athos@610: // -*- c++ -*-
athos@633: #ifndef HUGO_MINCOSTFLOW_H
athos@633: #define HUGO_MINCOSTFLOW_H
athos@610: 
athos@610: ///\ingroup galgs
athos@610: ///\file
athos@610: ///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost 
athos@610: 
athos@611: 
athos@610: #include <hugo/dijkstra.h>
athos@610: #include <hugo/graph_wrapper.h>
athos@610: #include <hugo/maps.h>
athos@610: #include <vector>
athos@610: #include <for_each_macros.h>
athos@610: 
athos@610: namespace hugo {
athos@610: 
athos@610: /// \addtogroup galgs
athos@610: /// @{
athos@610: 
athos@610:   ///\brief Implementation of an algorithm for finding a flow of value \c k 
athos@610:   ///(for small values of \c k) having minimal total cost between 2 nodes 
athos@610:   /// 
athos@610:   ///
athos@633:   /// The class \ref hugo::MinCostFlow "MinCostFlow" implements
athos@633:   /// an algorithm for solving the following general minimum cost flow problem>
athos@633:   /// 
athos@633:   ///
athos@633:   ///
athos@633:   /// \warning It is assumed here that the problem has a feasible solution
athos@633:   ///
athos@610:   /// The range of the length (weight) function is nonnegative reals but 
athos@610:   /// the range of capacity function is the set of nonnegative integers. 
athos@610:   /// It is not a polinomial time algorithm for counting the minimum cost
athos@610:   /// maximal flow, since it counts the minimum cost flow for every value 0..M
athos@610:   /// where \c M is the value of the maximal flow.
athos@610:   ///
athos@610:   ///\author Attila Bernath
athos@635:   template <typename Graph, typename LengthMap, typename SupplyDemandMap>
athos@633:   class MinCostFlow {
athos@610: 
athos@610:     typedef typename LengthMap::ValueType Length;
athos@610: 
athos@633: 
athos@635:     typedef typename SupplyDemandMap::ValueType SupplyDemand;
athos@610:     
athos@610:     typedef typename Graph::Node Node;
athos@610:     typedef typename Graph::NodeIt NodeIt;
athos@610:     typedef typename Graph::Edge Edge;
athos@610:     typedef typename Graph::OutEdgeIt OutEdgeIt;
athos@610:     typedef typename Graph::template EdgeMap<int> EdgeIntMap;
athos@610: 
athos@610:     //    typedef ConstMap<Edge,int> ConstMap;
athos@610: 
athos@610:     typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;
athos@610:     typedef typename ResGraphType::Edge ResGraphEdge;
athos@610: 
athos@610:     class ModLengthMap {   
athos@610:       //typedef typename ResGraphType::template NodeMap<Length> NodeMap;
athos@610:       typedef typename Graph::template NodeMap<Length> NodeMap;
athos@610:       const ResGraphType& G;
athos@610:       //      const EdgeIntMap& rev;
athos@610:       const LengthMap &ol;
athos@610:       const NodeMap &pot;
athos@610:     public :
athos@610:       typedef typename LengthMap::KeyType KeyType;
athos@610:       typedef typename LengthMap::ValueType ValueType;
athos@610: 	
athos@610:       ValueType operator[](typename ResGraphType::Edge e) const {     
athos@610: 	if (G.forward(e))
athos@610: 	  return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
athos@610: 	else
athos@610: 	  return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
athos@610:       }     
athos@610: 	
athos@610:       ModLengthMap(const ResGraphType& _G,
athos@610: 		   const LengthMap &o,  const NodeMap &p) : 
athos@610: 	G(_G), /*rev(_rev),*/ ol(o), pot(p){}; 
athos@610:     };//ModLengthMap
athos@610: 
athos@610: 
athos@610:   protected:
athos@610:     
athos@610:     //Input
athos@610:     const Graph& G;
athos@610:     const LengthMap& length;
athos@635:     const SupplyDemandMap& supply_demand;//supply or demand of nodes
athos@610: 
athos@610: 
athos@610:     //auxiliary variables
athos@610: 
athos@610:     //To store the flow
athos@610:     EdgeIntMap flow; 
athos@610:     //To store the potentila (dual variables)
athos@610:     typename Graph::template NodeMap<Length> potential;
athos@633:     //To store excess-deficit values
athos@635:     SupplyDemandMap excess_deficit;
athos@610:     
athos@610: 
athos@610:     Length total_length;
athos@610: 
athos@610: 
athos@610:   public :
athos@610: 
athos@610: 
athos@635:     MinCostFlow(Graph& _G, LengthMap& _length, SupplyDemandMap& _supply_demand) : G(_G), 
athos@635:       length(_length), supply_demand(_supply_demand), flow(_G), potential(_G){ }
athos@610: 
athos@610:     
athos@610:     ///Runs the algorithm.
