athos@610: // -*- c++ -*-
athos@610: #ifndef HUGO_MINCOSTFLOWS_H
athos@610: #define HUGO_MINCOSTFLOWS_H
athos@610: 
alpar@758: ///\ingroup flowalgs
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: 
athos@610: namespace hugo {
athos@610: 
alpar@758: /// \addtogroup flowalgs
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@610:   /// The class \ref hugo::MinCostFlows "MinCostFlows" implements
athos@610:   /// an algorithm for finding a flow of value \c k 
marci@893:   /// having minimal total cost 
athos@610:   /// from a given source node to a given target node in an
marci@893:   /// edge-weighted directed graph. To this end, 
marci@893:   /// the edge-capacities and edge-weitghs have to be nonnegative. 
marci@893:   /// The edge-capacities should be integers, but the edge-weights can be 
marci@893:   /// integers, reals or of other comparable numeric type.
marci@893:   /// This algorithm is intended to use only for small values of \c k, 
marci@893:   /// since it is only polynomial in k, 
marci@893:   /// not in the length of k (which is log k). 
marci@893:   /// In order to find the minimum cost flow of value \c k it 
athos@860:   /// finds the minimum cost flow of value \c i for every 
marci@893:   /// \c i between 0 and \c k. 
athos@860:   ///
athos@860:   ///\param Graph The directed graph type the algorithm runs on.
athos@860:   ///\param LengthMap The type of the length map.
athos@860:   ///\param CapacityMap The capacity map type.
athos@610:   ///
athos@610:   ///\author Attila Bernath
athos@610:   template <typename Graph, typename LengthMap, typename CapacityMap>
athos@610:   class MinCostFlows {
athos@610: 
athos@610:     typedef typename LengthMap::ValueType Length;
athos@610: 
athos@610:     //Warning: this should be integer type
athos@610:     typedef typename CapacityMap::ValueType Capacity;
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: 
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 Graph::template NodeMap<Length> NodeMap;
athos@610:       const ResGraphType& G;
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@610:     const CapacityMap& capacity;
athos@610: 
athos@610: 
athos@610:     //auxiliary variables
athos@610: 
athos@610:     //To store the flow
athos@610:     EdgeIntMap flow; 
alpar@785:     //To store the potential (dual variables)
athos@661:     typedef typename Graph::template NodeMap<Length> PotentialMap;
athos@661:     PotentialMap potential;
athos@610:     
athos@610: 
athos@610:     Length total_length;
athos@610: 
athos@610: 
athos@610:   public :
athos@610: 
athos@860:     /// The constructor of the class.
athos@860:     
athos@860:     ///\param _G The directed graph the algorithm runs on. 
athos@860:     ///\param _length The length (weight or cost) of the edges. 
athos@860:     ///\param _cap The capacity of the edges. 
athos@610:     MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G), 
athos@610:       length(_length), capacity(_cap), flow(_G), potential(_G){ }
athos@610: 
athos@610:     
athos@610:     ///Runs the algorithm.
athos@860:     
athos@610:     ///Runs the algorithm.
athos@860:     ///Returns k if there is a flow of value at least k edge-disjoint 
athos@860:     ///from s to t.
athos@860:     ///Otherwise it returns the maximum value of a flow from s to t.
athos@860:     ///
athos@860:     ///\param s The source node.
athos@860:     ///\param t The target node.
athos@860:     ///\param k The value of the flow we are looking for.
athos@860:     ///
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@610:     int run(Node s, Node t, int k) {
athos@610: 
athos@610:       //Resetting variables from previous runs
athos@610:       total_length = 0;
athos@610:       
marci@788:       for (typename Graph::EdgeIt e(G); e!=INVALID; ++e) flow.set(e, 0);
athos@634: 
athos@634:       //Initialize the potential to zero
marci@788:       for (typename Graph::NodeIt n(G); n!=INVALID; ++n) potential.set(n, 0);
athos@610:       
athos@610:       
athos@610:       //We need a residual graph
athos@610:       ResGraphType res_graph(G, capacity, flow);
athos@610: 
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@610:       int i;
athos@610:       for (i=0; i<k; ++i){
athos@610: 	dijkstra.run(s);
athos@610: 	if (!dijkstra.reached(t)){
athos@860: 	  //There are no flow of value k from s to t
athos@610: 	  break;
athos@610: 	};
athos@610: 	
athos@634: 	//We have to change the potential
marci@788:         for(typename ResGraphType::NodeIt n(res_graph); n!=INVALID; ++n)
athos@633: 	  potential[n] += dijkstra.distMap()[n];
athos@634: 
athos@610: 
athos@610: 	//Augmenting on the sortest path
athos@610: 	Node n=t;
athos@610: 	ResGraphEdge e;
athos@610: 	while (n!=s){
athos@610: 	  e = dijkstra.pred(n);
athos@610: 	  n = dijkstra.predNode(n);
athos@610: 	  res_graph.augment(e,1);
athos@610: 	  //Let's update the total length
athos@610: 	  if (res_graph.forward(e))
athos@610: 	    total_length += length[e];
athos@610: 	  else 
athos@610: 	    total_length -= length[e];	    
athos@610: 	}
athos@610: 
athos@610: 	  
athos@610:       }
athos@610:       
athos@610: 
athos@610:       return i;
athos@610:     }
athos@610: 
athos@610: 
athos@610: 
athos@860:     /// Gives back the total weight of the found flow.
athos@610: 
athos@860:     ///This function gives back the total weight of the found flow.
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@860:     ///Returns a const reference to the EdgeMap \c flow. 
athos@860: 
athos@860:     ///Returns a const reference to the EdgeMap \c flow. 
athos@860:     ///\pre \ref run() must
athos@610:     ///be called before using this function.
athos@610:     const EdgeIntMap &getFlow() const { return flow;}
athos@610: 
athos@860:     ///Returns a const reference to the NodeMap \c potential (the dual solution).
athos@860: 
athos@860:     ///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@661:     const PotentialMap &getPotential() const { return potential;}
athos@610: 
athos@860:     /// Checking the complementary slackness optimality criteria
athos@860: 
athos@610:     ///This function checks, whether the given solution is optimal
athos@860:     ///If executed after the call of \c run() then it should return with true.
athos@860:     ///This function only checks optimality, doesn't bother with feasibility.
athos@860:     ///It is meant for testing purposes.
athos@610:     ///
athos@610:     bool checkComplementarySlackness(){
athos@610:       Length mod_pot;
athos@610:       Length fl_e;
marci@788:         for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) {
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];
marci@894: 	if (0<fl_e && fl_e<capacity[e]) {
marci@894: 	  /// \todo better comparison is needed for real types, moreover, 
marci@894: 	  /// this comparison here is superfluous.
athos@610: 	  if (mod_pot != 0)
athos@610: 	    return false;
marci@894: 	} 
marci@894: 	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@610:   }; //class MinCostFlows
athos@610: 
athos@610:   ///@}
athos@610: 
athos@610: } //namespace hugo
athos@610: 
athos@633: #endif //HUGO_MINCOSTFLOWS_H