alpar@906: /* -*- C++ -*-
alpar@906:  *
alpar@1956:  * This file is a part of LEMON, a generic C++ optimization library
alpar@1956:  *
alpar@1956:  * Copyright (C) 2003-2006
alpar@1956:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@1359:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@906:  *
alpar@906:  * Permission to use, modify and distribute this software is granted
alpar@906:  * provided that this copyright notice appears in all copies. For
alpar@906:  * precise terms see the accompanying LICENSE file.
alpar@906:  *
alpar@906:  * This software is provided "AS IS" with no warranty of any kind,
alpar@906:  * express or implied, and with no claim as to its suitability for any
alpar@906:  * purpose.
alpar@906:  *
alpar@906:  */
alpar@906: 
alpar@921: #ifndef LEMON_SUURBALLE_H
alpar@921: #define LEMON_SUURBALLE_H
alpar@899: 
alpar@899: ///\ingroup flowalgs
alpar@899: ///\file
alpar@899: ///\brief An algorithm for finding k paths of minimal total length.
alpar@899: 
alpar@899: 
alpar@921: #include <lemon/maps.h>
alpar@899: #include <vector>
deba@2276: #include <lemon/ssp_min_cost_flow.h>
alpar@899: 
alpar@921: namespace lemon {
alpar@899: 
alpar@899: /// \addtogroup flowalgs
alpar@899: /// @{
alpar@899: 
deba@2276:   ///\brief Implementation of an algorithm for finding k edge-disjoint
deba@2276:   /// paths between 2 nodes of minimal total length
alpar@899:   ///
alpar@921:   /// The class \ref lemon::Suurballe implements
alpar@899:   /// an algorithm for finding k edge-disjoint paths
alpar@899:   /// from a given source node to a given target node in an
alpar@899:   /// edge-weighted directed graph having minimal total weight (length).
alpar@899:   ///
athos@1527:   ///\warning Length values should be nonnegative!
alpar@899:   /// 
alpar@899:   ///\param Graph The directed graph type the algorithm runs on.
alpar@899:   ///\param LengthMap The type of the length map (values should be nonnegative).
alpar@899:   ///
alpar@968:   ///\note It it questionable whether it is correct to call this method after
alpar@1020:   ///%Suurballe for it is just a special case of Edmonds' and Karp's algorithm
alpar@968:   ///for finding minimum cost flows. In fact, this implementation just
deba@2276:   ///wraps the SspMinCostFlow algorithms. The paper of both %Suurballe and
alpar@899:   ///Edmonds-Karp published in 1972, therefore it is possibly right to
alpar@899:   ///state that they are
alpar@899:   ///independent results. Most frequently this special case is referred as
alpar@899:   ///%Suurballe method in the literature, especially in communication
alpar@899:   ///network context.
alpar@899:   ///\author Attila Bernath
alpar@899:   template <typename Graph, typename LengthMap>
alpar@899:   class Suurballe{
alpar@899: 
alpar@899: 
alpar@987:     typedef typename LengthMap::Value Length;
alpar@899:     
alpar@899:     typedef typename Graph::Node Node;
alpar@899:     typedef typename Graph::NodeIt NodeIt;
alpar@899:     typedef typename Graph::Edge Edge;
alpar@899:     typedef typename Graph::OutEdgeIt OutEdgeIt;
alpar@899:     typedef typename Graph::template EdgeMap<int> EdgeIntMap;
alpar@899: 
alpar@899:     typedef ConstMap<Edge,int> ConstMap;
alpar@899: 
alpar@899:     const Graph& G;
alpar@899: 
marci@941:     Node s;
marci@941:     Node t;
marci@941: 
alpar@899:     //Auxiliary variables
alpar@899:     //This is the capacity map for the mincostflow problem
alpar@899:     ConstMap const1map;
alpar@899:     //This MinCostFlow instance will actually solve the problem
deba@2276:     SspMinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow;
alpar@899: 
alpar@899:     //Container to store found paths
alpar@899:     std::vector< std::vector<Edge> > paths;
alpar@899: 
alpar@899:   public :
alpar@899: 
alpar@899: 
deba@2276:     /// \brief The constructor of the class.
deba@2276:     ///
deba@2276:     /// \param _G The directed graph the algorithm runs on. 
deba@2276:     /// \param _length The length (weight or cost) of the edges. 
deba@2276:     /// \param _s Source node.
deba@2276:     /// \param _t Target node.
marci@941:     Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) : 
marci@941:       G(_G), s(_s), t(_t), const1map(1), 
marci@941:       min_cost_flow(_G, _length, const1map, _s, _t) { }
alpar@899: 
deba@2276:     /// \brief Runs the algorithm.
alpar@899:     ///
deba@2276:     /// Runs the algorithm.
deba@2276:     /// Returns k if there are at least k edge-disjoint paths from s to t.
