1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/suurballe.h Mon May 23 04:48:14 2005 +0000
1.3 @@ -0,0 +1,209 @@
1.4 +/* -*- C++ -*-
1.5 + * lemon/suurballe.h - Part of LEMON, a generic C++ optimization library
1.6 + *
1.7 + * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.8 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.9 + *
1.10 + * Permission to use, modify and distribute this software is granted
1.11 + * provided that this copyright notice appears in all copies. For
1.12 + * precise terms see the accompanying LICENSE file.
1.13 + *
1.14 + * This software is provided "AS IS" with no warranty of any kind,
1.15 + * express or implied, and with no claim as to its suitability for any
1.16 + * purpose.
1.17 + *
1.18 + */
1.19 +
1.20 +#ifndef LEMON_SUURBALLE_H
1.21 +#define LEMON_SUURBALLE_H
1.22 +
1.23 +///\ingroup flowalgs
1.24 +///\file
1.25 +///\brief An algorithm for finding k paths of minimal total length.
1.26 +
1.27 +
1.28 +#include <lemon/maps.h>
1.29 +#include <vector>
1.30 +#include <lemon/min_cost_flow.h>
1.31 +
1.32 +namespace lemon {
1.33 +
1.34 +/// \addtogroup flowalgs
1.35 +/// @{
1.36 +
1.37 + ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes
1.38 + /// of minimal total length
1.39 + ///
1.40 + /// The class \ref lemon::Suurballe implements
1.41 + /// an algorithm for finding k edge-disjoint paths
1.42 + /// from a given source node to a given target node in an
1.43 + /// edge-weighted directed graph having minimal total weight (length).
1.44 + ///
1.45 + ///\warning Length values should be nonnegative.
1.46 + ///
1.47 + ///\param Graph The directed graph type the algorithm runs on.
1.48 + ///\param LengthMap The type of the length map (values should be nonnegative).
1.49 + ///
1.50 + ///\note It it questionable whether it is correct to call this method after
1.51 + ///%Suurballe for it is just a special case of Edmonds' and Karp's algorithm
1.52 + ///for finding minimum cost flows. In fact, this implementation just
1.53 + ///wraps the MinCostFlow algorithms. The paper of both %Suurballe and
1.54 + ///Edmonds-Karp published in 1972, therefore it is possibly right to
1.55 + ///state that they are
1.56 + ///independent results. Most frequently this special case is referred as
1.57 + ///%Suurballe method in the literature, especially in communication
1.58 + ///network context.
1.59 + ///\author Attila Bernath
1.60 + template <typename Graph, typename LengthMap>
1.61 + class Suurballe{
1.62 +
1.63 +
1.64 + typedef typename LengthMap::Value Length;
1.65 +
1.66 + typedef typename Graph::Node Node;
1.67 + typedef typename Graph::NodeIt NodeIt;
1.68 + typedef typename Graph::Edge Edge;
1.69 + typedef typename Graph::OutEdgeIt OutEdgeIt;
1.70 + typedef typename Graph::template EdgeMap<int> EdgeIntMap;
1.71 +
1.72 + typedef ConstMap<Edge,int> ConstMap;
1.73 +
1.74 + const Graph& G;
1.75 +
1.76 + Node s;
1.77 + Node t;
1.78 +
1.79 + //Auxiliary variables
1.80 + //This is the capacity map for the mincostflow problem
1.81 + ConstMap const1map;
1.82 + //This MinCostFlow instance will actually solve the problem
1.83 + MinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow;
1.84 +
1.85 + //Container to store found paths
1.86 + std::vector< std::vector<Edge> > paths;
1.87 +
1.88 + public :
1.89 +
1.90 +
1.91 + /*! \brief The constructor of the class.
1.92 +
1.93 + \param _G The directed graph the algorithm runs on.
1.94 + \param _length The length (weight or cost) of the edges.
1.95 + \param _s Source node.
1.96 + \param _t Target node.
1.97 + */
1.98 + Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) :
1.99 + G(_G), s(_s), t(_t), const1map(1),
1.100 + min_cost_flow(_G, _length, const1map, _s, _t) { }
1.101 +
1.102 + ///Runs the algorithm.
1.103 +
1.104 + ///Runs the algorithm.
