[906] | 1 | /* -*- C++ -*- |
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[921] | 2 | * src/lemon/suurballe.h - Part of LEMON, a generic C++ optimization library |
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[906] | 3 | * |
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| 4 | * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 5 | * (Egervary Combinatorial Optimization Research Group, EGRES). |
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| 6 | * |
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| 7 | * Permission to use, modify and distribute this software is granted |
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| 8 | * provided that this copyright notice appears in all copies. For |
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| 9 | * precise terms see the accompanying LICENSE file. |
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| 10 | * |
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| 11 | * This software is provided "AS IS" with no warranty of any kind, |
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| 12 | * express or implied, and with no claim as to its suitability for any |
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| 13 | * purpose. |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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[921] | 17 | #ifndef LEMON_SUURBALLE_H |
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| 18 | #define LEMON_SUURBALLE_H |
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[899] | 19 | |
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| 20 | ///\ingroup flowalgs |
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| 21 | ///\file |
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| 22 | ///\brief An algorithm for finding k paths of minimal total length. |
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| 23 | |
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| 24 | |
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[921] | 25 | #include <lemon/maps.h> |
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[899] | 26 | #include <vector> |
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[921] | 27 | #include <lemon/min_cost_flow.h> |
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[899] | 28 | |
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[921] | 29 | namespace lemon { |
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[899] | 30 | |
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| 31 | /// \addtogroup flowalgs |
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| 32 | /// @{ |
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| 33 | |
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| 34 | ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes |
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| 35 | /// of minimal total length |
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| 36 | /// |
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[921] | 37 | /// The class \ref lemon::Suurballe implements |
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[899] | 38 | /// an algorithm for finding k edge-disjoint paths |
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| 39 | /// from a given source node to a given target node in an |
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| 40 | /// edge-weighted directed graph having minimal total weight (length). |
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| 41 | /// |
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| 42 | ///\warning Length values should be nonnegative. |
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| 43 | /// |
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| 44 | ///\param Graph The directed graph type the algorithm runs on. |
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| 45 | ///\param LengthMap The type of the length map (values should be nonnegative). |
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| 46 | /// |
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| 47 | ///\note It it questionable if it is correct to call this method after |
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| 48 | ///%Suurballe for it is just a special case of Edmond's and Karp's algorithm |
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| 49 | ///for finding minimum cost flows. In fact, this implementation is just |
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| 50 | ///wraps the MinCostFlow algorithms. The paper of both %Suurballe and |
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| 51 | ///Edmonds-Karp published in 1972, therefore it is possibly right to |
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| 52 | ///state that they are |
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| 53 | ///independent results. Most frequently this special case is referred as |
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| 54 | ///%Suurballe method in the literature, especially in communication |
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| 55 | ///network context. |
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| 56 | ///\author Attila Bernath |
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| 57 | template <typename Graph, typename LengthMap> |
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| 58 | class Suurballe{ |
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| 59 | |
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| 60 | |
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| 61 | typedef typename LengthMap::ValueType Length; |
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| 62 | |
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| 63 | typedef typename Graph::Node Node; |
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| 64 | typedef typename Graph::NodeIt NodeIt; |
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| 65 | typedef typename Graph::Edge Edge; |
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| 66 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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| 67 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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| 68 | |
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| 69 | typedef ConstMap<Edge,int> ConstMap; |
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| 70 | |
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| 71 | const Graph& G; |
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| 72 | |
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[941] | 73 | Node s; |
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| 74 | Node t; |
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| 75 | |
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[899] | 76 | //Auxiliary variables |
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| 77 | //This is the capacity map for the mincostflow problem |
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| 78 | ConstMap const1map; |
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| 79 | //This MinCostFlow instance will actually solve the problem |
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[941] | 80 | MinCostFlow<Graph, LengthMap, ConstMap> min_cost_flow; |
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[899] | 81 | |
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| 82 | //Container to store found paths |
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| 83 | std::vector< std::vector<Edge> > paths; |
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| 84 | |
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| 85 | public : |
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| 86 | |
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| 87 | |
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[941] | 88 | /*! \brief The constructor of the class. |
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[899] | 89 | |
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[941] | 90 | \param _G The directed graph the algorithm runs on. |
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| 91 | \param _length The length (weight or cost) of the edges. |
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| 92 | \param _s Source node. |
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| 93 | \param _t Target node. |
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| 94 | */ |
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| 95 | Suurballe(Graph& _G, LengthMap& _length, Node _s, Node _t) : |
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| 96 | G(_G), s(_s), t(_t), const1map(1), |
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| 97 | min_cost_flow(_G, _length, const1map, _s, _t) { } |
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[899] | 98 | |
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| 99 | ///Runs the algorithm. |
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| 100 | |
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| 101 | ///Runs the algorithm. |
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| 102 | ///Returns k if there are at least k edge-disjoint paths from s to t. |
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[941] | 103 | ///Otherwise it returns the number of edge-disjoint paths found |
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| 104 | ///from s to t. |
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[899] | 105 | /// |
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| 106 | ///\param k How many paths are we looking for? |
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| 107 | /// |
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[941] | 108 | int run(int k) { |
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| 109 | int i = min_cost_flow.run(k); |
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[899] | 110 | |
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| 111 | //Let's find the paths |
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| 112 | //We put the paths into stl vectors (as an inner representation). |
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| 113 | //In the meantime we lose the information stored in 'reversed'. |
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| 114 | //We suppose the lengths to be positive now. |
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| 115 | |
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[941] | 116 | //We don't want to change the flow of min_cost_flow, so we make a copy |
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[899] | 117 | //The name here suggests that the flow has only 0/1 values. |
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| 118 | EdgeIntMap reversed(G); |
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| 119 | |
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| 120 | for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) |
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[941] | 121 | reversed[e] = min_cost_flow.getFlow()[e]; |
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[899] | 122 | |
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| 123 | paths.clear(); |
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| 124 | //total_length=0; |
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| 125 | paths.resize(k); |
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| 126 | for (int j=0; j<i; ++j){ |
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| 127 | Node n=s; |
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| 128 | |
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| 129 | while (n!=t){ |
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| 130 | |
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[946] | 131 | OutEdgeIt e(G, n); |
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[899] | 132 | |
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| 133 | while (!reversed[e]){ |
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| 134 | ++e; |
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| 135 | } |
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| 136 | n = G.head(e); |
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| 137 | paths[j].push_back(e); |
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| 138 | //total_length += length[e]; |
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| 139 | reversed[e] = 1-reversed[e]; |
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| 140 | } |
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| 141 | |
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| 142 | } |
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| 143 | return i; |
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| 144 | } |
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| 145 | |
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| 146 | |
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[941] | 147 | ///Returns the total length of the paths. |
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[899] | 148 | |
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| 149 | ///This function gives back the total length of the found paths. |
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| 150 | Length totalLength(){ |
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[941] | 151 | return min_cost_flow.totalLength(); |
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[899] | 152 | } |
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| 153 | |
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| 154 | ///Returns the found flow. |
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| 155 | |
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| 156 | ///This function returns a const reference to the EdgeMap \c flow. |
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[941] | 157 | const EdgeIntMap &getFlow() const { return min_cost_flow.flow;} |
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[899] | 158 | |
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| 159 | /// Returns the optimal dual solution |
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| 160 | |
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| 161 | ///This function returns a const reference to the NodeMap |
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| 162 | ///\c potential (the dual solution). |
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[941] | 163 | const EdgeIntMap &getPotential() const { return min_cost_flow.potential;} |
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[899] | 164 | |
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| 165 | ///Checks whether the complementary slackness holds. |
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| 166 | |
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| 167 | ///This function checks, whether the given solution is optimal. |
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| 168 | ///Currently this function only checks optimality, |
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| 169 | ///doesn't bother with feasibility |
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| 170 | ///It is meant for testing purposes. |
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| 171 | bool checkComplementarySlackness(){ |
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[941] | 172 | return min_cost_flow.checkComplementarySlackness(); |
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[899] | 173 | } |
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| 174 | |
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| 175 | ///Read the found paths. |
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| 176 | |
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| 177 | ///This function gives back the \c j-th path in argument p. |
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| 178 | ///Assumes that \c run() has been run and nothing changed since then. |
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| 179 | /// \warning It is assumed that \c p is constructed to |
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| 180 | ///be a path of graph \c G. |
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| 181 | ///If \c j is not less than the result of previous \c run, |
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| 182 | ///then the result here will be an empty path (\c j can be 0 as well). |
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| 183 | /// |
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[921] | 184 | ///\param Path The type of the path structure to put the result to (must meet lemon path concept). |
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[899] | 185 | ///\param p The path to put the result to |
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| 186 | ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively) |
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| 187 | template<typename Path> |
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| 188 | void getPath(Path& p, size_t j){ |
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| 189 | |
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| 190 | p.clear(); |
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| 191 | if (j>paths.size()-1){ |
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| 192 | return; |
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| 193 | } |
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| 194 | typename Path::Builder B(p); |
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| 195 | for(typename std::vector<Edge>::iterator i=paths[j].begin(); |
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| 196 | i!=paths[j].end(); ++i ){ |
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| 197 | B.pushBack(*i); |
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| 198 | } |
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| 199 | |
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| 200 | B.commit(); |
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| 201 | } |
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| 202 | |
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| 203 | }; //class Suurballe |
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| 204 | |
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| 205 | ///@} |
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| 206 | |
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[921] | 207 | } //namespace lemon |
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[899] | 208 | |
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[921] | 209 | #endif //LEMON_SUURBALLE_H |
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