jacint@98: // -*- C++ -*-
jacint@98: /*
jacint@98: preflow_hl2.h
jacint@98: by jacint. 
jacint@98: Runs the highest label variant of the preflow push algorithm with 
jacint@109: running time O(n^2\sqrt(m)). 
jacint@98: 
jacint@109: Heuristics:
jacint@98: 
jacint@109:   gap: we iterate through the nodes for finding the nodes above 
jacint@109:        the gap and under level n. So it is quite slow.
jacint@109:   numb: we maintain the number of nodes in level i.
jacint@109:   highest label
jacint@109:   
jacint@109: 'A' is a parameter for the gap, we only upgrade the nodes to level n,
jacint@109:   if the gap is under A*n.
jacint@98: 
jacint@109: The constructor runs the algorithm.
jacint@98: 
jacint@109: Members:
jacint@98: 
jacint@109: T maxFlow() : returns the value of a maximum flow
jacint@98: 
jacint@109: T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) 
jacint@98: 
jacint@109: FlowMap Flow() : returns the fixed maximum flow x
jacint@98: 
jacint@109: void minCut(CutMap& M) : sets M to the characteristic vector of a 
jacint@98:      minimum cut. M should be a map of bools initialized to false.
jacint@98: 
jacint@109: void minMinCut(CutMap& M) : sets M to the characteristic vector of the 
jacint@98:      minimum min cut. M should be a map of bools initialized to false.
jacint@98: 
jacint@109: void maxMinCut(CutMap& M) : sets M to the characteristic vector of the 
jacint@98:      maximum min cut. M should be a map of bools initialized to false.
jacint@98: 
jacint@98: */
jacint@98: 
jacint@98: #ifndef PREFLOW_HL2_H
jacint@98: #define PREFLOW_HL2_H
jacint@98: 
jacint@109: #define A .9
jacint@98: 
jacint@98: #include <vector>
jacint@98: #include <stack>
jacint@98: #include <queue>
jacint@98: 
alpar@105: namespace hugo {
jacint@98: 
jacint@98:   template <typename Graph, typename T, 
jacint@109:     typename FlowMap=typename Graph::EdgeMap<T>, 
jacint@109:     typename CapMap=typename Graph::EdgeMap<T> >
jacint@98:   class preflow_hl2 {
jacint@98:     
jacint@98:     typedef typename Graph::NodeIt NodeIt;
jacint@98:     typedef typename Graph::EdgeIt EdgeIt;
jacint@98:     typedef typename Graph::EachNodeIt EachNodeIt;
jacint@98:     typedef typename Graph::OutEdgeIt OutEdgeIt;
jacint@98:     typedef typename Graph::InEdgeIt InEdgeIt;
jacint@98:     
jacint@98:     Graph& G;
jacint@98:     NodeIt s;
jacint@98:     NodeIt t;
jacint@98:     FlowMap flow;
jacint@98:     CapMap& capacity;  
jacint@98:     T value;
jacint@98:     
jacint@98:   public:
jacint@98: 
jacint@98:     preflow_hl2(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) :
jacint@109:       G(_G), s(_s), t(_t), flow(_G), capacity(_capacity) { 
jacint@98: 
jacint@98:       int n=G.nodeNum(); 
jacint@98:       int b=n-2; 
jacint@98:       /*
jacint@98: 	b is a bound on the highest level of an active node. 
jacint@98:       */
jacint@98: 
jacint@109:       typename Graph::NodeMap<int> level(G,n);      
jacint@109:       typename Graph::NodeMap<T> excess(G); 
jacint@109: 
jacint@101:       std::vector<int> numb(n);    
jacint@98:       /*
jacint@98: 	The number of nodes on level i < n. It is
jacint@98: 	initialized to n+1, because of the reverse_bfs-part.
jacint@98:       */
jacint@98: 
jacint@98:       std::vector<std::stack<NodeIt> > stack(2*n-1);    
jacint@98:       //Stack of the active nodes in level i.
jacint@98: 
jacint@98: 
jacint@98:       /*Reverse_bfs from t, to find the starting level.*/
jacint@98:       level.set(t,0);
jacint@98:       std::queue<NodeIt> bfs_queue;
jacint@98:       bfs_queue.push(t);
jacint@98: 
jacint@98:       while (!bfs_queue.empty()) {
jacint@98: 
jacint@98: 	NodeIt v=bfs_queue.front();	
jacint@98: 	bfs_queue.pop();
jacint@98: 	int l=level.get(v)+1;
jacint@98: 
jacint@98: 	for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {
jacint@98: 	  NodeIt w=G.tail(e);
jacint@98: 	  if ( level.get(w) == n ) {
jacint@98: 	    bfs_queue.push(w);
jacint@98: 	    ++numb[l];
jacint@98: 	    level.set(w, l);
jacint@98: 	  }
jacint@98: 	}
jacint@98:       }
jacint@109: 	
jacint@98:       level.set(s,n);
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98:       /* Starting flow. It is everywhere 0 at the moment. */     
jacint@98:       for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) 
jacint@98: 	{
jacint@101: 	  T c=capacity.get(e);
jacint@101: 	  if ( c == 0 ) continue;
jacint@98: 	  NodeIt w=G.head(e);
jacint@98: 	  if ( w!=s ) {	  
jacint@98: 	    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@98: 	}
jacint@109:       
jacint@98:       /* 
jacint@98: 	 End of preprocessing 
jacint@98:       */
jacint@98: 
jacint@98: 
jacint@98:       /*
jacint@98: 	Push/relabel on the highest level active nodes.
