1 | /* -*- C++ -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library |
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4 | * |
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5 | * Copyright (C) 2003-2007 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_STEINER_H |
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20 | #define LEMON_STEINER_H |
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21 | |
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22 | ///\ingroup approx |
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23 | ///\file |
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24 | ///\brief Algorithm for the 2-approximation of Steiner Tree problem. |
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25 | /// |
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26 | |
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27 | #include <lemon/smart_graph.h> |
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28 | #include <lemon/graph_utils.h> |
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29 | #include <lemon/error.h> |
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30 | |
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31 | #include <lemon/ugraph_adaptor.h> |
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32 | #include <lemon/maps.h> |
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33 | |
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34 | #include <lemon/dijkstra.h> |
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35 | #include <lemon/prim.h> |
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36 | |
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37 | |
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38 | namespace lemon { |
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39 | |
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40 | /// \ingroup approx |
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41 | |
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42 | /// \brief Algorithm for the 2-approximation of Steiner Tree problem |
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43 | /// |
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44 | /// The Steiner-tree problem is the next: Given a connected |
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45 | /// undirected graph, a cost function on the edges and a subset of |
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46 | /// the nodes. Construct a tree with minimum cost which covers the |
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47 | /// given subset of the nodes. The problem is NP-hard moreover |
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48 | /// it is APX-complete too. |
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49 | /// |
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50 | /// Mehlhorn's approximation algorithm is implemented in this class, |
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51 | /// which gives a 2-approximation for the Steiner-tree problem. The |
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52 | /// algorithm's time complexity is O(nlog(n)+e). |
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53 | template <typename UGraph, |
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54 | typename CostMap = typename UGraph:: template UEdgeMap<double> > |
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55 | class SteinerTree { |
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56 | public: |
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57 | |
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58 | UGRAPH_TYPEDEFS(typename UGraph); |
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59 | |
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60 | typedef typename CostMap::Value Value; |
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61 | |
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62 | private: |
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63 | |
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64 | class CompMap { |
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65 | public: |
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66 | typedef Node Key; |
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67 | typedef Edge Value; |
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68 | |
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69 | private: |
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70 | const UGraph& _graph; |
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71 | typename UGraph::template NodeMap<int> _comp; |
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72 | |
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73 | public: |
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74 | CompMap(const UGraph& graph) : _graph(graph), _comp(graph) {} |
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75 | |
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76 | void set(const Node& node, const Edge& edge) { |
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77 | if (edge != INVALID) { |
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78 | _comp.set(node, _comp[_graph.source(edge)]); |
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79 | } else { |
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80 | _comp.set(node, -1); |
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81 | } |
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82 | } |
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83 | |
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84 | int comp(const Node& node) const { return _comp[node]; } |
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85 | void comp(const Node& node, int value) { _comp.set(node, value); } |
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86 | }; |
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87 | |
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88 | typedef typename UGraph::template NodeMap<Edge> PredMap; |
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89 | |
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90 | typedef ForkWriteMap<PredMap, CompMap> ForkedMap; |
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91 | |
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92 | |
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93 | struct External { |
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94 | int source, target; |
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95 | UEdge uedge; |
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96 | Value value; |
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97 | |
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98 | External(int s, int t, const UEdge& e, const Value& v) |
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99 | : source(s), target(t), uedge(e), value(v) {} |
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100 | }; |
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101 | |
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102 | struct ExternalLess { |
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103 | bool operator()(const External& left, const External& right) const { |
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104 | return (left.source < right.source) || |
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105 | (left.source == right.source && left.target < right.target); |
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106 | } |
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107 | }; |
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108 | |
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109 | |
