athos@276: // -*- c++ -*-
athos@523: #ifndef HUGO_MINCOSTFLOWS_H
athos@523: #define HUGO_MINCOSTFLOWS_H
athos@276: 
klao@491: ///\ingroup galgs
alpar@294: ///\file
athos@523: ///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost 
alpar@294: 
athos@276: #include <iostream>
athos@551: #include <hugo/dijkstra.h>
athos@276: #include <graph_wrapper.h>
athos@551: #include <hugo/maps.h>
athos@551: #include <vector>
athos@530: #include <for_each_macros.h>
athos@306: 
athos@276: namespace hugo {
athos@276: 
alpar@430: /// \addtogroup galgs
alpar@430: /// @{
athos@322: 
athos@523:   ///\brief Implementation of an algorithm for finding a flow of value \c k 
athos@523:   ///(for small values of \c k) having minimal total cost between 2 nodes 
athos@523:   /// 
klao@310:   ///
athos@523:   /// The class \ref hugo::MinCostFlows "MinCostFlows" implements
athos@523:   /// an algorithm for finding a flow of value \c k 
athos@523:   ///(for small values of \c k) having minimal total cost  
klao@310:   /// from a given source node to a given target node in an
athos@523:   /// edge-weighted directed graph having nonnegative integer capacities.
athos@523:   /// The range of the length (weight) function is nonnegative reals but 
athos@523:   /// the range of capacity function is the set of nonnegative integers. 
athos@523:   /// It is not a polinomial time algorithm for counting the minimum cost
athos@523:   /// maximal flow, since it counts the minimum cost flow for every value 0..M
athos@523:   /// where \c M is the value of the maximal flow.
alpar@456:   ///
alpar@456:   ///\author Attila Bernath
athos@530:   template <typename Graph, typename LengthMap, typename CapacityMap>
athos@523:   class MinCostFlows {
athos@276: 
klao@310:     typedef typename LengthMap::ValueType Length;
athos@527: 
athos@530:     //Warning: this should be integer type
athos@530:     typedef typename CapacityMap::ValueType Capacity;
athos@511:     
athos@276:     typedef typename Graph::Node Node;
athos@276:     typedef typename Graph::NodeIt NodeIt;
athos@276:     typedef typename Graph::Edge Edge;
athos@276:     typedef typename Graph::OutEdgeIt OutEdgeIt;
athos@511:     typedef typename Graph::template EdgeMap<int> EdgeIntMap;
athos@306: 
athos@527:     //    typedef ConstMap<Edge,int> ConstMap;
athos@306: 
athos@530:     typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;
athos@530:     typedef typename ResGraphType::Edge ResGraphEdge;
athos@547: 
athos@306:     class ModLengthMap {   
athos@547:       //typedef typename ResGraphType::template NodeMap<Length> NodeMap;
athos@547:       typedef typename Graph::template NodeMap<Length> NodeMap;
athos@306:       const ResGraphType& G;
athos@527:       //      const EdgeIntMap& rev;
klao@310:       const LengthMap &ol;
klao@310:       const NodeMap &pot;
athos@306:     public :
athos@306:       typedef typename LengthMap::KeyType KeyType;
athos@306:       typedef typename LengthMap::ValueType ValueType;
athos@511: 	
athos@306:       ValueType operator[](typename ResGraphType::Edge e) const {     
athos@527: 	if (G.forward(e))
athos@527: 	  return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
athos@527: 	else
athos@527: 	  return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
athos@306:       }     
athos@511: 	
athos@530:       ModLengthMap(const ResGraphType& _G,
klao@310: 		   const LengthMap &o,  const NodeMap &p) : 
athos@527: 	G(_G), /*rev(_rev),*/ ol(o), pot(p){}; 
athos@511:     };//ModLengthMap
athos@511: 
athos@511: 
athos@306:     
athos@527:     //Input
athos@276:     const Graph& G;
athos@276:     const LengthMap& length;
athos@530:     const CapacityMap& capacity;
athos@276: 
alpar@328:     //auxiliary variables
athos@322: 
athos@551:     //To store the flow
athos@527:     EdgeIntMap flow; 
athos@551:     //To store the potentila (dual variables)
athos@547:     typename Graph::template NodeMap<Length> potential;
athos@276:     
athos@322:     //Container to store found paths
athos@551:     //std::vector< std::vector<Edge> > paths;
athos@511:     //typedef DirPath<Graph> DPath;
athos@511:     //DPath paths;
athos@511: 
athos@511: 
athos@511:     Length total_length;
athos@322: 
athos@276:   public :
klao@310: 
athos@276: 
athos@530:     MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G), 
athos@547:       length(_length), capacity(_cap), flow(_G), potential(_G){ }
athos@276: 
alpar@294:     
alpar@329:     ///Runs the algorithm.
alpar@329: 
alpar@329:     ///Runs the algorithm.
athos@306:     ///Returns k if there are at least k edge-disjoint paths from s to t.