jacint@109:       */
jacint@98:       /*While there exists an active node.*/
jacint@98:       while (b) { 
jacint@109: 	if ( stack[b].empty() ) { 
jacint@98: 	  --b;
jacint@109: 	  continue;
jacint@109: 	} 
jacint@109: 	
jacint@109: 	NodeIt w=stack[b].top();   
jacint@109: 	stack[b].pop();           
jacint@109: 	int lev=level.get(w);
jacint@109: 	T exc=excess.get(w);
jacint@109: 	int newlevel=2*n;      //In newlevel we bound the next level of w.
jacint@109: 	
jacint@98: 	  for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
jacint@98: 	    
jacint@98: 	    if ( flow.get(e) == capacity.get(e) ) continue; 
jacint@98: 	    NodeIt v=G.head(e);            
jacint@98: 	    //e=wv	    
jacint@98: 	    
jacint@98: 	    if( lev > level.get(v) ) {      
jacint@98: 	      /*Push is allowed now*/
jacint@98: 	      
jacint@98: 	      if ( excess.get(v)==0 && v != s && v !=t ) 
jacint@98: 		stack[level.get(v)].push(v); 
jacint@98: 	      /*v becomes active.*/
jacint@98: 	      
jacint@109: 	      T cap=capacity.get(e);
jacint@109: 	      T flo=flow.get(e);
jacint@109: 	      T remcap=cap-flo;
jacint@98: 	      
jacint@98: 	      if ( remcap >= exc ) {       
jacint@98: 		/*A nonsaturating push.*/
jacint@98: 		
jacint@98: 		flow.set(e, flo+exc);
jacint@98: 		excess.set(v, excess.get(v)+exc);
jacint@98: 		exc=0;
jacint@98: 		break; 
jacint@98: 		
jacint@98: 	      } else { 
jacint@98: 		/*A saturating push.*/
jacint@98: 		
jacint@98: 		flow.set(e, cap );
jacint@98: 		excess.set(v, excess.get(v)+remcap);
jacint@98: 		exc-=remcap;
jacint@98: 	      }
jacint@98: 	    } else if ( newlevel > level.get(v) ) newlevel = level.get(v);
jacint@98: 	    
jacint@98: 	  } //for out edges wv 
jacint@98: 	
jacint@98: 	
jacint@98: 	if ( exc > 0 ) {	
jacint@98: 	  for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
jacint@98: 	    
jacint@98: 	    if( flow.get(e) == 0 ) continue; 
jacint@98: 	    NodeIt v=G.tail(e);  
jacint@98: 	    //e=vw
jacint@98: 	    
jacint@98: 	    if( lev > level.get(v) ) {  
jacint@98: 	      /*Push is allowed now*/
jacint@98: 	      
jacint@98: 	      if ( excess.get(v)==0 && v != s && v !=t) 
jacint@98: 		stack[level.get(v)].push(v); 
jacint@98: 	      /*v becomes active.*/
jacint@98: 	      
jacint@109: 	      T flo=flow.get(e);
jacint@98: 	      
jacint@98: 	      if ( flo >= exc ) { 
jacint@98: 		/*A nonsaturating push.*/
jacint@98: 		
jacint@98: 		flow.set(e, flo-exc);
jacint@98: 		excess.set(v, excess.get(v)+exc);
jacint@98: 		exc=0;
jacint@98: 		break; 
jacint@98: 	      } else {                                               
jacint@98: 		/*A saturating push.*/
jacint@98: 		
jacint@98: 		excess.set(v, excess.get(v)+flo);
jacint@98: 		exc-=flo;
jacint@98: 		flow.set(e,0);
jacint@98: 	      }  
jacint@98: 	    } else if ( newlevel > level.get(v) ) newlevel = level.get(v);
jacint@98: 	    
jacint@98: 	  } //for in edges vw
jacint@98: 	  
jacint@98: 	} // if w still has excess after the out edge for cycle
jacint@109: 	
jacint@109: 	excess.set(w, exc);
jacint@109: 	
jacint@109: 
jacint@109: 	
jacint@109: 
jacint@109: 	/*
jacint@109: 	  Relabel
jacint@109: 	*/
jacint@109: 	
jacint@109: 	if ( exc > 0 ) {
jacint@109: 	  //now 'lev' is the old level of w
jacint@109: 	  level.set(w,++newlevel);
jacint@98: 	  
jacint@109: 	  if ( lev < n ) {
jacint@109: 	    --numb[lev];
jacint@109: 	    
jacint@109: 	    if ( !numb[lev] && lev < A*n ) {  //If the level of w gets empty. 
