athos@610: // -*- c++ -*-
athos@610: #ifndef HUGO_MINLENGTHPATHS_H
athos@610: #define HUGO_MINLENGTHPATHS_H
athos@610: 
alpar@759: ///\ingroup flowalgs
athos@610: ///\file
athos@610: ///\brief An algorithm for finding k paths of minimal total length.
athos@610: 
athos@611: 
athos@610: #include <hugo/maps.h>
athos@610: #include <vector>
athos@610: #include <hugo/mincostflows.h>
athos@610: 
athos@610: namespace hugo {
athos@610: 
alpar@759: /// \addtogroup flowalgs
athos@610: /// @{
athos@610: 
athos@860:   ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes 
athos@610:   /// of minimal total length 
athos@610:   ///
athos@860:   /// The class \ref hugo::MinLengthPaths implements
athos@610:   /// an algorithm for finding k edge-disjoint paths
athos@610:   /// from a given source node to a given target node in an
athos@860:   /// edge-weighted directed graph having minimal total weight (length).
athos@610:   ///
athos@860:   ///\warning Length values should be nonnegative.
athos@860:   /// 
athos@860:   ///\param Graph The directed graph type the algorithm runs on.
athos@860:   ///\param LengthMap The type of the length map (values should be nonnegative).
athos@610:   ///
athos@610:   ///\author Attila Bernath
athos@610:   template <typename Graph, typename LengthMap>
athos@610:   class MinLengthPaths{
athos@610: 
athos@610: 
athos@610:     typedef typename LengthMap::ValueType Length;
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:     //Input
athos@610:     const Graph& G;
athos@610: 
athos@610:     //Auxiliary variables
athos@610:     //This is the capacity map for the mincostflow problem
athos@610:     ConstMap const1map;
athos@610:     //This MinCostFlows instance will actually solve the problem
athos@610:     MinCostFlows<Graph, LengthMap, ConstMap> mincost_flow;
athos@610: 
athos@610:     //Container to store found paths
athos@610:     std::vector< std::vector<Edge> > paths;
athos@610: 
athos@610:   public :
athos@610: 
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@610:     MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G),
athos@610:       const1map(1), mincost_flow(_G, _length, const1map){}
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.
alpar@851:     ///Otherwise it returns the number of found edge-disjoint paths from s to t.
athos@860:     ///
athos@860:     ///\param s The source node.
athos@860:     ///\param t The target node.
athos@860:     ///\param k How many paths are we looking for?
athos@860:     ///
athos@610:     int run(Node s, Node t, int k) {
athos@610: 
athos@610:       int i = mincost_flow.run(s,t,k);
athos@860:     
athos@610: 
athos@610:       //Let's find the paths
athos@610:       //We put the paths into stl vectors (as an inner representation). 
athos@610:       //In the meantime we lose the information stored in 'reversed'.
athos@610:       //We suppose the lengths to be positive now.
athos@610: 
athos@610:       //We don't want to change the flow of mincost_flow, so we make a copy
athos@610:       //The name here suggests that the flow has only 0/1 values.
athos@610:       EdgeIntMap reversed(G); 
athos@610: 
marci@788:       for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) 
athos@610: 	reversed[e] = mincost_flow.getFlow()[e];
athos@610:       
athos@610:       paths.clear();
athos@610:       //total_length=0;
athos@610:       paths.resize(k);
athos@610:       for (int j=0; j<i; ++j){
athos@610: 	Node n=s;
athos@610: 	OutEdgeIt e;
athos@610: 
athos@610: 	while (n!=t){
athos@610: 
athos@610: 
athos@610: 	  G.first(e,n);
athos@610: 	  
athos@610: 	  while (!reversed[e]){
hegyi@776: 	    ++e;
athos@610: 	  }
athos@610: 	  n = G.head(e);
athos@610: 	  paths[j].push_back(e);
athos@610: 	  //total_length += length[e];
athos@610: 	  reversed[e] = 1-reversed[e];
athos@610: 	}
athos@610: 	
athos@610:       }
athos@610:       return i;
athos@610:     }
athos@610: 
athos@610:     
athos@860:     ///Returns the total length of the paths
alpar@851:     
athos@610:     ///This function gives back the total length of the found paths.
alpar@851:     ///\pre \ref run() must
alpar@851:     ///be called before using this function.
athos@610:     Length totalLength(){
athos@610:       return mincost_flow.totalLength();
athos@610:     }
athos@610: 
athos@860:     ///Returns the found flow.
alpar@851: 
alpar@851:     ///This function returns a const reference to the EdgeMap \c flow.
alpar@851:     ///\pre \ref run() must
athos@610:     ///be called before using this function.
athos@610:     const EdgeIntMap &getFlow() const { return mincost_flow.flow;}
athos@610: 
athos@860:     /// Returns the optimal dual solution
alpar@851:     
alpar@851:     ///This function returns a const reference to the NodeMap
alpar@851:     ///\c potential (the dual solution).
athos@610:     /// \pre \ref run() must be called before using this function.
athos@610:     const EdgeIntMap &getPotential() const { return mincost_flow.potential;}
athos@610: 
alpar@851:     ///Checks whether the complementary slackness holds.
alpar@851: 
athos@860:     ///This function checks, whether the given solution is optimal.
athos@860:     ///It should return true after calling \ref run() 
alpar@851:     ///Currently this function only checks optimality,
alpar@851:     ///doesn't bother with feasibility
athos@860:     ///It is meant for testing purposes.
athos@610:     ///
athos@610:     bool checkComplementarySlackness(){
athos@610:       return mincost_flow.checkComplementarySlackness();
athos@610:     }
athos@610: 
alpar@851:     ///Read the found paths.
alpar@851:     
athos@610:     ///This function gives back the \c j-th path in argument p.
athos@610:     ///Assumes that \c run() has been run and nothing changed since then.
alpar@851:     /// \warning It is assumed that \c p is constructed to
alpar@851:     ///be a path of graph \c G.
alpar@851:     ///If \c j is not less than the result of previous \c run,
alpar@851:     ///then the result here will be an empty path (\c j can be 0 as well).
athos@860:     ///
athos@860:     ///\param Path The type of the path structure to put the result to (must meet hugo path concept).
athos@860:     ///\param p The path to put the result to 
athos@860:     ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively)
alpar@851:     template<typename Path>
alpar@851:     void getPath(Path& p, size_t j){
athos@860: 
athos@610:       p.clear();
athos@610:       if (j>paths.size()-1){
athos@610: 	return;
athos@610:       }
alpar@853:       typename Path::Builder B(p);
athos@610:       for(typename std::vector<Edge>::iterator i=paths[j].begin(); 
athos@610: 	  i!=paths[j].end(); ++i ){
athos@610: 	B.pushBack(*i);
athos@610:       }
athos@610: 
athos@610:       B.commit();
athos@610:     }
athos@610: 
athos@610:   }; //class MinLengthPaths
athos@610: 
athos@610:   ///@}
athos@610: 
athos@610: } //namespace hugo
athos@610: 
athos@610: #endif //HUGO_MINLENGTHPATHS_H