jacint@101: // -*- C++ -*-
jacint@101: /*
jacint@101: preflow_hl3.h
jacint@101: by jacint. 
jacint@101: 
jacint@109: Heuristics: 
jacint@101: 
jacint@109:  suck gap : if there is a gap, then we put all 
jacint@109:    nodes reachable from the relabelled node to level n
jacint@109:  2 phase
jacint@109:  highest label
jacint@101: 
jacint@109: The constructor runs the algorithm.
jacint@101: 
jacint@109: Members:
jacint@101: 
jacint@109: T maxFlow() : returns the value of a maximum flow
jacint@101: 
jacint@109: T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) 
jacint@101: 
jacint@109: FlowMap Flow() : returns the fixed maximum flow x
jacint@101: 
jacint@109: void minCut(CutMap& M) : sets M to the characteristic vector of a 
jacint@101:      minimum cut. M should be a map of bools initialized to false.
jacint@101: 
jacint@109: void minMinCut(CutMap& M) : sets M to the characteristic vector of the 
jacint@101:      minimum min cut. M should be a map of bools initialized to false.
jacint@101: 
jacint@109: void maxMinCut(CutMap& M) : sets M to the characteristic vector of the 
jacint@101:      maximum min cut. M should be a map of bools initialized to false.
jacint@101: 
jacint@101: */
jacint@101: 
jacint@101: #ifndef PREFLOW_HL3_H
jacint@101: #define PREFLOW_HL3_H
jacint@101: 
jacint@101: #include <vector>
jacint@101: #include <stack>
jacint@101: #include <queue>
jacint@101: 
jacint@109: #include <time_measure.h> //for test
jacint@109: 
alpar@105: namespace hugo {
jacint@101: 
jacint@101:   template <typename Graph, typename T, 
jacint@109:     typename FlowMap=typename Graph::EdgeMap<T>, 
jacint@109:     typename CapMap=typename Graph::EdgeMap<T> >
jacint@101:   class preflow_hl3 {
jacint@101:     
jacint@101:     typedef typename Graph::NodeIt NodeIt;
jacint@101:     typedef typename Graph::EdgeIt EdgeIt;
jacint@101:     typedef typename Graph::EachNodeIt EachNodeIt;
jacint@101:     typedef typename Graph::OutEdgeIt OutEdgeIt;
jacint@101:     typedef typename Graph::InEdgeIt InEdgeIt;
jacint@101:     
jacint@101:     Graph& G;
jacint@101:     NodeIt s;
jacint@101:     NodeIt t;
jacint@101:     FlowMap flow;
jacint@101:     CapMap& capacity;  
jacint@101:     T value;
jacint@101:     
jacint@101:   public:
jacint@101: 
jacint@109:     double time; //for test
jacint@109: 
jacint@101:     preflow_hl3(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) :
jacint@109:       G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) {
jacint@109:       
jacint@101:       bool phase=0;
jacint@101:       int n=G.nodeNum(); 
jacint@101:       int b=n-2; 
jacint@101:       /*
jacint@101: 	b is a bound on the highest level of the stack. 
jacint@101: 	In the beginning it is at most n-2.
jacint@101:       */
jacint@101: 
jacint@109:       typename Graph::NodeMap<int> level(G,n);      
jacint@109:       typename Graph::NodeMap<T> excess(G); 
jacint@101:       
jacint@101:       std::vector<int> numb(n);    
jacint@101:       /*
jacint@101: 	The number of nodes on level i < n. It is
jacint@101: 	initialized to n+1, because of the reverse_bfs-part.
jacint@101: 	Needed only in phase 0.
jacint@101:       */
jacint@101: 
jacint@101:       std::vector<std::stack<NodeIt> > stack(n);    
jacint@101:       //Stack of the active nodes in level i < n.
jacint@101:       //We use it in both phases.