athos@610: 
athos@610:     ///Runs the algorithm.
athos@635: 
athos@610:     ///\todo May be it does make sense to be able to start with a nonzero 
athos@610:     /// feasible primal-dual solution pair as well.
athos@633:     int run() {
athos@610: 
athos@610:       //Resetting variables from previous runs
athos@635:       //total_length = 0;
athos@635: 
athos@635:       typedef typename Graph::template NodeMap<int> HeapMap;
athos@635:       typedef Heap<Node, SupplyDemand, typename Graph::template NodeMap<int>,
athos@635: 	std::greater<SupplyDemand> > 	HeapType;
athos@635: 
athos@635:       //A heap for the excess nodes
athos@635:       HeapMap excess_nodes_map(G,-1);
athos@635:       HeapType excess_nodes(excess_nodes_map);
athos@635: 
athos@635:       //A heap for the deficit nodes
athos@635:       HeapMap deficit_nodes_map(G,-1);
athos@635:       HeapType deficit_nodes(deficit_nodes_map);
athos@635: 
athos@610:       
athos@610:       FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
athos@610: 	flow.set(e,0);
athos@610:       }
athos@633: 
athos@633:       //Initial value for delta
athos@635:       SupplyDemand delta = 0;
athos@635: 
athos@610:       FOR_EACH_LOC(typename Graph::NodeIt, n, G){
athos@635:        	excess_deficit.set(n,supply_demand[n]);
athos@635: 	//A supply node
athos@635: 	if (excess_deficit[n] > 0){
athos@635: 	  excess_nodes.push(n,excess_deficit[n]);
athos@633: 	}
athos@635: 	//A demand node
athos@635: 	if (excess_deficit[n] < 0){
athos@635: 	  deficit_nodes.push(n, - excess_deficit[n]);
athos@635: 	}
athos@635: 	//Finding out starting value of delta
athos@635: 	if (delta < abs(excess_deficit[n])){
athos@635: 	  delta = abs(excess_deficit[n]);
athos@635: 	}
athos@633: 	//Initialize the copy of the Dijkstra potential to zero
athos@610: 	potential.set(n,0);
athos@610:       }
athos@610: 
athos@635:       //It'll be allright as an initial value, though this value 
athos@635:       //can be the maximum deficit here
athos@635:       SupplyDemand max_excess = delta;
athos@610:       
athos@633:       //We need a residual graph which is uncapacitated
athos@633:       ResGraphType res_graph(G, flow);
athos@610: 
athos@633: 
athos@610:       
athos@610:       ModLengthMap mod_length(res_graph, length, potential);
athos@610: 
athos@610:       Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
athos@610: 
athos@633: 
athos@635:       while (max_excess > 0){
athos@635: 
athos@610: 	
athos@635: 	//Merge and stuff
athos@635: 
athos@635: 	Node s = excess_nodes.top(); 
athos@635: 	SupplyDemand max_excess = excess_nodes[s];
athos@635: 	Node t = deficit_nodes.top(); 
athos@635: 	if (max_excess < dificit_nodes[t]){
athos@635: 	  max_excess = dificit_nodes[t];
athos@635: 	}
athos@635: 
athos@635: 
athos@635: 	while(max_excess > ){
athos@635: 
athos@635: 	  
athos@635: 	  //s es t valasztasa
athos@635: 
athos@635: 	  //Dijkstra part	
athos@635: 	  dijkstra.run(s);
athos@635: 
athos@635: 	  /*We know from theory that t can be reached
athos@635: 	  if (!dijkstra.reached(t)){
athos@635: 	    //There are no k paths from s to t
athos@635: 	    break;
athos@635: 	  };
athos@635: 	  */
athos@635: 	  
athos@635: 	  //We have to change the potential
athos@635: 	  FOR_EACH_LOC(typename ResGraphType::NodeIt, n, res_graph){
athos@635: 	    potential[n] += dijkstra.distMap()[n];
athos@635: 	  }
athos@635: 
athos@635: 
athos@635: 	  //Augmenting on the sortest path
athos@635: 	  Node n=t;
athos@635: 	  ResGraphEdge e;
athos@635: 	  while (n!=s){
athos@635: 	    e = dijkstra.pred(n);
athos@635: 	    n = dijkstra.predNode(n);
athos@635: 	    res_graph.augment(e,delta);
athos@635: 	    /*
athos@635: 	    //Let's update the total length
athos@635: 	    if (res_graph.forward(e))
