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
athos@610: ///(for small values of \c k) having minimal total cost
athos@610: /// from a given source node to a given target node in an
athos@610: /// edge-weighted directed graph having nonnegative integer capacities.
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@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: // 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@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@610:
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@610:
athos@610: ///Runs the algorithm.
athos@610: ///Returns k if there are at least k edge-disjoint paths from s to t.
athos@610: ///Otherwise it returns the number of found edge-disjoint paths from s to t.
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@610: //There are no k paths 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@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@661: const PotentialMap &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;
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];
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@610: }; //class MinCostFlows
athos@610:
athos@610: ///@}
athos@610:
athos@610: } //namespace hugo
athos@610:
athos@633: #endif //HUGO_MINCOSTFLOWS_H