jacint@101: 
jacint@101: 
jacint@101:       /*Reverse_bfs from t, to find the starting level.*/
jacint@101:       level.set(t,0);
jacint@101:       std::queue<NodeIt> bfs_queue;
jacint@101:       bfs_queue.push(t);
jacint@101: 
jacint@101:       while (!bfs_queue.empty()) {
jacint@101: 
jacint@101: 	NodeIt v=bfs_queue.front();	
jacint@101: 	bfs_queue.pop();
jacint@101: 	int l=level.get(v)+1;
jacint@101: 
jacint@101: 	for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {
jacint@101: 	  NodeIt w=G.tail(e);
jacint@101: 	  if ( level.get(w) == n ) {
jacint@101: 	    bfs_queue.push(w);
jacint@101: 	    ++numb[l];
jacint@101: 	    level.set(w, l);
jacint@101: 	  }
jacint@101: 	}
jacint@101:       }
jacint@101:       
jacint@101:       level.set(s,n);
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101:       /* Starting flow. It is everywhere 0 at the moment. */     
jacint@101:       for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) 
jacint@101: 	{
jacint@101: 	  T c=capacity.get(e);
jacint@101: 	  if ( c == 0 ) continue;
jacint@101: 	  NodeIt w=G.head(e);
jacint@101: 	  if ( level.get(w) < n ) {	  
jacint@101: 	    if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); 
jacint@101: 	    flow.set(e, c); 
jacint@101: 	    excess.set(w, excess.get(w)+c);
jacint@101: 	  }
jacint@101: 	}
jacint@101: 
jacint@101:       /* 
jacint@101: 	 End of preprocessing 
jacint@101:       */
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101:       /*
jacint@101: 	Push/relabel on the highest level active nodes.
jacint@101:       */	
jacint@101:       /*While there exists an active node.*/
jacint@101:       while ( true ) {
jacint@101: 
jacint@101: 	if ( b == 0 ) {
jacint@101: 	  if ( phase ) break; 
jacint@101: 	  phase=1;
jacint@109: 	  time=currTime();
jacint@109: 	  
jacint@101: 	  level.set(s,0);
jacint@101: 
jacint@101: 	  std::queue<NodeIt> bfs_queue;
jacint@101: 	  bfs_queue.push(s);
jacint@101: 	  
jacint@101: 	  while (!bfs_queue.empty()) {
jacint@101: 	    
jacint@101: 	    NodeIt v=bfs_queue.front();	
jacint@101: 	    bfs_queue.pop();
jacint@101: 	    int l=level.get(v)+1;
jacint@101: 
jacint@101: 	    for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {
jacint@101: 	      if ( capacity.get(e) == flow.get(e) ) continue;
jacint@101: 	      NodeIt u=G.tail(e);
jacint@101: 	      if ( level.get(u) == n ) { 
jacint@101: 		bfs_queue.push(u);
jacint@101: 		level.set(u, l);
jacint@101: 		if ( excess.get(u) > 0 ) stack[l].push(u);
jacint@101: 	      }
jacint@101: 	    }
jacint@101: 
jacint@101: 	    for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) {
jacint@101: 	      if ( 0 == flow.get(e) ) continue;
jacint@101: 	      NodeIt u=G.head(e);
jacint@101: 	      if ( level.get(u) == n ) { 
jacint@101: 		bfs_queue.push(u);
jacint@101: 		level.set(u, l);
jacint@101: 		if ( excess.get(u) > 0 ) stack[l].push(u);
jacint@101: 	      }
jacint@101: 	    }
jacint@101: 	  }
jacint@101: 
jacint@101: 	  b=n-2;
jacint@101: 	}
jacint@101: 
jacint@101: 	if ( stack[b].empty() ) --b;
jacint@101: 	else {
jacint@101: 	  
jacint@109: 	  NodeIt w=stack[b].top(); 
jacint@101: 	  stack[b].pop();           
jacint@101: 	  int lev=level.get(w);
jacint@109: 	  T exc=excess.get(w);
jacint@109: 	  int newlevel=n;          //bound on the next level of w.
