A little has been done. Some important questions arised.
2 * src/lemon/suurballe.h - Part of LEMON, a generic C++ optimization library
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Combinatorial Optimization Research Group, EGRES).
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
17 #ifndef LEMON_SUURBALLE_H
18 #define LEMON_SUURBALLE_H
22 ///\brief An algorithm for finding k paths of minimal total length.
25 #include <lemon/maps.h>
27 #include <lemon/min_cost_flow.h>
31 /// \addtogroup flowalgs
34 ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes
35 /// of minimal total length
37 /// The class \ref lemon::Suurballe implements
38 /// an algorithm for finding k edge-disjoint paths
39 /// from a given source node to a given target node in an
40 /// edge-weighted directed graph having minimal total weight (length).
42 ///\warning Length values should be nonnegative.
44 ///\param Graph The directed graph type the algorithm runs on.
45 ///\param LengthMap The type of the length map (values should be nonnegative).
47 ///\note It it questionable whether it is correct to call this method after
48 ///%Suurballe for it is just a special case of Edmonds' and Karp's algorithm
49 ///for finding minimum cost flows. In fact, this implementation just
50 ///wraps the MinCostFlow algorithms. The paper of both %Suurballe and
51 ///Edmonds-Karp published in 1972, therefore it is possibly right to
52 ///state that they are
53 ///independent results. Most frequently this special case is referred as
54 ///%Suurballe method in the literature, especially in communication
56 ///\author Attila Bernath
57 template <typename Graph, typename LengthMap>
61 typedef typename LengthMap::Value Length;
63 typedef typename Graph::Node Node;
64 typedef typename Graph::NodeIt NodeIt;
65 typedef typename Graph::Edge Edge;
66 typedef typename Graph::OutEdgeIt OutEdgeIt;
67 typedef typename Graph::template EdgeMap<int> EdgeIntMap;
69 typedef ConstMap<Edge,int> ConstMap;
77 //This is the capacity map for the mincostflow problem
79 //This MinCostFlow instance will actually solve the problem
80 MinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow;
82 //Container to store found paths
83 std::vector< std::vector<Edge> > paths;
88 /*! \brief The constructor of the class.
90 \param _G The directed graph the algorithm runs on.
91 \param _length The length (weight or cost) of the edges.
92 \param _s Source node.
93 \param _t Target node.
95 Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) :
96 G(_G), s(_s), t(_t), const1map(1),
97 min_cost_flow(_G, _length, const1map, _s, _t) { }
99 ///Runs the algorithm.
101 ///Runs the algorithm.
102 ///Returns k if there are at least k edge-disjoint paths from s to t.
103 ///Otherwise it returns the number of edge-disjoint paths found
106 ///\param k How many paths are we looking for?
109 int i = min_cost_flow.run(k);
111 //Let's find the paths
112 //We put the paths into stl vectors (as an inner representation).
113 //In the meantime we lose the information stored in 'reversed'.
114 //We suppose the lengths to be positive now.
116 //We don't want to change the flow of min_cost_flow, so we make a copy
117 //The name here suggests that the flow has only 0/1 values.
118 EdgeIntMap reversed(G);
120 for(typename Graph::EdgeIt e(G); e!=INVALID; ++e)
121 reversed[e] = min_cost_flow.getFlow()[e];
126 for (int j=0; j<i; ++j){
133 while (!reversed[e]){
137 paths[j].push_back(e);
138 //total_length += length[e];
139 reversed[e] = 1-reversed[e];
147 ///Returns the total length of the paths.
149 ///This function gives back the total length of the found paths.
150 Length totalLength(){
151 return min_cost_flow.totalLength();
154 ///Returns the found flow.
156 ///This function returns a const reference to the EdgeMap \c flow.
157 const EdgeIntMap &getFlow() const { return min_cost_flow.flow;}
159 /// Returns the optimal dual solution
161 ///This function returns a const reference to the NodeMap
162 ///\c potential (the dual solution).
163 const EdgeIntMap &getPotential() const { return min_cost_flow.potential;}
165 ///Checks whether the complementary slackness holds.
167 ///This function checks, whether the given solution is optimal.
168 ///Currently this function only checks optimality,
169 ///doesn't bother with feasibility
170 ///It is meant for testing purposes.
171 bool checkComplementarySlackness(){
172 return min_cost_flow.checkComplementarySlackness();
175 ///Read the found paths.
177 ///This function gives back the \c j-th path in argument p.
178 ///Assumes that \c run() has been run and nothing changed since then.
179 /// \warning It is assumed that \c p is constructed to
180 ///be a path of graph \c G.
181 ///If \c j is not less than the result of previous \c run,
182 ///then the result here will be an empty path (\c j can be 0 as well).
184 ///\param Path The type of the path structure to put the result to (must meet lemon path concept).
185 ///\param p The path to put the result to
186 ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively)
187 template<typename Path>
188 void getPath(Path& p, size_t j){
191 if (j>paths.size()-1){
194 typename Path::Builder B(p);
195 for(typename std::vector<Edge>::iterator i=paths[j].begin();
196 i!=paths[j].end(); ++i ){
209 #endif //LEMON_SUURBALLE_H