jacint@109: 	      
jacint@109: 	      for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) {
jacint@109: 		if (level.get(v) > lev && level.get(v) < n ) level.set(v,n);  
jacint@109: 	      }
jacint@109: 	      for (int i=lev+1 ; i!=n ; ++i) numb[i]=0; 
jacint@109: 	      if ( newlevel < n ) newlevel=n; 
jacint@109: 	    } else { 
jacint@109: 	      if ( newlevel < n ) ++numb[newlevel]; 
jacint@109: 	    }
jacint@109: 	  } 
jacint@98: 	  
jacint@109: 	  stack[newlevel].push(w);
jacint@109: 	  b=newlevel;
jacint@109: 	  
jacint@109: 	}
jacint@109: 	
jacint@98:       } // while(b)
jacint@109:       
jacint@109:       
jacint@98:       value = excess.get(t);
jacint@98:       /*Max flow value.*/
jacint@98: 
jacint@98: 
jacint@98:     } //void run()
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98:     /*
jacint@98:       Returns the maximum value of a flow.
jacint@98:      */
jacint@98: 
jacint@109:     T maxFlow() {
jacint@98:       return value;
jacint@98:     }
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98:     /*
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@98:     */
jacint@98: 
jacint@109:     T flowOnEdge(const EdgeIt e) {
jacint@98:       return flow.get(e);
jacint@98:     }
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98:     /*
jacint@98:       Returns the maximum flow x found by the algorithm.
jacint@98:     */
jacint@98: 
jacint@109:     FlowMap Flow() {
jacint@98:       return flow;
jacint@98:     }
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98:     /*
jacint@98:       Returns the minimum min cut, by a bfs from s in the residual graph.
jacint@98:     */
jacint@98:     
jacint@98:     template<typename CutMap>
jacint@109:     void minCut(CutMap& M) {
jacint@98:     
jacint@98:       std::queue<NodeIt> queue;
jacint@98:       
jacint@98:       M.set(s,true);      
jacint@98:       queue.push(s);
jacint@98: 
jacint@98:       while (!queue.empty()) {
jacint@98:         NodeIt w=queue.front();
jacint@98: 	queue.pop();
jacint@109: 	
jacint@98: 	for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
jacint@98: 	  NodeIt v=G.head(e);
jacint@98: 	  if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
jacint@98: 	    queue.push(v);
jacint@98: 	    M.set(v, true);
jacint@98: 	  }
jacint@98: 	} 
jacint@98: 
jacint@98: 	for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
jacint@98: 	  NodeIt v=G.tail(e);
jacint@98: 	  if (!M.get(v) && flow.get(e) > 0 ) {
jacint@98: 	    queue.push(v);
jacint@98: 	    M.set(v, true);
jacint@98: 	  }
jacint@109: 	}
jacint@98: 
jacint@98:       }
jacint@98:     }
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98:     /*
jacint@98:       Returns the maximum min cut, by a reverse bfs 
jacint@98:       from t in the residual graph.
jacint@98:     */
jacint@98:     
jacint@98:     template<typename CutMap>
jacint@109:     void maxMinCut(CutMap& M) {
jacint@98:     
jacint@98:       std::queue<NodeIt> queue;
jacint@98:       
jacint@98:       M.set(t,true);        
jacint@98:       queue.push(t);
jacint@98: 
jacint@98:       while (!queue.empty()) {
jacint@98:         NodeIt w=queue.front();
jacint@98: 	queue.pop();
jacint@98: 
jacint@98: 	for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
jacint@98: 	  NodeIt v=G.tail(e);
jacint@98: 	  if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
jacint@98: 	    queue.push(v);
jacint@98: 	    M.set(v, true);
jacint@98: 	  }
jacint@98: 	}
jacint@98: 
jacint@98: 	for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
jacint@98: 	  NodeIt v=G.head(e);
jacint@98: 	  if (!M.get(v) && flow.get(e) > 0 ) {
jacint@98: 	    queue.push(v);
jacint@98: 	    M.set(v, true);
jacint@98: 	  }
jacint@98: 	}
jacint@98:       }
jacint@98: 
jacint@98:       for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) {
jacint@98: 	M.set(v, !M.get(v));
jacint@98:       }
jacint@98: 
jacint@98:     }
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98:     template<typename CutMap>
jacint@109:     void minMinCut(CutMap& M) {
jacint@109:       minCut(M);
jacint@98:     }
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98:   };
jacint@109: }//namespace marci
jacint@98: #endif 
jacint@98: 
jacint@98: 
jacint@98: 
jacint@98: