source: lemon-0.x/src/work/jacint/preflow.h @ 317:6e6db1c49bc1

// -*- C++ -*-
/*
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.

Constructors:

Preflow(Graph, Node, Node, CapMap, FlowMap)

Members:

void run()

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

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 HUGO_PREFLOW_H
#define HUGO_PREFLOW_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> >
  class Preflow {
    
    typedef typename Graph::Node Node;
    typedef typename Graph::Edge Edge;
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    typedef typename Graph::InEdgeIt InEdgeIt;
    
    const Graph& G;
    Node s;
    Node t;
    FlowMap& flow;
    const CapMap& capacity;  
    T value;

  public:
    Preflow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, 
            FlowMap& _flow ) :
      G(_G), s(_s), t(_t), flow(_flow), capacity(_capacity) {}


    void run() {

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

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

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

      while (!bfs_queue.empty()) {

        Node v=bfs_queue.front();       
        bfs_queue.pop();
        int l=level[v]+1;

        InEdgeIt e;
        for(G.first(e,v); G.valid(e); G.next(e)) {
          Node w=G.tail(e);
          if ( level[w] == n && w != s ) {
            bfs_queue.push(w);
            Node first=level_list[l];
            if ( G.valid(first) ) 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. */     
      OutEdgeIt e;
      for(G.first(e,s); G.valid(e); G.next(e)) 
        {
          T c=capacity[e];
          if ( c == 0 ) continue;
          Node w=G.head(e);
          if ( level[w] < n ) {   
            if ( excess[w] == 0 && w!=t ) {
              next.set(w,active[level[w]]);
              active[level[w]]=w;
            }
            flow.set(e, c); 
            excess.set(w, excess[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;
            level.set(s,0);
            std::queue<Node> bfs_queue;
            bfs_queue.push(s);
            
            while (!bfs_queue.empty()) {
              
              Node v=bfs_queue.front(); 
              bfs_queue.pop();
              int l=level[v]+1;
              
              InEdgeIt e;
              for(G.first(e,v); G.valid(e); G.next(e)) {
                if ( capacity[e] == flow[e] ) continue;
                Node u=G.tail(e);
                if ( level[u] >= n ) { 
                  bfs_queue.push(u);
                  level.set(u, l);
                  if ( excess[u] > 0 ) {
                    next.set(u,active[l]);
                    active[l]=u;
                  }
                }
              }
            
              OutEdgeIt f;
              for(G.first(f,v); G.valid(f); G.next(f)) {
                if ( 0 == flow[f] ) continue;
                Node u=G.head(f);
                if ( level[u] >= n ) { 
                  bfs_queue.push(u);
                  level.set(u, l);
                  if ( excess[u] > 0 ) {
                    next.set(u,active[l]);
                    active[l]=u;
                  }
                }
              }
            }
            b=n-2;
            }
            
        }
          
          
        if ( !G.valid(active[b]) ) --b; 
        else {
          end=false;  

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

            if ( G.valid(right_n) ) {
              if ( G.valid(left_n) ) {
                right.set(left_n, right_n);
                left.set(right_n, left_n);
              } else {
                level_list[lev]=right_n;   
                left.set(right_n, INVALID);
              } 
            } else {
              if ( G.valid(left_n) ) {
                right.set(left_n, INVALID);
              } else { 
                level_list[lev]=INVALID;   
              } 
            } 
            //unlacing ends
                
            //gapping starts
            if ( !G.valid(level_list[lev]) ) {
              
              for (int i=lev; i!=k ; ) {
                Node v=level_list[++i];
                while ( G.valid(v) ) {
                  level.set(v,n);
                  v=right[v];
                }
                level_list[i]=INVALID;
                if ( !what_heur ) active[i]=INVALID;
              }      

              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;
                Node first=level_list[newlevel];
                if ( G.valid(first) ) left.set(first,w);
                right.set(w,first);
                left.set(w,INVALID);
                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[t];
      /*Max flow value.*/
     
    } //void run()





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

    T flowValue() {
      return value;
    }


    FlowMap Flow() {
      return flow;
      }


    
    void Flow(FlowMap& _flow ) {
      NodeIt v;
      for(G.first(v) ; G.valid(v); G.next(v))
        _flow.set(v,flow[v]);
    }



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

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

        OutEdgeIt e;
        for(G.first(e,w) ; G.valid(e); G.next(e)) {
          Node v=G.head(e);
          if (!M[v] && flow[e] < capacity[e] ) {
            queue.push(v);
            M.set(v, true);
          }
        } 

        InEdgeIt f;
        for(G.first(f,w) ; G.valid(f); G.next(f)) {
          Node v=G.tail(f);
          if (!M[v] && flow[f] > 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<Node> queue;
      
      M.set(t,true);        
      queue.push(t);

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


        InEdgeIt e;
        for(G.first(e,w) ; G.valid(e); G.next(e)) {
          Node v=G.tail(e);
          if (!M[v] && flow[e] < capacity[e] ) {
            queue.push(v);
            M.set(v, true);
          }
        }
        
        OutEdgeIt f;
        for(G.first(f,w) ; G.valid(f); G.next(f)) {
          Node v=G.head(f);
          if (!M[v] && flow[f] > 0 ) {
            queue.push(v);
            M.set(v, true);
          }
        }
      }

      NodeIt v;
      for(G.first(v) ; G.valid(v); G.next(v)) {
        M.set(v, !M[v]);
      }

    }



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


  };

} //namespace hugo

#endif //PREFLOW_H