jacint@101: 	  
jacint@101: 	  for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
jacint@101: 	    
jacint@101: 	    if ( flow.get(e) == capacity.get(e) ) continue; 
jacint@101: 	    NodeIt v=G.head(e);            
jacint@101: 	    //e=wv	    
jacint@101: 	    
jacint@101: 	    if( lev > level.get(v) ) {      
jacint@101: 	      /*Push is allowed now*/
jacint@101: 	      
jacint@101: 	      if ( excess.get(v)==0 && v !=t && v!=s ) 
jacint@101: 		stack[level.get(v)].push(v); 
jacint@101: 	      /*v becomes active.*/
jacint@101: 	      
jacint@109: 	      T cap=capacity.get(e);
jacint@109: 	      T flo=flow.get(e);
jacint@109: 	      T remcap=cap-flo;
jacint@101: 	      
jacint@101: 	      if ( remcap >= exc ) {       
jacint@101: 		/*A nonsaturating push.*/
jacint@101: 		
jacint@101: 		flow.set(e, flo+exc);
jacint@101: 		excess.set(v, excess.get(v)+exc);
jacint@101: 		exc=0;
jacint@101: 		break; 
jacint@101: 		
jacint@101: 	      } else { 
jacint@101: 		/*A saturating push.*/
jacint@101: 		
jacint@101: 		flow.set(e, cap );
jacint@101: 		excess.set(v, excess.get(v)+remcap);
jacint@101: 		exc-=remcap;
jacint@101: 	      }
jacint@101: 	    } else if ( newlevel > level.get(v) ) newlevel = level.get(v);
jacint@101: 	    
jacint@101: 	  } //for out edges wv 
jacint@101: 	
jacint@101: 	
jacint@101: 	if ( exc > 0 ) {	
jacint@101: 	  for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
jacint@101: 	    
jacint@101: 	    if( flow.get(e) == 0 ) continue; 
jacint@101: 	    NodeIt v=G.tail(e);  
jacint@101: 	    //e=vw
jacint@101: 	    
jacint@101: 	    if( lev > level.get(v) ) {  
jacint@101: 	      /*Push is allowed now*/
jacint@101: 	      
jacint@101: 	      if ( excess.get(v)==0 && v !=t && v!=s ) 
jacint@101: 		stack[level.get(v)].push(v); 
jacint@101: 	      /*v becomes active.*/
jacint@101: 	      
jacint@109: 	      T flo=flow.get(e);
jacint@101: 	      
jacint@101: 	      if ( flo >= exc ) { 
jacint@101: 		/*A nonsaturating push.*/
jacint@101: 		
jacint@101: 		flow.set(e, flo-exc);
jacint@101: 		excess.set(v, excess.get(v)+exc);
jacint@101: 		exc=0;
jacint@101: 		break; 
jacint@101: 	      } else {                                               
jacint@101: 		/*A saturating push.*/
jacint@101: 		
jacint@101: 		excess.set(v, excess.get(v)+flo);
jacint@101: 		exc-=flo;
jacint@101: 		flow.set(e,0);
jacint@101: 	      }  
jacint@101: 	    } else if ( newlevel > level.get(v) ) newlevel = level.get(v);
jacint@101: 	    
jacint@101: 	  } //for in edges vw
jacint@101: 	  
jacint@101: 	} // if w still has excess after the out edge for cycle
jacint@101: 	
jacint@101: 	excess.set(w, exc);
jacint@101: 	  
jacint@101: 
jacint@101: 	/*
jacint@101: 	  Relabel
jacint@101: 	*/
jacint@101: 	
jacint@101: 	if ( exc > 0 ) {
jacint@101: 	  //now 'lev' is the old level of w
jacint@101: 	
jacint@101: 	  if ( phase ) {
jacint@101: 	    level.set(w,++newlevel);
jacint@101: 	    stack[newlevel].push(w);
jacint@101: 	    b=newlevel;
jacint@101: 	  } else {
jacint@101: 
jacint@101: 	    if ( newlevel >= n-2 || --numb[lev] == 0 ) {
jacint@101: 	      
jacint@101: 	      level.set(w,n);
jacint@101: 	      
jacint@101: 	      if ( newlevel < n ) {
jacint@101: 		
jacint@101: 		std::queue<NodeIt> bfs_queue;
jacint@101: 		bfs_queue.push(w);
jacint@101: 
jacint@101: 		while (!bfs_queue.empty()) {
jacint@101: 
jacint@101: 		  NodeIt v=bfs_queue.front();	
jacint@101: 		  bfs_queue.pop();
jacint@101: 
jacint@101: 		  for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) {
jacint@101: 		    if ( capacity.get(e) == flow.get(e) ) continue;
jacint@101: 		    NodeIt u=G.head(e);
jacint@101: 		    if ( level.get(u) < n ) { 
jacint@101: 		      bfs_queue.push(u);
jacint@101: 		      --numb[level.get(u)];
jacint@101: 		      level.set(u, n);
jacint@101: 		    }
jacint@101: 		  }
jacint@101: 
jacint@101: 		  for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {
jacint@101: 		    if ( 0 == flow.get(e) ) continue;
jacint@101: 		    NodeIt u=G.tail(e);
jacint@101: 		    if ( level.get(u) < n ) { 
jacint@101: 		      bfs_queue.push(u);
jacint@101: 		      --numb[level.get(u)];
jacint@101: 		      level.set(u, n);
jacint@101: 		    }
jacint@101: 		  }
jacint@101: 		}
jacint@101: 	      }
jacint@101: 	      b=n-1;
jacint@101: 
jacint@101: 	    } else {
jacint@101: 	      level.set(w,++newlevel);
jacint@101: 	      stack[newlevel].push(w);
jacint@101: 	      ++numb[newlevel];
jacint@101: 	      b=newlevel;
jacint@101: 	    }
jacint@101: 	  }
jacint@101: 	}
jacint@101: 
jacint@101:  
jacint@101: 	
jacint@101: 	} // if stack[b] is nonempty
jacint@101: 	
jacint@101:       } // while(true)
jacint@101: 
jacint@101: 
jacint@101:       value = excess.get(t);
jacint@101:       /*Max flow value.*/
jacint@101: 
jacint@101: 
jacint@101:     } //void run()
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101:     /*
jacint@101:       Returns the maximum value of a flow.
