source: lemon-0.x/src/work/jacint/preflow.h @ 201:b9158a014fe8

// -*- C++ -*-
/*
preflow.h
by jacint. 
Heuristics: 
 2 phase
 gap
 list 'level_list' on the nodes on level i implemented by hand
 stack 'active' on the active nodes on level i implemented by hand
 runs heuristic 'highest label' for H1*n relabels
 runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
 
Parameters H0 and H1 are initialized to 20 and 10.

The best preflow I could ever write.

The constructor runs the algorithm.

Members:

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

T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) 

FlowMap Flow() : returns the fixed maximum flow x

void minMinCut(CutMap& M) : sets M to the characteristic vector of the 
     minimum min cut. M should be a map of bools initialized to false.

void maxMinCut(CutMap& M) : sets M to the characteristic vector of the 
     maximum min cut. M should be a map of bools initialized to false.

void minCut(CutMap& M) : sets M to the characteristic vector of 
     a min cut. M should be a map of bools initialized to false.

*/

#ifndef PREFLOW_H
#define PREFLOW_H

#define H0 20
#define H1 1

#include <vector>
#include <queue>

#include <time_measure.h>

namespace hugo {

  template <typename Graph, typename T, 
    typename FlowMap=typename Graph::EdgeMap<T>,
    typename CapMap=typename Graph::EdgeMap<T> >
  class preflow {
    
    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;  
    T value;

  public:
    double time;
    preflow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) :
      G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity)
    {

      bool phase=0;        //phase 0 is the 1st phase, phase 1 is the 2nd
      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 ( phase ) break;
          
          if ( !what_heur && !end && k > 0 ) {
            b=k;
            end=true;
          } else {
            phase=1;
            time=currTime();
            level.set(s,0);
            std::queue<NodeIt> bfs_queue;
            bfs_queue.push(s);
            
            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) {
                if ( capacity.get(e) == flow.get(e) ) continue;
                NodeIt u=G.tail(e);
                if ( level.get(u) >= n ) { 
                  bfs_queue.push(u);
                  level.set(u, l);
                  if ( excess.get(u) > 0 ) {
                    next.set(u,active[l]);
                    active[l]=u;
                  }
                }
              }
            
              for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) {
                if ( 0 == flow.get(e) ) continue;
                NodeIt u=G.head(e);
                if ( level.get(u) >= n ) { 
                  bfs_queue.push(u);
                  level.set(u, l);
                  if ( excess.get(u) > 0 ) {
                    next.set(u,active[l]);
                    active[l]=u;
                  }
                }
              }
            }
            b=n-2;
            }
            
        }
          
          
        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
        
          if ( phase ) {
            level.set(w,++newlevel);
            next.set(w,active[newlevel]);
            active[newlevel]=w;
            b=newlevel;
          } else {
            //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; 
              }
            }
          } //phase 0
          
          
        } // if ( exc > 0 )
          
        
        }  // if stack[b] is nonempty
        
      } // while(true)


      value = excess.get(t);
      /*Max flow value.*/
     
    } //void run()





    /*
      Returns the maximum value of a flow.
     */

    T maxFlow() {
      return value;
    }



    /*
      For the maximum flow x found by the algorithm, 
      it returns the flow value on edge e, i.e. x(e). 
    */
   
    T flowOnEdge(EdgeIt e) {
      return flow.get(e);
    }



    FlowMap Flow() {
      return flow;
      }


    
    void Flow(FlowMap& _flow ) {
      for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v)
        _flow.set(v,flow.get(v));
        }



    /*
      Returns the minimum min cut, by a bfs from s in the residual graph.
    */
   
    template<typename _CutMap>
    void minMinCut(_CutMap& M) {
    
      std::queue<NodeIt> queue;
      
      M.set(s,true);      
      queue.push(s);

      while (!queue.empty()) {
        NodeIt w=queue.front();
        queue.pop();

        for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
          NodeIt v=G.head(e);
          if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
            queue.push(v);
            M.set(v, true);
          }
        } 

        for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
          NodeIt v=G.tail(e);
          if (!M.get(v) && flow.get(e) > 0 ) {
            queue.push(v);
            M.set(v, true);
          }
        } 
      }
    }


  
    /*
      Returns the maximum min cut, by a reverse bfs 
      from t in the residual graph.
    */
    
    template<typename _CutMap>
    void maxMinCut(_CutMap& M) {
    
      std::queue<NodeIt> queue;
      
      M.set(t,true);        
      queue.push(t);

      while (!queue.empty()) {
        NodeIt w=queue.front();
        queue.pop();

        for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
          NodeIt v=G.tail(e);
          if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
            queue.push(v);
            M.set(v, true);
          }
        }

        for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
          NodeIt v=G.head(e);
          if (!M.get(v) && flow.get(e) > 0 ) {
            queue.push(v);
            M.set(v, true);
          }
        }
      }

      for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) {
        M.set(v, !M.get(v));
      }

    }



    template<typename CutMap>
    void minCut(CutMap& M) {
      minMinCut(M);
    }


  };

} //namespace hugo

#endif //PREFLOW_H