athos@635: 	      total_length += length[e];
athos@635: 	    else 
athos@635: 	      total_length -= length[e];	    
athos@635: 	    */
athos@635: 	  }
athos@635: 
athos@635: 	  //Update the excess_nodes heap
athos@635: 	  if (delta >= excess_nodes[s]){
athos@635: 	    if (delta > excess_nodes[s])
athos@635: 	      deficit_nodes.push(s,delta - excess_nodes[s]);
athos@635: 	    excess_nodes.pop();
athos@635: 	    
athos@635: 	  } 
athos@635: 	  else{
athos@635: 	    excess_nodes[s] -= delta;
athos@635: 	  }
athos@635: 	  //Update the deficit_nodes heap
athos@635: 	  if (delta >= deficit_nodes[t]){
athos@635: 	    if (delta > deficit_nodes[t])
athos@635: 	      excess_nodes.push(t,delta - deficit_nodes[t]);
athos@635: 	    deficit_nodes.pop();
athos@635: 	    
athos@635: 	  } 
athos@635: 	  else{
athos@635: 	    deficit_nodes[t] -= delta;
athos@635: 	  }
athos@635: 	  //Dijkstra part ends here
athos@633: 	}
athos@633: 
athos@633: 	/*
athos@635: 	 * End of the delta scaling phase 
athos@635: 	*/
athos@633: 
athos@635: 	//Whatever this means
athos@635: 	delta = delta / 2;
athos@635: 
athos@635: 	/*This is not necessary here
athos@635: 	//Update the max_excess
athos@635: 	max_excess = 0;
athos@635: 	FOR_EACH_LOC(typename Graph::NodeIt, n, G){
athos@635: 	  if (max_excess < excess_deficit[n]){
athos@635: 	    max_excess = excess_deficit[n];
athos@610: 	  }
athos@610: 	}
athos@633: 	*/
athos@635: 	//Reset delta if still too big
athos@635: 	if (8*number_of_nodes*max_excess <= delta){
athos@635: 	  delta = max_excess;
athos@635: 	  
athos@610: 	}
athos@610: 	  
athos@635:       }//while(max_excess > 0)
athos@610:       
athos@610: 
athos@610:       return i;
athos@610:     }
athos@610: 
athos@610: 
athos@610: 
athos@610: 
athos@610:     ///This function gives back the total length of the found paths.
athos@610:     ///Assumes that \c run() has been run and nothing changed since then.
athos@610:     Length totalLength(){
athos@610:       return total_length;
athos@610:     }
athos@610: 
athos@610:     ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must
athos@610:     ///be called before using this function.
athos@610:     const EdgeIntMap &getFlow() const { return flow;}
athos@610: 
athos@610:   ///Returns a const reference to the NodeMap \c potential (the dual solution).
athos@610:     /// \pre \ref run() must be called before using this function.
athos@610:     const EdgeIntMap &getPotential() const { return potential;}
athos@610: 
athos@610:     ///This function checks, whether the given solution is optimal
athos@610:     ///Running after a \c run() should return with true
athos@610:     ///In this "state of the art" this only check optimality, doesn't bother with feasibility
athos@610:     ///
athos@610:     ///\todo Is this OK here?
athos@610:     bool checkComplementarySlackness(){
athos@610:       Length mod_pot;
athos@610:       Length fl_e;
athos@610:       FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
athos@610: 	//C^{\Pi}_{i,j}
athos@610: 	mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
athos@610: 	fl_e = flow[e];
athos@610: 	//	std::cout << fl_e << std::endl;
athos@610: 	if (0<fl_e && fl_e<capacity[e]){
athos@610: 	  if (mod_pot != 0)
athos@610: 	    return false;
athos@610: 	}
athos@610: 	else{
athos@610: 	  if (mod_pot > 0 && fl_e != 0)
athos@610: 	    return false;
athos@610: 	  if (mod_pot < 0 && fl_e != capacity[e])
athos@610: 	    return false;
athos@610: 	}
athos@610:       }
athos@610:       return true;
athos@610:     }
athos@610:     
athos@610: 
athos@633:   }; //class MinCostFlow
athos@610: 
athos@610:   ///@}
athos@610: 
athos@610: } //namespace hugo
athos@610: 
athos@610: #endif //HUGO_MINCOSTFLOW_H