deba@2276:     /// Otherwise it returns the number of edge-disjoint paths found 
deba@2276:     /// from s to t.
deba@2276:     ///
deba@2276:     /// \param k How many paths are we looking for?
alpar@899:     ///
marci@941:     int run(int k) {
marci@941:       int i = min_cost_flow.run(k);
alpar@899: 
alpar@899:       //Let's find the paths
alpar@899:       //We put the paths into stl vectors (as an inner representation). 
alpar@899:       //In the meantime we lose the information stored in 'reversed'.
alpar@899:       //We suppose the lengths to be positive now.
alpar@899: 
marci@941:       //We don't want to change the flow of min_cost_flow, so we make a copy
alpar@899:       //The name here suggests that the flow has only 0/1 values.
alpar@899:       EdgeIntMap reversed(G); 
alpar@899: 
alpar@899:       for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) 
marci@941: 	reversed[e] = min_cost_flow.getFlow()[e];
alpar@899:       
alpar@899:       paths.clear();
alpar@899:       paths.resize(k);
alpar@899:       for (int j=0; j<i; ++j){
alpar@899: 	Node n=s;
alpar@899: 
alpar@899: 	while (n!=t){
alpar@899: 
klao@946: 	  OutEdgeIt e(G, n);
alpar@899: 	  
alpar@899: 	  while (!reversed[e]){
alpar@899: 	    ++e;
alpar@899: 	  }
alpar@986: 	  n = G.target(e);
alpar@899: 	  paths[j].push_back(e);
alpar@899: 	  reversed[e] = 1-reversed[e];
alpar@899: 	}
alpar@899: 	
alpar@899:       }
alpar@899:       return i;
alpar@899:     }
alpar@899: 
alpar@899:     
deba@2276:     /// \brief Returns the total length of the paths.
deba@2276:     ///
deba@2276:     /// This function gives back the total length of the found paths.
alpar@899:     Length totalLength(){
marci@941:       return min_cost_flow.totalLength();
alpar@899:     }
alpar@899: 
deba@2276:     /// \brief Returns the found flow.
deba@2276:     ///
deba@2276:     /// This function returns a const reference to the EdgeMap \c flow.
marci@941:     const EdgeIntMap &getFlow() const { return min_cost_flow.flow;}
alpar@899: 
deba@2276:     /// \brief Returns the optimal dual solution
deba@2276:     ///
deba@2276:     /// This function returns a const reference to the NodeMap \c
deba@2276:     /// potential (the dual solution).
marci@941:     const EdgeIntMap &getPotential() const { return min_cost_flow.potential;}
alpar@899: 
deba@2276:     /// \brief Checks whether the complementary slackness holds.
deba@2276:     ///
deba@2276:     /// This function checks, whether the given solution is optimal.
deba@2276:     /// Currently this function only checks optimality, doesn't bother
deba@2276:     /// with feasibility.  It is meant for testing purposes.
alpar@899:     bool checkComplementarySlackness(){
marci@941:       return min_cost_flow.checkComplementarySlackness();
alpar@899:     }
alpar@899: 
deba@2276:     /// \brief Read the found paths.
alpar@899:     ///
deba@2276:     /// This function gives back the \c j-th path in argument p.
deba@2276:     /// Assumes that \c run() has been run and nothing has changed
deba@2276:     /// since then.
deba@2276:     ///
deba@2276:     /// \warning It is assumed that \c p is constructed to be a path
deba@2276:     /// of graph \c G.  If \c j is not less than the result of
deba@2276:     /// previous \c run, then the result here will be an empty path
deba@2276:     /// (\c j can be 0 as well).
deba@2276:     ///
deba@2276:     /// \param Path The type of the path structure to put the result
deba@2276:     /// to (must meet lemon path concept).
deba@2276:     /// \param p The path to put the result to.
deba@2276:     /// \param j Which path you want to get from the found paths (in a
deba@2276:     /// real application you would get the found paths iteratively).
alpar@899:     template<typename Path>
alpar@899:     void getPath(Path& p, size_t j){
alpar@899: 
alpar@899:       p.clear();
alpar@899:       if (j>paths.size()-1){
alpar@899: 	return;
alpar@899:       }
alpar@899:       typename Path::Builder B(p);
alpar@899:       for(typename std::vector<Edge>::iterator i=paths[j].begin(); 
alpar@899: 	  i!=paths[j].end(); ++i ){
alpar@899: 	B.pushBack(*i);
alpar@899:       }
alpar@899: 
alpar@899:       B.commit();
alpar@899:     }
alpar@899: 
alpar@899:   }; //class Suurballe
alpar@899: 
alpar@899:   ///@}
alpar@899: 
alpar@921: } //namespace lemon
alpar@899: 
alpar@921: #endif //LEMON_SUURBALLE_H