source: lemon-0.x/src/work/jacint/preflow_max_flow.h @ 134:e606071614f0

// -*- C++ -*-
/*
preflow_max_flow.h
by jacint. 
Runs the first phase of preflow.h

The constructor runs the algorithm.

Members:

T maxFlow() : returns the value of a maximum flow

CutMap minCut() : returns the characteristic vector of a min cut. 
*/

#ifndef PREFLOW_MAX_FLOW_H
#define PREFLOW_MAX_FLOW_H

#define H0 20
#define H1 1

#include <vector>
#include <queue>

namespace hugo {

  template <typename Graph, typename T, 
    typename FlowMap=typename Graph::EdgeMap<T>,
    typename CapMap=typename Graph::EdgeMap<T>, 
    typename CutMap=typename Graph::NodeMap<bool> >
  class preflow_max_flow {
    
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EdgeIt EdgeIt;
    typedef typename Graph::EachNodeIt EachNodeIt;
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    typedef typename Graph::InEdgeIt InEdgeIt;
    
    Graph& G;
    NodeIt s;
    NodeIt t;
    FlowMap flow;
    CapMap& capacity;  
    CutMap cut;
    T value;

  public:
    
    preflow_max_flow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) :
      G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), cut(_G, false)
    {

      int n=G.nodeNum(); 
      int heur0=(int)(H0*n);  //time while running 'bound decrease' 
      int heur1=(int)(H1*n);  //time while running 'highest label'
      int heur=heur1;         //starting time interval (#of relabels)
      bool what_heur=1;       
      /*
        what_heur is 0 in case 'bound decrease' 
        and 1 in case 'highest label'
      */
      bool end=false;     
      /*
        Needed for 'bound decrease', 'true'
        means no active nodes are above bound b.
      */
      int relabel=0;
      int k=n-2;  //bound on the highest level under n containing a node
      int b=k;    //bound on the highest level under n of an active node
      
      typename Graph::NodeMap<int> level(G,n);      
      typename Graph::NodeMap<T> excess(G); 

      std::vector<NodeIt> active(n);
      typename Graph::NodeMap<NodeIt> next(G);
      //Stack of the active nodes in level i < n.
      //We use it in both phases.

      typename Graph::NodeMap<NodeIt> left(G);
      typename Graph::NodeMap<NodeIt> right(G);
      std::vector<NodeIt> level_list(n);
      /*
        List of the nodes in level i<n.
      */

      /*Reverse_bfs from t, to find the starting level.*/
      level.set(t,0);
      std::queue<NodeIt> bfs_queue;
      bfs_queue.push(t);

      while (!bfs_queue.empty()) {

        NodeIt v=bfs_queue.front();     
        bfs_queue.pop();
        int l=level.get(v)+1;

        for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {
          NodeIt w=G.tail(e);
          if ( level.get(w) == n && w != s ) {
            bfs_queue.push(w);
            NodeIt first=level_list[l];
            if ( first != 0 ) left.set(first,w);
            right.set(w,first);
            level_list[l]=w;
            level.set(w, l);
          }
        }
      }
      
      level.set(s,n);
      

      /* Starting flow. It is everywhere 0 at the moment. */     
      for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) 
        {
          T c=capacity.get(e);
          if ( c == 0 ) continue;
          NodeIt w=G.head(e);
          if ( level.get(w) < n ) {       
            if ( excess.get(w) == 0 && w!=t ) {
              next.set(w,active[level.get(w)]);
              active[level.get(w)]=w;
            }
            flow.set(e, c); 
            excess.set(w, excess.get(w)+c);
          }
        }

      /* 
         End of preprocessing 
      */



      /*
        Push/relabel on the highest level active nodes.
      */        
      while ( true ) {
        
        if ( b == 0 ) {
          if ( !what_heur && !end && k > 0 ) {
            b=k;
            end=true;
          } else break;
        }
          
          
        if ( active[b] == 0 ) --b; 
        else {
          end=false;  

          NodeIt w=active[b];
          active[b]=next.get(w);
          int lev=level.get(w);
          T exc=excess.get(w);
          int newlevel=n;       //bound on the next level of w
          
          for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
            
            if ( flow.get(e) == capacity.get(e) ) continue; 
            NodeIt v=G.head(e);            
            //e=wv          
            
            if( lev > level.get(v) ) {      
              /*Push is allowed now*/
              
              if ( excess.get(v)==0 && v!=t && v!=s ) {
                int lev_v=level.get(v);
                next.set(v,active[lev_v]);
                active[lev_v]=v;
              }
              
              T cap=capacity.get(e);
              T flo=flow.get(e);
              T remcap=cap-flo;
              
              if ( remcap >= exc ) {       
                /*A nonsaturating push.*/
                
                flow.set(e, flo+exc);
                excess.set(v, excess.get(v)+exc);
                exc=0;
                break; 
                
              } else { 
                /*A saturating push.*/
                
                flow.set(e, cap);
                excess.set(v, excess.get(v)+remcap);
                exc-=remcap;
              }
            } else if ( newlevel > level.get(v) ){
              newlevel = level.get(v);
            }       
            
          } //for out edges wv 
        
        
        if ( exc > 0 ) {        
          for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
            
            if( flow.get(e) == 0 ) continue; 
            NodeIt v=G.tail(e);  
            //e=vw
            
            if( lev > level.get(v) ) {  
              /*Push is allowed now*/
              
              if ( excess.get(v)==0 && v!=t && v!=s ) {
                int lev_v=level.get(v);
                next.set(v,active[lev_v]);
                active[lev_v]=v;
              }
              
              T flo=flow.get(e);
              
              if ( flo >= exc ) { 
                /*A nonsaturating push.*/
                
                flow.set(e, flo-exc);
                excess.set(v, excess.get(v)+exc);
                exc=0;
                break; 
              } else {                                               
                /*A saturating push.*/
                
                excess.set(v, excess.get(v)+flo);
                exc-=flo;
                flow.set(e,0);
              }  
            } else if ( newlevel > level.get(v) ) {
              newlevel = level.get(v);
            }       
          } //for in edges vw
          
        } // if w still has excess after the out edge for cycle
        
        excess.set(w, exc);
         
        /*
          Relabel
        */
        

        if ( exc > 0 ) {
          //now 'lev' is the old level of w
        
          //unlacing starts
          NodeIt right_n=right.get(w);
          NodeIt left_n=left.get(w);
          
          if ( right_n != 0 ) {
            if ( left_n != 0 ) {
              right.set(left_n, right_n);
              left.set(right_n, left_n);
            } else {
              level_list[lev]=right_n;   
              left.set(right_n, 0);
            } 
          } else {
            if ( left_n != 0 ) {
              right.set(left_n, 0);
            } else { 
              level_list[lev]=0;   
              
            } 
          } 
          //unlacing ends
          
          //gapping starts
          if ( level_list[lev]==0 ) {
            
            for (int i=lev; i!=k ; ) {
              NodeIt v=level_list[++i];
              while ( v != 0 ) {
                level.set(v,n);
                v=right.get(v);
              }
              level_list[i]=0;
              if ( !what_heur ) active[i]=0;
            }        
            
            level.set(w,n);
            b=lev-1;
            k=b;
            //gapping ends
          } else {
            
            if ( newlevel == n ) level.set(w,n); 
            else {
              level.set(w,++newlevel);
              next.set(w,active[newlevel]);
              active[newlevel]=w;
              if ( what_heur ) b=newlevel;
              if ( k < newlevel ) ++k;
              NodeIt first=level_list[newlevel];
              if ( first != 0 ) left.set(first,w);
              right.set(w,first);
              left.set(w,0);
              level_list[newlevel]=w;
            }
          }
          
          
          ++relabel; 
          if ( relabel >= heur ) {
            relabel=0;
            if ( what_heur ) {
              what_heur=0;
              heur=heur0;
              end=false;
            } else {
              what_heur=1;
              heur=heur1;
              b=k; 
            }
          }
          
  
        } // if ( exc > 0 )
        
        
        }  // if stack[b] is nonempty
        
      } // while(true)


      
      for( EachNodeIt v=G.template first<EachNodeIt>(); 
           v.valid(); ++v) 
        if (level.get(v) >= n ) cut.set(v,true);
      
      value = excess.get(t);
      /*Max flow value.*/
     
    } //void run()




    T maxFlow() {
      return value;
    }



    CutMap minCut() {
      return cut;
    }


  };
}//namespace 
#endif