1.105 + ///Returns k if there are at least k edge-disjoint paths from s to t.
1.106 + ///Otherwise it returns the number of edge-disjoint paths found
1.107 + ///from s to t.
1.108 + ///
1.109 + ///\param k How many paths are we looking for?
1.110 + ///
1.111 + int run(int k) {
1.112 + int i = min_cost_flow.run(k);
1.113 +
1.114 + //Let's find the paths
1.115 + //We put the paths into stl vectors (as an inner representation).
1.116 + //In the meantime we lose the information stored in 'reversed'.
1.117 + //We suppose the lengths to be positive now.
1.118 +
1.119 + //We don't want to change the flow of min_cost_flow, so we make a copy
1.120 + //The name here suggests that the flow has only 0/1 values.
1.121 + EdgeIntMap reversed(G);
1.122 +
1.123 + for(typename Graph::EdgeIt e(G); e!=INVALID; ++e)
1.124 + reversed[e] = min_cost_flow.getFlow()[e];
1.125 +
1.126 + paths.clear();
1.127 + //total_length=0;
1.128 + paths.resize(k);
1.129 + for (int j=0; j<i; ++j){
1.130 + Node n=s;
1.131 +
1.132 + while (n!=t){
1.133 +
1.134 + OutEdgeIt e(G, n);
1.135 +
1.136 + while (!reversed[e]){
1.137 + ++e;
1.138 + }
1.139 + n = G.target(e);
1.140 + paths[j].push_back(e);
1.141 + //total_length += length[e];
1.142 + reversed[e] = 1-reversed[e];
1.143 + }
1.144 +
1.145 + }
1.146 + return i;
1.147 + }
1.148 +
1.149 +
1.150 + ///Returns the total length of the paths.
1.151 +
1.152 + ///This function gives back the total length of the found paths.
1.153 + Length totalLength(){
1.154 + return min_cost_flow.totalLength();
1.155 + }
1.156 +
1.157 + ///Returns the found flow.
1.158 +
1.159 + ///This function returns a const reference to the EdgeMap \c flow.
1.160 + const EdgeIntMap &getFlow() const { return min_cost_flow.flow;}
1.161 +
1.162 + /// Returns the optimal dual solution
1.163 +
1.164 + ///This function returns a const reference to the NodeMap
1.165 + ///\c potential (the dual solution).
1.166 + const EdgeIntMap &getPotential() const { return min_cost_flow.potential;}
1.167 +
1.168 + ///Checks whether the complementary slackness holds.
1.169 +
1.170 + ///This function checks, whether the given solution is optimal.
1.171 + ///Currently this function only checks optimality,
1.172 + ///doesn't bother with feasibility
1.173 + ///It is meant for testing purposes.
1.174 + bool checkComplementarySlackness(){
1.175 + return min_cost_flow.checkComplementarySlackness();
1.176 + }
1.177 +
1.178 + ///Read the found paths.
1.179 +
1.180 + ///This function gives back the \c j-th path in argument p.
1.181 + ///Assumes that \c run() has been run and nothing changed since then.
1.182 + /// \warning It is assumed that \c p is constructed to
1.183 + ///be a path of graph \c G.
1.184 + ///If \c j is not less than the result of previous \c run,
1.185 + ///then the result here will be an empty path (\c j can be 0 as well).
1.186 + ///
1.187 + ///\param Path The type of the path structure to put the result to (must meet lemon path concept).
1.188 + ///\param p The path to put the result to
1.189 + ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively)
1.190 + template<typename Path>
1.191 + void getPath(Path& p, size_t j){
1.192 +
1.193 + p.clear();
1.194 + if (j>paths.size()-1){
1.195 + return;
1.196 + }
1.197 + typename Path::Builder B(p);
1.198 + for(typename std::vector<Edge>::iterator i=paths[j].begin();
1.199 + i!=paths[j].end(); ++i ){
1.200 + B.pushBack(*i);
1.201 + }
1.202 +
1.203 + B.commit();
1.204 + }
1.205 +
1.206 + }; //class Suurballe
1.207 +
1.208 + ///@}
1.209 +
1.210 +} //namespace lemon
1.211 +
1.212 +#endif //LEMON_SUURBALLE_H