jacint@72: // -*- C++ -*-
jacint@72: /*
jacint@83: preflow_push_hl.h
jacint@72: by jacint. 
jacint@72: Runs the highest label variant of the preflow push algorithm with 
jacint@72: running time O(n^2\sqrt(m)). 
jacint@72: 
jacint@72: Member functions:
jacint@72: 
jacint@72: void run() : runs the algorithm
jacint@72: 
jacint@72:  The following functions should be used after run() was already run.
jacint@72: 
jacint@72: T maxflow() : returns the value of a maximum flow
jacint@72: 
jacint@83: T flowonedge(EdgeIt e) : for a fixed maximum flow x it returns x(e) 
jacint@72: 
jacint@83: Graph::EdgeMap<T> allflow() : returns the fixed maximum flow x
jacint@72: 
jacint@83: Graph::NodeMap<bool> mincut() : returns a 
jacint@72:      characteristic vector of a minimum cut. (An empty level 
jacint@72:      in the algorithm gives a minimum cut.)
jacint@72: */
jacint@72: 
jacint@72: #ifndef PREFLOW_PUSH_HL_H
jacint@72: #define PREFLOW_PUSH_HL_H
jacint@72: 
jacint@85: //#include <algorithm>
jacint@72: #include <vector>
jacint@72: #include <stack>
jacint@72: 
jacint@78: #include <reverse_bfs.h>
jacint@72: 
jacint@72: namespace marci {
jacint@72: 
jacint@78:   template <typename Graph, typename T>
jacint@72:   class preflow_push_hl {
jacint@72:     
jacint@72:     typedef typename Graph::NodeIt NodeIt;
jacint@72:     typedef typename Graph::EdgeIt EdgeIt;
jacint@72:     typedef typename Graph::EachNodeIt EachNodeIt;
jacint@72:     typedef typename Graph::OutEdgeIt OutEdgeIt;
jacint@72:     typedef typename Graph::InEdgeIt InEdgeIt;
jacint@72:     
jacint@72:     Graph& G;
jacint@72:     NodeIt s;
jacint@72:     NodeIt t;
jacint@78:     typename Graph::EdgeMap<T> flow;
jacint@78:     typename Graph::EdgeMap<T> capacity; 
jacint@72:     T value;
jacint@78:     typename Graph::NodeMap<bool> mincutvector;
jacint@72: 
jacint@72:   public:
jacint@72: 
jacint@72:     preflow_push_hl(Graph& _G, NodeIt _s, NodeIt _t, 
jacint@78: 		    typename Graph::EdgeMap<T>& _capacity) :
jacint@83:       G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), 
jacint@83:       mincutvector(_G, true) { }
jacint@72: 
jacint@72: 
jacint@72:     /*
jacint@72:       The run() function runs the highest label preflow-push, 
jacint@72:       running time: O(n^2\sqrt(m))
jacint@72:     */
jacint@72:     void run() {
jacint@72:  
jacint@83:       typename Graph::NodeMap<int> level(G);      
jacint@84:       typename Graph::NodeMap<T> excess(G); 
jacint@85: 
jacint@84:       int n=G.nodeNum(); 
jacint@83:       int b=n-2; 
jacint@83:       /*
jacint@83: 	b is a bound on the highest level of an active node. 
jacint@83: 	In the beginning it is at most n-2.
jacint@83:       */
jacint@72: 
jacint@85:       std::vector<int> numb(n);     //The number of nodes on level i < n.
jacint@83:       std::vector<std::stack<NodeIt> > stack(2*n-1);    
jacint@83:       //Stack of the active nodes in level i.
jacint@72: 
jacint@72: 
jacint@72:       /*Reverse_bfs from t, to find the starting level.*/
jacint@78:       reverse_bfs<Graph> bfs(G, t);
jacint@72:       bfs.run();
jacint@83:       for(EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) 
jacint@83: 	{
jacint@85: 	  int dist=bfs.dist(v);
jacint@85: 	  level.set(v, dist);
jacint@85: 	  ++numb[dist];
jacint@83: 	}
jacint@72: 
jacint@72:       level.set(s,n);
jacint@72: 
jacint@72: 
jacint@83:       /* Starting flow. It is everywhere 0 at the moment. */     
jacint@83:       for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) 
jacint@72: 	{
jacint@83: 	  if ( capacity.get(e) > 0 ) {
jacint@83: 	    NodeIt w=G.head(e);
jacint@85: 	    if ( w!=s ) {	  
jacint@85: 	      if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); 
jacint@85: 	      flow.set(e, capacity.get(e)); 
jacint@85: 	      excess.set(w, excess.get(w)+capacity.get(e));
jacint@85: 	    }
jacint@83: 	  }
jacint@72: 	}
jacint@72: 
jacint@72:       /* 
jacint@72: 	 End of preprocessing 
jacint@72:       */
jacint@72: 
jacint@72: 
jacint@72: 
jacint@72:       /*
jacint@84: 	Push/relabel on the highest level active nodes.