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110 | typedef typename UGraph::template NodeMap<bool> FilterMap; |
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111 | |
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112 | typedef typename UGraph::template UEdgeMap<bool> TreeMap; |
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113 | |
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114 | const UGraph& _graph; |
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115 | const CostMap& _cost; |
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116 | |
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117 | typename Dijkstra<UGraph, CostMap>:: |
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118 | template DefPredMap<ForkedMap>::Create _dijkstra; |
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119 | |
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120 | PredMap* _pred; |
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121 | CompMap* _comp; |
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122 | ForkedMap* _forked; |
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123 | |
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124 | int _terminal_num; |
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125 | |
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126 | FilterMap *_filter; |
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127 | TreeMap *_tree; |
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128 | |
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129 | Value _value; |
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130 | |
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131 | public: |
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132 | |
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133 | /// \brief Constructor |
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134 | |
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135 | /// Constructor |
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136 | /// |
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137 | SteinerTree(const UGraph &graph, const CostMap &cost) |
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138 | : _graph(graph), _cost(cost), _dijkstra(graph, _cost), |
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139 | _pred(0), _comp(0), _forked(0), _filter(0), _tree(0) {} |
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140 | |
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141 | /// \brief Initializes the internal data structures. |
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142 | /// |
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143 | /// Initializes the internal data structures. |
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144 | void init() { |
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145 | if (!_pred) _pred = new PredMap(_graph); |
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146 | if (!_comp) _comp = new CompMap(_graph); |
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147 | if (!_forked) _forked = new ForkedMap(*_pred, *_comp); |
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148 | if (!_filter) _filter = new FilterMap(_graph); |
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149 | if (!_tree) _tree = new TreeMap(_graph); |
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150 | _dijkstra.predMap(*_forked); |
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151 | _dijkstra.init(); |
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152 | _terminal_num = 0; |
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153 | for (NodeIt it(_graph); it != INVALID; ++it) { |
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154 | _filter->set(it, false); |
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155 | } |
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156 | } |
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157 | |
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158 | /// \brief Adds a new terminal node. |
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159 | /// |
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160 | /// Adds a new terminal node to the Steiner-tree problem. |
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161 | void addTerminal(const Node& node) { |
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162 | if (!_dijkstra.reached(node)) { |
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163 | _dijkstra.addSource(node); |
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164 | _comp->comp(node, _terminal_num); |
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165 | ++_terminal_num; |
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166 | } |
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167 | } |
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168 | |
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169 | /// \brief Executes the algorithm. |
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170 | /// |
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171 | /// Executes the algorithm. |
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172 | /// |
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173 | /// \pre init() must be called and at least some nodes should be |
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174 | /// added with addTerminal() before using this function. |
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175 | /// |
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176 | /// This method constructs an approximation of the Steiner-Tree. |
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177 | void start() { |
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178 | _dijkstra.start(); |
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179 | |
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180 | std::vector<External> externals; |
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181 | for (UEdgeIt it(_graph); it != INVALID; ++it) { |
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182 | Node s = _graph.source(it); |
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183 | Node t = _graph.target(it); |
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184 | if (_comp->comp(s) == _comp->comp(t)) continue; |
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185 | |
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186 | Value cost = _dijkstra.dist(s) + _dijkstra.dist(t) + _cost[it]; |
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187 | |
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188 | if (_comp->comp(s) < _comp->comp(t)) { |
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189 | externals.push_back(External(_comp->comp(s), _comp->comp(t), |
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190 | it, cost)); |
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191 | } else { |
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192 | externals.push_back(External(_comp->comp(t), _comp->comp(s), |
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193 | it, cost)); |
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194 | } |
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195 | } |
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196 | std::sort(externals.begin(), externals.end(), ExternalLess()); |
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197 | |
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198 | SmartUGraph aux_graph; |
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199 | std::vector<SmartUGraph::Node> aux_nodes; |
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200 | |