jacint@101:      */
jacint@101: 
jacint@109:     T maxFlow() {
jacint@101:       return value;
jacint@101:     }
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101:     /*
jacint@109:       For the maximum flow x found by the algorithm, 
jacint@109:       it returns the flow value on edge e, i.e. x(e). 
jacint@101:     */
jacint@101: 
jacint@109:     T flowOnEdge(EdgeIt e) {
jacint@101:       return flow.get(e);
jacint@101:     }
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101:     /*
jacint@101:       Returns the maximum flow x found by the algorithm.
jacint@101:     */
jacint@101: 
jacint@109:     FlowMap Flow() {
jacint@101:       return flow;
jacint@101:     }
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101:     /*
jacint@101:       Returns the minimum min cut, by a bfs from s in the residual graph.
jacint@101:     */
jacint@101:     
jacint@101:     template<typename CutMap>
jacint@109:     void minCut(CutMap& M) {
jacint@101:     
jacint@101:       std::queue<NodeIt> queue;
jacint@101:       
jacint@101:       M.set(s,true);      
jacint@101:       queue.push(s);
jacint@101: 
jacint@101:       while (!queue.empty()) {
jacint@101:         NodeIt w=queue.front();
jacint@101: 	queue.pop();
jacint@101: 
jacint@101: 	for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
jacint@101: 	  NodeIt v=G.head(e);
jacint@101: 	  if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
jacint@101: 	    queue.push(v);
jacint@101: 	    M.set(v, true);
jacint@101: 	  }
jacint@101: 	} 
jacint@101: 
jacint@101: 	for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
jacint@101: 	  NodeIt v=G.tail(e);
jacint@101: 	  if (!M.get(v) && flow.get(e) > 0 ) {
jacint@101: 	    queue.push(v);
jacint@101: 	    M.set(v, true);
jacint@101: 	  }
jacint@101: 	} 
jacint@101: 
jacint@101:       }
jacint@101: 
jacint@101:     }
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101:     /*
jacint@101:       Returns the maximum min cut, by a reverse bfs 
jacint@101:       from t in the residual graph.
jacint@101:     */
jacint@101:     
jacint@101:     template<typename CutMap>
jacint@109:     void maxMinCut(CutMap& M) {
jacint@101:     
jacint@101:       std::queue<NodeIt> queue;
jacint@101:       
jacint@101:       M.set(t,true);        
jacint@101:       queue.push(t);
jacint@101: 
jacint@101:       while (!queue.empty()) {
jacint@101:         NodeIt w=queue.front();
jacint@101: 	queue.pop();
jacint@101: 
jacint@101: 	for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
jacint@101: 	  NodeIt v=G.tail(e);
jacint@101: 	  if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
jacint@101: 	    queue.push(v);
jacint@101: 	    M.set(v, true);
jacint@101: 	  }
jacint@101: 	}
jacint@101: 
jacint@101: 	for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
jacint@101: 	  NodeIt v=G.head(e);
jacint@101: 	  if (!M.get(v) && flow.get(e) > 0 ) {
jacint@101: 	    queue.push(v);
jacint@101: 	    M.set(v, true);
jacint@101: 	  }
jacint@101: 	}
jacint@101:       }
jacint@101: 
jacint@101:       for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) {
jacint@101: 	M.set(v, !M.get(v));
jacint@101:       }
jacint@101: 
jacint@101:     }
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101:     template<typename CutMap>
jacint@109:     void minMinCut(CutMap& M) {
jacint@109:       minCut(M);
jacint@101:     }
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101:   };
jacint@109: }//namespace
jacint@101: #endif 
jacint@101: 
jacint@101: 
jacint@101: 
jacint@101: