \ref maxMinCut give proper results.
   272     ///\pre \ref preflowPhase1 must be called before.
   273     void preflowPhase2()
   274     {
   275 
   276       int k=n-2;  //bound on the highest level under n containing a node
   277       int b=k;    //bound on the highest level under n of an active node
   278 
   279     
   280       VecFirst first(n, INVALID);
   281       NNMap next(*g, INVALID); //maybe INVALID is not needed
   282       level.set(s,0);
   283       std::queue<Node> bfs_queue;
   284       bfs_queue.push(s);
   285 
   286       while (!bfs_queue.empty()) {
   287 
   288 	Node v=bfs_queue.front();
   289 	bfs_queue.pop();
   290 	int l=level[v]+1;
   291 
   292 	for(InEdgeIt e(*g,v); e!=INVALID; ++e) {
   293 	  if ( (*capacity)[e] <= (*flow)[e] ) continue;
   294 	  Node u=g->tail(e);
   295 	  if ( level[u] >= n ) {
   296 	    bfs_queue.push(u);
   297 	    level.set(u, l);
   298 	    if ( excess[u] > 0 ) {
   299 	      next.set(u,first[l]);
   300 	      first[l]=u;
   301 	    }
   302 	  }
   303 	}
   304 
   305 	for(OutEdgeIt e(*g,v); e!=INVALID; ++e) {
   306 	  if ( 0 >= (*flow)[e] ) continue;
   307 	  Node u=g->head(e);
   308 	  if ( level[u] >= n ) {
   309 	    bfs_queue.push(u);
   310 	    level.set(u, l);
   311 	    if ( excess[u] > 0 ) {
   312 	      next.set(u,first[l]);
   313 	      first[l]=u;
   314 	    }
   315 	  }
   316 	}
   317       }
   318       b=n-2;
   319 
   320       while ( true ) {
   321 
   322 	if ( b == 0 ) break;
   323 
   324 	if ( first[b]==INVALID ) --b;
   325 	else {
   326 
   327 	  Node w=first[b];
   328 	  first[b]=next[w];
   329 	  int newlevel=push(w,next, first/*active*/);
   330 
   331 	  //relabel
   332 	  if ( excess[w] > 0 ) {
   333 	    level.set(w,++newlevel);
   334 	    next.set(w,first[newlevel]);
   335 	    first[newlevel]=w;
   336 	    b=newlevel;
   337 	  }
   338 	} 
   339       } // while(true)
   340 
   341       status=AFTER_PRE_FLOW_PHASE_2;
   342     }
   343 
   344 
   345     /// Returns the value of the maximum flow.
   346 
   347     /// Returns the excess of the target node \ref t. 
   348     /// After running \ref preflowPhase1, this is the value of 
   349     /// the maximum flow.
   350     /// It can be called already after running \ref preflowPhase1.
   351     Num flowValue() const {
   352       //       Num a=0;
   353       //       for(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e];
   354       //       for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) a-=(*flow)[e];
   355       //       return a;
   356       return excess[t];
   357       //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan   
   358     }
   359 
   360 
   361     ///Returns a minimum value cut after calling \ref preflowPhase1.
   362 
   363     ///After the first phase of the preflow algorithm the maximum flow
   364     ///value and a minimum value cut can already be computed. This
   365     ///method can be called after running \ref preflowPhase1 for
   366     ///obtaining a minimum value cut.
   367     /// \warning Gives proper result only right after calling \ref
   368     /// preflowPhase1.
   369     /// \todo We have to make some status variable which shows the
   370     /// actual state
   371     /// of the class. This enables us to determine which methods are valid
   372     /// for MinCut computation
   373     template<typename _CutMap>
   374     void actMinCut(_CutMap& M) const {
   375       switch (status) {
   376 	case AFTER_PRE_FLOW_PHASE_1:
   377 	for(NodeIt v(*g); v!=INVALID; ++v) {
   378 	  if (level[v] < n) {
   379 	    M.set(v, false);
   380 	  } else {
   381 	    M.set(v, true);
   382 	  }
   383 	}
   384 	break;
   385 	case AFTER_PRE_FLOW_PHASE_2:
   386 	case AFTER_NOTHING:
   387 	case AFTER_AUGMENTING:
   388 	case AFTER_FAST_AUGMENTING:
   389 	minMinCut(M);
   390 	break;
   391       }
   392     }
   393 
   394     ///Returns the inclusionwise minimum of the minimum value cuts.
   395 
   396     ///Sets \c M to the characteristic vector of the minimum value cut
   397     ///which is inclusionwise minimum. It is computed by processing
   398     ///a bfs from the source node \c s in the residual graph.
   399     ///\pre M should be a node map of bools initialized to false.
   400     ///\pre \c flow must be a maximum flow.
   401     template<typename _CutMap>
   402     void minMinCut(_CutMap& M) const {
   403       std::queue<Node> queue;
   404 
   405       M.set(s,true);
   406       queue.push(s);
   407 
   408       while (!queue.empty()) {
   409         Node w=queue.front();
   410 	queue.pop();
   411 
   412 	for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
   413 	  Node v=g->head(e);
   414 	  if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
   415 	    queue.push(v);
   416 	    M.set(v, true);
   417 	  }
   418 	}
   419 
   420 	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
   421 	  Node v=g->tail(e);
   422 	  if (!M[v] && (*flow)[e] > 0 ) {
   423 	    queue.push(v);
   424 	    M.set(v, true);
   425 	  }
   426 	}
   427       }
   428     }
   429 
   430     ///Returns the inclusionwise maximum of the minimum value cuts.
   431 
   432     ///Sets \c M to the characteristic vector of the minimum value cut
   433     ///which is inclusionwise maximum. It is computed by processing a
   434     ///backward bfs from the target node \c t in the residual graph.
   435     ///\pre M should be a node map of bools initialized to false.
   436     ///\pre \c flow must be a maximum flow. 
   437     template<typename _CutMap>
   438     void maxMinCut(_CutMap& M) const {
   439 
   440       for(NodeIt v(*g) ; v!=INVALID; ++v) M.set(v, true);
   441 
   442       std::queue<Node> queue;
   443 
   444       M.set(t,false);
   445       queue.push(t);
   446 
   447       while (!queue.empty()) {
   448         Node w=queue.front();
   449 	queue.pop();
   450 
   451 	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
   452 	  Node v=g->tail(e);
   453 	  if (M[v] && (*flow)[e] < (*capacity)[e] ) {
   454 	    queue.push(v);
   455 	    M.set(v, false);
   456 	  }
   457 	}
   458 
   459 	for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
   460 	  Node v=g->head(e);
   461 	  if (M[v] && (*flow)[e] > 0 ) {
   462 	    queue.push(v);
   463 	    M.set(v, false);
   464 	  }
   465 	}
   466       }
   467     }
   468 
   469     ///Returns a minimum value cut.
   470 
   471     ///Sets \c M to the characteristic vector of a minimum value cut.
   472     ///\pre M should be a node map of bools initialized to false.
   473     ///\pre \c flow must be a maximum flow.    
   474     template<typename CutMap>
   475     void minCut(CutMap& M) const { minMinCut(M); }
   476 
   477     ///Sets the source node to \c _s.
   478 
   479     ///Sets the source node to \c _s.
   480     /// 
   481     void setSource(Node _s) { s=_s; status=AFTER_NOTHING; }
   482 
   483     ///Sets the target node to \c _t.
   484 
   485     ///Sets the target node to \c _t.
   486     ///
   487     void setTarget(Node _t) { t=_t; status=AFTER_NOTHING; }
   488 
   489     /// Sets the edge map of the capacities to _cap.
   490 
   491     /// Sets the edge map of the capacities to _cap.
   492     /// 
   493     void setCap(const CapMap& _cap)
   494     { capacity=&_cap; status=AFTER_NOTHING; }
   495 
   496     /// Sets the edge map of the flows to _flow.
   497 
   498     /// Sets the edge map of the flows to _flow.
   499     /// 
   500     void setFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; }
   501 
   502 
   503   private:
   504 
   505     int push(Node w, NNMap& next, VecFirst& first) {
   506 
   507       int lev=level[w];
   508       Num exc=excess[w];
   509       int newlevel=n;       //bound on the next level of w
   510 
   511       for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
   512 	if ( (*flow)[e] >= (*capacity)[e] ) continue;
   513 	Node v=g->head(e);
   514 
   515 	if( lev > level[v] ) { //Push is allowed now
   516 	  
   517 	  if ( excess[v]<=0 && v!=t && v!=s ) {
   518 	    next.set(v,first[level[v]]);
   519 	    first[level[v]]=v;
   520 	  }
   521 
   522 	  Num cap=(*capacity)[e];
   523 	  Num flo=(*flow)[e];
   524 	  Num remcap=cap-flo;
   525 	  
   526 	  if ( remcap >= exc ) { //A nonsaturating push.
   527 	    
   528 	    flow->set(e, flo+exc);
   529 	    excess.set(v, excess[v]+exc);
   530 	    exc=0;
   531 	    break;
   532 
   533 	  } else { //A saturating push.
   534 	    flow->set(e, cap);
   535 	    excess.set(v, excess[v]+remcap);
   536 	    exc-=remcap;
   537 	  }
   538 	} else if ( newlevel > level[v] ) newlevel = level[v];
   539       } //for out edges wv
   540 
   541       if ( exc > 0 ) {
   542 	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
   543 	  
   544 	  if( (*flow)[e] <= 0 ) continue;
   545 	  Node v=g->tail(e);
   546 
   547 	  if( lev > level[v] ) { //Push is allowed now
   548 
   549 	    if ( excess[v]<=0 && v!=t && v!=s ) {
   550 	      next.set(v,first[level[v]]);
   551 	      first[level[v]]=v;
   552 	    }
   553 
   554 	    Num flo=(*flow)[e];
   555 
   556 	    if ( flo >= exc ) { //A nonsaturating push.
   557 
   558 	      flow->set(e, flo-exc);
   559 	      excess.set(v, excess[v]+exc);
   560 	      exc=0;
   561 	      break;
   562 	    } else {  //A saturating push.
   563 
   564 	      excess.set(v, excess[v]+flo);
   565 	      exc-=flo;
   566 	      flow->set(e,0);
   567 	    }
   568 	  } else if ( newlevel > level[v] ) newlevel = level[v];
   569 	} //for in edges vw
   570 
   571       } // if w still has excess after the out edge for cycle
   572 
   573       excess.set(w, exc);
   574       
   575       return newlevel;
   576     }
   577     
   578     
   579     
   580     void preflowPreproc(FlowEnum fe, NNMap& next, VecFirst& first,
   581 			VecNode& level_list, NNMap& left, NNMap& right)
   582     {
   583       switch (fe) {  //setting excess
   584 	case NO_FLOW: 
   585 	for(EdgeIt e(*g); e!=INVALID; ++e) flow->set(e,0);
   586 	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
   587 	break;
   588 	case ZERO_FLOW: 
   589 	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
   590 	break;
   591 	case GEN_FLOW:
   592 	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
   593 	{
   594 	  Num exc=0;
   595 	  for(InEdgeIt e(*g,t) ; e!=INVALID; ++e) exc+=(*flow)[e];
   596 	  for(OutEdgeIt e(*g,t) ; e!=INVALID; ++e) exc-=(*flow)[e];
   597 	  excess.set(t,exc);
   598 	}
   599 	break;
   600 	default:
   601 	break;
   602       }
   603       
   604       for(NodeIt v(*g); v!=INVALID; ++v) level.set(v,n);
   605       //setting each node to level n
   606       
   607       std::queue<Node> bfs_queue;
   608 
   609 
   610       switch (fe) {
   611       case NO_FLOW:   //flow is already set to const zero
   612       case ZERO_FLOW:
   613 	//Reverse_bfs from t, to find the starting level.
   614 	level.set(t,0);
   615 	bfs_queue.push(t);
   616 	
   617 	while (!bfs_queue.empty()) {
   618 	  
   619 	  Node v=bfs_queue.front();
   620 	  bfs_queue.pop();
   621 	  int l=level[v]+1;
   622 	  
   623 	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) {
   624 	    Node w=g->tail(e);
   625 	    if ( level[w] == n && w != s ) {
   626 	      bfs_queue.push(w);
   627 	      Node z=level_list[l];
   628 	      if ( z!=INVALID ) left.set(z,w);
   629 	      right.set(w,z);
   630 	      level_list[l]=w;
   631 	      level.set(w, l);
   632 	    }
   633 	  }
   634 	}
   635 	
   636 	//the starting flow
   637 	for(OutEdgeIt e(*g,s) ; e!=INVALID; ++e)
   638 	  {
   639 	    Num c=(*capacity)[e];
   640 	    if ( c <= 0 ) continue;
   641 	    Node w=g->head(e);
   642 	    if ( level[w] < n ) {
   643 	      if ( excess[w] <= 0 && w!=t ) //putting into the stack
   644 		{ 
   645 		  next.set(w,first[level[w]]);
   646 		  first[level[w]]=w;
   647 		}
   648 	      flow->set(e, c);
   649 	      excess.set(w, excess[w]+c);
   650 	    }
   651 	  }
   652 	break;
   653       case GEN_FLOW:
   654 	//Reverse_bfs from t in the residual graph,
   655 	//to find the starting level.
   656 	level.set(t,0);
   657 	bfs_queue.push(t);
   658 	
   659 	while (!bfs_queue.empty()) {
   660 	  
   661 	  Node v=bfs_queue.front();
   662 	  bfs_queue.pop();
   663 	  int l=level[v]+1;
   664 	  
   665 	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) {
   666 	    if ( (*capacity)[e] <= (*flow)[e] ) continue;
   667 	    Node w=g->tail(e);
   668 	    if ( level[w] == n && w != s ) {
   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 	  
   678 	  for(OutEdgeIt e(*g,v) ; e!=INVALID; ++e) {
   679 	    if ( 0 >= (*flow)[e] ) continue;
   680 	    Node w=g->head(e);
   681 	    if ( level[w] == n && w != s ) {
   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 	}
   691 	
   692 	//the starting flow
   693 	for(OutEdgeIt e(*g,s); e!=INVALID; ++e)
   694 	  {
   695 	    Num rem=(*capacity)[e]-(*flow)[e];
   696 	    if ( rem <= 0 ) continue;
   697 	    Node w=g->head(e);
   698 	    if ( level[w] < n ) {
   699 	      if ( excess[w] <= 0 && w!=t ) //putting into the stack
   700 		{
   701 		  next.set(w,first[level[w]]);
   702 		  first[level[w]]=w;
   703 		}   
   704 	      flow->set(e, (*capacity)[e]);
   705 	      excess.set(w, excess[w]+rem);
   706 	    }
   707 	  }
   708 	
   709 	for(InEdgeIt e(*g,s); e!=INVALID; ++e)
   710 	  {
   711 	    if ( (*flow)[e] <= 0 ) continue;
   712 	    Node w=g->tail(e);
   713 	    if ( level[w] < n ) {
   714 	      if ( excess[w] <= 0 && w!=t )
   715 		{
   716 		  next.set(w,first[level[w]]);
   717 		  first[level[w]]=w;
   718 		}  
   719 	      excess.set(w, excess[w]+(*flow)[e]);
   720 	      flow->set(e, 0);
   721 	    }
   722 	  }
   723 	break;
   724       case PRE_FLOW:
   725 	//Reverse_bfs from t in the residual graph,
   726 	//to find the starting level.
   727 	level.set(t,0);
   728 	bfs_queue.push(t);
   729 	
   730 	while (!bfs_queue.empty()) {
   731 	  
   732 	  Node v=bfs_queue.front();
   733 	  bfs_queue.pop();
   734 	  int l=level[v]+1;
   735 	  
   736 	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) {
   737 	    if ( (*capacity)[e] <= (*flow)[e] ) continue;
   738 	    Node w=g->tail(e);
   739 	    if ( level[w] == n && w != s ) {
   740 	      bfs_queue.push(w);
   741 	      Node z=level_list[l];
   742 	      if ( z!=INVALID ) left.set(z,w);
   743 	      right.set(w,z);
   744 	      level_list[l]=w;
   745 	      level.set(w, l);
   746 	    }
   747 	  }
   748 	  
   749 	  for(OutEdgeIt e(*g,v) ; e!=INVALID; ++e) {
   750 	    if ( 0 >= (*flow)[e] ) continue;
   751 	    Node w=g->head(e);
   752 	    if ( level[w] == n && w != s ) {
   753 	      bfs_queue.push(w);
   754 	      Node z=level_list[l];
   755 	      if ( z!=INVALID ) left.set(z,w);
   756 	      right.set(w,z);
   757 	      level_list[l]=w;
   758 	      level.set(w, l);
   759 	    }
   760 	  }
   761 	}
   762 	
   763 	
   764 	//the starting flow
   765 	for(OutEdgeIt e(*g,s) ; e!=INVALID; ++e) {
   766 	  Num rem=(*capacity)[e]-(*flow)[e];
   767 	  if ( rem <= 0 ) continue;
   768 	  Node w=g->head(e);
   769 	  if ( level[w] < n ) {
   770 	    flow->set(e, (*capacity)[e]);
   771 	    excess.set(w, excess[w]+rem);
   772 	  }
   773 	}
   774 	
   775 	for(InEdgeIt e(*g,s) ; e!=INVALID; ++e) {
   776 	  if ( (*flow)[e] <= 0 ) continue;
   777 	  Node w=g->tail(e);
   778 	  if ( level[w] < n ) {
   779 	    excess.set(w, excess[w]+(*flow)[e]);
   780 	    flow->set(e, 0);
   781 	  }
   782 	}
   783 	
   784 	//computing the excess
   785 	for(NodeIt w(*g); w!=INVALID; ++w) {
   786 	  Num exc=0;
   787 	  
   788 	  for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) exc+=(*flow)[e];
   789 	  for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) exc-=(*flow)[e];
   790 	  
   791 	  excess.set(w,exc);
   792 	  
   793 	  //putting the active nodes into the stack
   794 	  int lev=level[w];
   795 	    if ( exc > 0 && lev < n && Node(w) != t ) 
   796 	      ///\bug	    if ( exc > 0 && lev < n && w != t ) temporarily for working with wrappers. 
   797 	    {
   798 	      next.set(w,first[lev]);
   799 	      first[lev]=w;
   800 	    }
   801 	}
   802 	break;
   803       } //switch
   804     } //preflowPreproc
   805 
   806 
   807     void relabel(Node w, int newlevel, NNMap& next, VecFirst& first,
   808 		 VecNode& level_list, NNMap& left,
   809 		 NNMap& right, int& b, int& k, bool what_heur )
   810     {
   811 
   812       int lev=level[w];
   813 
   814       Node right_n=right[w];
   815       Node left_n=left[w];
   816 
   817       //unlacing starts
   818       if ( right_n!=INVALID ) {
   819 	if ( left_n!=INVALID ) {
   820 	  right.set(left_n, right_n);
   821 	  left.set(right_n, left_n);
   822 	} else {
   823 	  level_list[lev]=right_n;
   824 	  left.set(right_n, INVALID);
   825 	}
   826       } else {
   827 	if ( left_n!=INVALID ) {
   828 	  right.set(left_n, INVALID);
   829 	} else {
   830 	  level_list[lev]=INVALID;
   831 	}
   832       }
   833       //unlacing ends
   834 
   835       if ( level_list[lev]==INVALID ) {
   836 
   837 	//gapping starts
   838 	for (int i=lev; i!=k ; ) {
   839 	  Node v=level_list[++i];
   840 	  while ( v!=INVALID ) {
   841 	    level.set(v,n);
   842 	    v=right[v];
   843 	  }
   844 	  level_list[i]=INVALID;
   845 	  if ( !what_heur ) first[i]=INVALID;
   846 	}
   847 
   848 	level.set(w,n);
   849 	b=lev-1;
   850 	k=b;
   851 	//gapping ends
   852 
   853       } else {
   854 
   855 	if ( newlevel == n ) level.set(w,n);
   856 	else {
   857 	  level.set(w,++newlevel);
   858 	  next.set(w,first[newlevel]);
   859 	  first[newlevel]=w;
   860 	  if ( what_heur ) b=newlevel;
   861 	  if ( k < newlevel ) ++k;      //now k=newlevel
   862 	  Node z=level_list[newlevel];
   863 	  if ( z!=INVALID ) left.set(z,w);
   864 	  right.set(w,z);
   865 	  left.set(w,INVALID);
   866 	  level_list[newlevel]=w;
   867 	}
   868       }
   869     } //relabel
   870 
   871     void printexcess() {////
   872       std::cout << "Excesses:" <<std::endl;
   873 
   874       for(NodeIt v(*g); v!=INVALID ; ++v) {
   875 	std::cout << 1+(g->id(v)) << ":" << excess[v]<<std::endl; 
   876       }
   877     }
   878 
   879     void printlevel() {////
   880       std::cout << "Levels:" <<std::endl;
   881 
   882       for(NodeIt v(*g); v!=INVALID ; ++v) {
   883 	std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; 
   884       }
   885     }
   886 
   887     void printactive() {////
   888       std::cout << "Levels:" <<std::endl;
   889 
   890       for(NodeIt v(*g); v!=INVALID ; ++v) {
   891 	std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; 
   892       }
   893     }
   894 
   895 
   896   };  //class MaxFlow
   897 } //namespace hugo
   898 
   899 #endif //HUGO_MAX_FLOW_H
   900 
   901 
   902 
   903