jacint@72:       */
jacint@72: 	
jacint@85:       /*While there exists an active node.*/
jacint@72:       while (b) { 
jacint@72: 
jacint@85: 	/*We decrease the bound if there is no active node of level b.*/
jacint@72: 	if (stack[b].empty()) {
jacint@72: 	  --b;
jacint@72: 	} else {
jacint@72: 
jacint@84: 	  NodeIt w=stack[b].top();        //w is a highest label active node.
jacint@84: 	  stack[b].pop();           
jacint@72: 	
jacint@84: 	  int newlevel=2*n-2;             //In newlevel we bound the next level of w.
jacint@72: 	
jacint@72: 	  for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
jacint@84: 	    
jacint@84: 	    if ( flow.get(e) < capacity.get(e) ) {              
jacint@84: 	      /*e is an edge of the residual graph */
jacint@72: 
jacint@84: 	      NodeIt v=G.head(e);               /*e is the edge wv.*/
jacint@72: 
jacint@84: 	      if( level.get(w) == level.get(v)+1 ) {      
jacint@72: 		/*Push is allowed now*/
jacint@72: 
jacint@85: 		if ( excess.get(v)==0 && v != s && v !=t ) stack[level.get(v)].push(v); 
jacint@85: 		/*v becomes active.*/
jacint@85: 
jacint@85: 		if ( capacity.get(e)-flow.get(e) > excess.get(w) ) {       
jacint@72: 		  /*A nonsaturating push.*/
jacint@72: 		  
jacint@72: 		  flow.set(e, flow.get(e)+excess.get(w));
jacint@72: 		  excess.set(v, excess.get(v)+excess.get(w));
jacint@72: 		  excess.set(w,0);
jacint@72: 		  break; 
jacint@85: 
jacint@72: 		} else { 
jacint@72: 		  /*A saturating push.*/
jacint@72: 
jacint@72: 		  excess.set(v, excess.get(v)+capacity.get(e)-flow.get(e));
jacint@72: 		  excess.set(w, excess.get(w)-capacity.get(e)+flow.get(e));
jacint@72: 		  flow.set(e, capacity.get(e));
jacint@85: 		  if ( excess.get(w)==0 ) break;
jacint@85: 		  /*If w is not active any more, then we go on to the next node.*/
jacint@72: 		  
jacint@85: 		}
jacint@85: 	      } else {
jacint@85: 		newlevel = newlevel < level.get(v) ? newlevel : level.get(v);
jacint@85: 	      }
jacint@72: 	    
jacint@85: 	    } //if the out edge wv is in the res graph 
jacint@72: 	 
jacint@85: 	  } //for out edges wv 
jacint@72: 	  
jacint@72: 
jacint@85: 	  if ( excess.get(w) > 0 ) {	
jacint@85: 	    
jacint@85: 	    for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
jacint@85: 	      NodeIt v=G.tail(e);  /*e is the edge vw.*/
jacint@72: 
jacint@85: 	      if( flow.get(e) > 0 ) {             
jacint@85: 		/*e is an edge of the residual graph */
jacint@72: 
jacint@85: 		if( level.get(w)==level.get(v)+1 ) {  
jacint@85: 		  /*Push is allowed now*/
jacint@72: 		
jacint@85: 		  if ( excess.get(v)==0 && v != s && v !=t) stack[level.get(v)].push(v); 
jacint@72: 		  /*v becomes active.*/
jacint@72: 
jacint@85: 		  if ( flow.get(e) > excess.get(w) ) { 
jacint@85: 		    /*A nonsaturating push.*/
jacint@72: 		  
jacint@85: 		    flow.set(e, flow.get(e)-excess.get(w));
jacint@85: 		    excess.set(v, excess.get(v)+excess.get(w));
jacint@85: 		    excess.set(w,0);
jacint@85: 		    break; 
jacint@85: 		  } else {                                               
jacint@85: 		    /*A saturating push.*/
jacint@85: 		    
jacint@85: 		    excess.set(v, excess.get(v)+flow.get(e));
jacint@85: 		    excess.set(w, excess.get(w)-flow.get(e));
jacint@85: 		    flow.set(e,0);
jacint@85: 		    if ( excess.get(w)==0 ) break;
jacint@85: 		  }  
jacint@85: 		} else {
jacint@85: 		  newlevel = newlevel < level.get(v) ? newlevel : level.get(v);
jacint@85: 		}
jacint@85: 		
jacint@85: 	      } //if in edge vw is in the res graph 
jacint@72: 
jacint@85: 	    } //for in edges vw
jacint@72: 
jacint@85: 	  } // if w still has excess after the out edge for cycle
jacint@72: 
jacint@72: 
jacint@85: 	  /*
jacint@85: 	    Relabel
jacint@85: 	  */
jacint@85: 	  
jacint@85: 	  if ( excess.get(w) > 0 ) {
jacint@85: 	    
jacint@85: 	    int oldlevel=level.get(w);	    
jacint@72: 	    level.set(w,++newlevel);
jacint@85: 
jacint@85: 	    if ( oldlevel < n ) {
jacint@85: 	      --numb[oldlevel];
jacint@85: 
jacint@85: 	      if ( !numb[oldlevel] ) {  //If the level of w gets empty. 
jacint@85: 		
jacint@85: 		for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) {
jacint@85: 		  if (level.get(v) > oldlevel && level.get(v) < n ) level.set(v,n);  
jacint@85: 		}
jacint@85: 		for (int i=oldlevel+1 ; i!=n ; ++i) numb[i]=0; 
jacint@85: 		if ( newlevel < n ) newlevel=n; 
jacint@85: 	      } else { 
jacint@85: 		if ( newlevel < n ) ++numb[newlevel]; 
jacint@85: 	      }
jacint@85: 	    } else { 
jacint@85: 	    if ( newlevel < n ) ++numb[newlevel];
jacint@85: 	    }
jacint@85: 	    
jacint@72: 	    stack[newlevel].push(w);
jacint@72: 	    b=newlevel;
jacint@85: 
jacint@72: 	  }
jacint@72: 
jacint@85: 	} // if stack[b] is nonempty
jacint@72: 
jacint@85:       } // while(b)
jacint@85: 
jacint@72: 
jacint@72:       value = excess.get(t);
jacint@72:       /*Max flow value.*/
jacint@72: 
jacint@72: 
jacint@72:     } //void run()
jacint@72: 
jacint@72: 
jacint@72: 
jacint@72: 
jacint@72: 
jacint@72:     /*
jacint@72:       Returns the maximum value of a flow.
jacint@72:      */
jacint@72: 
jacint@72:     T maxflow() {
jacint@72:       return value;
jacint@72:     }
jacint@72: 
jacint@72: 
jacint@72: 
jacint@72:     /*
jacint@72:       For the maximum flow x found by the algorithm, it returns the flow value on Edge e, i.e. x(e). 
jacint@72:     */
jacint@72: 
jacint@72:     T flowonEdge(EdgeIt e) {
jacint@72:       return flow.get(e);
jacint@72:     }
jacint@72: 
jacint@72: 
jacint@72: 
jacint@72:     /*
jacint@72:       Returns the maximum flow x found by the algorithm.
jacint@72:     */
jacint@72: 
jacint@78:     typename Graph::EdgeMap<T> allflow() {
jacint@72:       return flow;
jacint@72:     }
jacint@72: 
jacint@72: 
jacint@72: 
jacint@72:     /*
jacint@72:       Returns a minimum cut by using a reverse bfs from t in the residual graph.
jacint@72:     */
jacint@72:     
jacint@78:     typename Graph::NodeMap<bool> mincut() {
jacint@72:     
jacint@72:       std::queue<NodeIt> queue;
jacint@72:       
jacint@72:       mincutvector.set(t,false);      
jacint@72:       queue.push(t);
jacint@72: 
jacint@72:       while (!queue.empty()) {
jacint@72:         NodeIt w=queue.front();
jacint@72: 	queue.pop();
jacint@72: 
jacint@72: 	for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
jacint@72: 	  NodeIt v=G.tail(e);
jacint@72: 	  if (mincutvector.get(v) && flow.get(e) < capacity.get(e) ) {
jacint@72: 	    queue.push(v);
jacint@72: 	    mincutvector.set(v, false);
jacint@72: 	  }
jacint@72: 	} // for
jacint@72: 
jacint@72: 	for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
jacint@72: 	  NodeIt v=G.head(e);
jacint@72: 	  if (mincutvector.get(v) && flow.get(e) > 0 ) {
jacint@72: 	    queue.push(v);
jacint@72: 	    mincutvector.set(v, false);
jacint@72: 	  }
jacint@72: 	} // for
jacint@72: 
jacint@72:       }
jacint@72: 
jacint@72:       return mincutvector;
jacint@72:     
jacint@72:     }
jacint@72:   };
jacint@72: }//namespace marci
jacint@72: #endif 
jacint@72: 
jacint@72: 
jacint@72: 
jacint@72: