alpar@896: // -*- c++ -*-
alpar@896: #ifndef HUGO_MINLENGTHPATHS_H
alpar@896: #define HUGO_MINLENGTHPATHS_H
alpar@896: 
alpar@896: ///\ingroup flowalgs
alpar@896: ///\file
alpar@896: ///\brief An algorithm for finding k paths of minimal total length.
alpar@896: 
alpar@896: 
alpar@896: #include <hugo/maps.h>
alpar@896: #include <vector>
alpar@896: #include <hugo/min_cost_flows.h>
alpar@896: 
alpar@896: namespace hugo {
alpar@896: 
alpar@896: /// \addtogroup flowalgs
alpar@896: /// @{
alpar@896: 
alpar@896:   ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes 
alpar@896:   /// of minimal total length 
alpar@896:   ///
alpar@896:   /// The class \ref hugo::MinLengthPaths implements
alpar@896:   /// an algorithm for finding k edge-disjoint paths
alpar@896:   /// from a given source node to a given target node in an
alpar@896:   /// edge-weighted directed graph having minimal total weight (length).
alpar@896:   ///
alpar@896:   ///\warning Length values should be nonnegative.
alpar@896:   /// 
alpar@896:   ///\param Graph The directed graph type the algorithm runs on.
alpar@896:   ///\param LengthMap The type of the length map (values should be nonnegative).
alpar@896:   ///
alpar@896:   ///\author Attila Bernath
alpar@896:   template <typename Graph, typename LengthMap>
alpar@896:   class MinLengthPaths{
alpar@896: 
alpar@896: 
alpar@896:     typedef typename LengthMap::ValueType Length;
alpar@896:     
alpar@896:     typedef typename Graph::Node Node;
alpar@896:     typedef typename Graph::NodeIt NodeIt;
alpar@896:     typedef typename Graph::Edge Edge;
alpar@896:     typedef typename Graph::OutEdgeIt OutEdgeIt;
alpar@896:     typedef typename Graph::template EdgeMap<int> EdgeIntMap;
alpar@896: 
alpar@896:     typedef ConstMap<Edge,int> ConstMap;
alpar@896: 
alpar@896:     //Input
alpar@896:     const Graph& G;
alpar@896: 
alpar@896:     //Auxiliary variables
alpar@896:     //This is the capacity map for the mincostflow problem
alpar@896:     ConstMap const1map;
alpar@896:     //This MinCostFlows instance will actually solve the problem
alpar@896:     MinCostFlows<Graph, LengthMap, ConstMap> mincost_flow;
alpar@896: 
alpar@896:     //Container to store found paths
alpar@896:     std::vector< std::vector<Edge> > paths;
alpar@896: 
alpar@896:   public :
alpar@896: 
alpar@896: 
alpar@896:     /// The constructor of the class.
alpar@896:     
alpar@896:     ///\param _G The directed graph the algorithm runs on. 
alpar@896:     ///\param _length The length (weight or cost) of the edges. 
alpar@896:     MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G),
alpar@896:       const1map(1), mincost_flow(_G, _length, const1map){}
alpar@896: 
alpar@896:     ///Runs the algorithm.
alpar@896: 
alpar@896:     ///Runs the algorithm.
alpar@896:     ///Returns k if there are at least k edge-disjoint paths from s to t.
alpar@896:     ///Otherwise it returns the number of found edge-disjoint paths from s to t.
alpar@896:     ///
alpar@896:     ///\param s The source node.
alpar@896:     ///\param t The target node.
alpar@896:     ///\param k How many paths are we looking for?
alpar@896:     ///
alpar@896:     int run(Node s, Node t, int k) {
alpar@896: 
alpar@896:       int i = mincost_flow.run(s,t,k);
alpar@896:     
alpar@896: 
alpar@896:       //Let's find the paths
alpar@896:       //We put the paths into stl vectors (as an inner representation). 
alpar@896:       //In the meantime we lose the information stored in 'reversed'.
alpar@896:       //We suppose the lengths to be positive now.
alpar@896: 
alpar@896:       //We don't want to change the flow of mincost_flow, so we make a copy
alpar@896:       //The name here suggests that the flow has only 0/1 values.
alpar@896:       EdgeIntMap reversed(G); 
alpar@896: 
alpar@896:       for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) 
alpar@896: 	reversed[e] = mincost_flow.getFlow()[e];
alpar@896:       
alpar@896:       paths.clear();
alpar@896:       //total_length=0;
alpar@896:       paths.resize(k);
alpar@896:       for (int j=0; j<i; ++j){
alpar@896: 	Node n=s;
alpar@896: 	OutEdgeIt e;
alpar@896: 
alpar@896: 	while (n!=t){
alpar@896: 
alpar@896: 
alpar@896: 	  G.first(e,n);
alpar@896: 	  
alpar@896: 	  while (!reversed[e]){
alpar@896: 	    ++e;
alpar@896: 	  }
alpar@896: 	  n = G.head(e);
alpar@896: 	  paths[j].push_back(e);
alpar@896: 	  //total_length += length[e];
alpar@896: 	  reversed[e] = 1-reversed[e];
alpar@896: 	}
alpar@896: 	
alpar@896:       }
alpar@896:       return i;
alpar@896:     }
alpar@896: 
alpar@896:     
alpar@896:     ///Returns the total length of the paths
alpar@896:     
alpar@896:     ///This function gives back the total length of the found paths.
alpar@896:     ///\pre \ref run() must
alpar@896:     ///be called before using this function.
alpar@896:     Length totalLength(){
alpar@896:       return mincost_flow.totalLength();
alpar@896:     }
alpar@896: 
alpar@896:     ///Returns the found flow.
alpar@896: 
alpar@896:     ///This function returns a const reference to the EdgeMap \c flow.
alpar@896:     ///\pre \ref run() must
alpar@896:     ///be called before using this function.
alpar@896:     const EdgeIntMap &getFlow() const { return mincost_flow.flow;}
alpar@896: 
alpar@896:     /// Returns the optimal dual solution
alpar@896:     
alpar@896:     ///This function returns a const reference to the NodeMap
alpar@896:     ///\c potential (the dual solution).
alpar@896:     /// \pre \ref run() must be called before using this function.
alpar@896:     const EdgeIntMap &getPotential() const { return mincost_flow.potential;}
alpar@896: 
alpar@896:     ///Checks whether the complementary slackness holds.
alpar@896: 
alpar@896:     ///This function checks, whether the given solution is optimal.
alpar@896:     ///It should return true after calling \ref run() 
alpar@896:     ///Currently this function only checks optimality,
alpar@896:     ///doesn't bother with feasibility
alpar@896:     ///It is meant for testing purposes.
alpar@896:     ///
alpar@896:     bool checkComplementarySlackness(){
alpar@896:       return mincost_flow.checkComplementarySlackness();
alpar@896:     }
alpar@896: 
alpar@896:     ///Read the found paths.
alpar@896:     
alpar@896:     ///This function gives back the \c j-th path in argument p.
alpar@896:     ///Assumes that \c run() has been run and nothing changed since then.
alpar@896:     /// \warning It is assumed that \c p is constructed to
alpar@896:     ///be a path of graph \c G.
alpar@896:     ///If \c j is not less than the result of previous \c run,
alpar@896:     ///then the result here will be an empty path (\c j can be 0 as well).
alpar@896:     ///
alpar@896:     ///\param Path The type of the path structure to put the result to (must meet hugo path concept).
alpar@896:     ///\param p The path to put the result to 
alpar@896:     ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively)
alpar@896:     template<typename Path>
alpar@896:     void getPath(Path& p, size_t j){
alpar@896: 
alpar@896:       p.clear();
alpar@896:       if (j>paths.size()-1){
alpar@896: 	return;
alpar@896:       }
alpar@896:       typename Path::Builder B(p);
alpar@896:       for(typename std::vector<Edge>::iterator i=paths[j].begin(); 
alpar@896: 	  i!=paths[j].end(); ++i ){
alpar@896: 	B.pushBack(*i);
alpar@896:       }
alpar@896: 
alpar@896:       B.commit();
alpar@896:     }
alpar@896: 
alpar@896:   }; //class MinLengthPaths
alpar@896: 
alpar@896:   ///@}
alpar@896: 
alpar@896: } //namespace hugo
alpar@896: 
alpar@896: #endif //HUGO_MINLENGTHPATHS_H