alpar@329:     ///Otherwise it returns the number of found edge-disjoint paths from s to t.
athos@306:     int run(Node s, Node t, int k) {
athos@276: 
athos@530:       //Resetting variables from previous runs
athos@530:       total_length = 0;
athos@547:       
athos@530:       FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
athos@530: 	flow.set(e,0);
athos@530:       }
athos@547:       
athos@547:       FOR_EACH_LOC(typename Graph::NodeIt, n, G){
athos@547: 	//cout << potential[n]<<endl;
athos@547: 	potential.set(n,0);
athos@547:       }
athos@547:       
athos@511: 
athos@530:       
athos@527:       //We need a residual graph
athos@527:       ResGraphType res_graph(G, capacity, flow);
athos@306: 
athos@306:       //Initialize the copy of the Dijkstra potential to zero
athos@547:       
athos@547:       //typename ResGraphType::template NodeMap<Length> potential(res_graph);
athos@547: 
athos@547: 
athos@547:       ModLengthMap mod_length(res_graph, length, potential);
athos@306: 
athos@306:       Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
athos@322: 
athos@322:       int i;
athos@322:       for (i=0; i<k; ++i){
athos@276: 	dijkstra.run(s);
athos@276: 	if (!dijkstra.reached(t)){
athos@314: 	  //There are no k paths from s to t
athos@322: 	  break;
athos@276: 	};
athos@306: 	
athos@306: 	{
athos@306: 	  //We have to copy the potential
athos@306: 	  typename ResGraphType::NodeIt n;
athos@306: 	  for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) {
athos@547: 	      potential[n] += dijkstra.distMap()[n];
athos@306: 	  }
athos@306: 	}
athos@306: 
athos@306: 
athos@527: 	//Augmenting on the sortest path
athos@276: 	Node n=t;
athos@530: 	ResGraphEdge e;
athos@276: 	while (n!=s){
athos@291: 	  e = dijkstra.pred(n);
athos@291: 	  n = dijkstra.predNode(n);
athos@530: 	  res_graph.augment(e,1);
athos@530: 	  //Let's update the total length
athos@530: 	  if (res_graph.forward(e))
athos@530: 	    total_length += length[e];
athos@530: 	  else 
athos@530: 	    total_length -= length[e];	    
athos@276: 	}
athos@276: 
athos@276: 	  
athos@276:       }
athos@322:       
athos@322: 
athos@322:       return i;
athos@276:     }
athos@276: 
athos@530: 
athos@530: 
athos@547: 
athos@511:     ///This function gives back the total length of the found paths.
athos@511:     ///Assumes that \c run() has been run and nothing changed since then.
athos@511:     Length totalLength(){
athos@511:       return total_length;
athos@511:     }
athos@511: 
athos@551:     //This function checks, whether the given solution is optimal
athos@551:     //Running after a \c run() should return with true
athos@554:     //In this "state of the art" this only check optimality, doesn't bother with feasibility
athos@551:     bool checkSolution(){
athos@551:       Length mod_pot;
athos@551:       Length fl_e;
athos@551:       FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
athos@551: 	//C^{\Pi}_{i,j}
athos@554: 	mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
athos@551: 	fl_e = flow[e];
athos@554: 	//	std::cout << fl_e << std::endl;
athos@551: 	if (0<fl_e && fl_e<capacity[e]){
athos@551: 	  if (mod_pot != 0)
athos@551: 	    return false;
athos@551: 	}
athos@551: 	else{
athos@551: 	  if (mod_pot > 0 && fl_e != 0)
athos@551: 	    return false;
athos@551: 	  if (mod_pot < 0 && fl_e != capacity[e])
athos@551: 	    return false;
athos@551: 	}
athos@551:       }
athos@551:       return true;
athos@551:     }
athos@551:     
athos@530:     /*
athos@530:       ///\todo To be implemented later
athos@530: 
athos@511:     ///This function gives back the \c j-th path in argument p.
athos@511:     ///Assumes that \c run() has been run and nothing changed since then.
athos@519:     /// \warning It is assumed that \c p is constructed to be a path of graph \c G. If \c j is greater than the result of previous \c run, then the result here will be an empty path.
athos@511:     template<typename DirPath>
athos@511:     void getPath(DirPath& p, int j){
athos@511:       p.clear();
athos@511:       typename DirPath::Builder B(p);
athos@511:       for(typename std::vector<Edge>::iterator i=paths[j].begin(); 
athos@511: 	  i!=paths[j].end(); ++i ){
athos@520: 	B.pushBack(*i);
athos@511:       }
athos@511: 
athos@511:       B.commit();
athos@511:     }
athos@276: 
athos@530:     */
athos@530: 
athos@530:   }; //class MinCostFlows
athos@276: 
alpar@430:   ///@}
athos@276: 
athos@276: } //namespace hugo
athos@276: 
athos@527: #endif //HUGO_MINCOSTFLOW_H