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201 | for (int i = 0; i < _terminal_num; ++i) { |
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202 | aux_nodes.push_back(aux_graph.addNode()); |
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203 | } |
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204 | |
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205 | SmartUGraph::UEdgeMap<Value> aux_cost(aux_graph); |
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206 | SmartUGraph::UEdgeMap<UEdge> cross(aux_graph); |
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207 | { |
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208 | int i = 0; |
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209 | while (i < int(externals.size())) { |
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210 | int sn = externals[i].source; |
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211 | int tn = externals[i].target; |
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212 | Value ev = externals[i].value; |
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213 | UEdge ee = externals[i].uedge; |
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214 | ++i; |
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215 | while (i < int(externals.size()) && |
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216 | sn == externals[i].source && tn == externals[i].target) { |
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217 | if (externals[i].value < ev) { |
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218 | ev = externals[i].value; |
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219 | ee = externals[i].uedge; |
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220 | } |
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221 | ++i; |
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222 | } |
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223 | SmartUGraph::UEdge ne = |
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224 | aux_graph.addEdge(aux_nodes[sn], aux_nodes[tn]); |
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225 | aux_cost.set(ne, ev); |
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226 | cross.set(ne, ee); |
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227 | } |
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228 | } |
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229 | |
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230 | std::vector<SmartUGraph::UEdge> aux_tree_edges; |
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231 | BackInserterBoolMap<std::vector<SmartUGraph::UEdge> > |
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232 | aux_tree_map(aux_tree_edges); |
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233 | prim(aux_graph, aux_cost, aux_tree_map); |
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234 | |
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235 | for (std::vector<SmartUGraph::UEdge>::iterator |
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236 | it = aux_tree_edges.begin(); it != aux_tree_edges.end(); ++it) { |
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237 | Node node; |
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238 | node = _graph.source(cross[*it]); |
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239 | while (node != INVALID && !(*_filter)[node]) { |
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240 | _filter->set(node, true); |
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241 | node = (*_pred)[node] != INVALID ? |
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242 | _graph.source((*_pred)[node]) : INVALID; |
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243 | } |
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244 | node = _graph.target(cross[*it]); |
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245 | while (node != INVALID && !(*_filter)[node]) { |
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246 | _filter->set(node, true); |
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247 | node = (*_pred)[node] != INVALID ? |
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248 | _graph.source((*_pred)[node]) : INVALID; |
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249 | } |
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250 | } |
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251 | |
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252 | _value = prim(nodeSubUGraphAdaptor(_graph, *_filter), _cost, *_tree); |
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253 | |
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254 | } |
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255 | |
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256 | /// \brief Checks if an edge is in the Steiner-tree or not. |
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257 | /// |
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258 | /// Checks if an edge is in the Steiner-tree or not. |
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259 | /// \param e is the edge that will be checked |
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260 | /// \return \c true if e is in the Steiner-tree, \c false otherwise |
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261 | bool tree(UEdge e){ |
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262 | return (*_tree)[e]; |
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263 | } |
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264 | |
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265 | /// \brief Checks if the node is in the Steiner-tree or not. |
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266 | /// |
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267 | /// Checks if a node is in the Steiner-tree or not. |
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268 | /// \param n is the node that will be checked |
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269 | /// \return \c true if n is in the Steiner-tree, \c false otherwise |
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270 | bool tree(Node n){ |
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271 | return (*_filter)[n]; |
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272 | } |
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273 | |
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274 | /// \brief Checks if the node is a Steiner-node. |
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275 | /// |
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276 | /// Checks if the node is a Steiner-node (i.e. a tree node but |
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277 | /// not terminal). |
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278 | /// \param n is the node that will be checked |
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279 | /// \return \c true if n is a Steiner-node, \c false otherwise |
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280 | bool steiner(Node n){ |
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281 | return (*_filter)[n] && (*_pred)[n] != INVALID; |
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282 | } |
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283 | |
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284 | /// \brief Checks if the node is a terminal. |
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285 | /// |
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286 | /// Checks if the node is a terminal. |
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287 | /// \param n is the node that will be checked |
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288 | /// \return \c true if n is a terminal, \c false otherwise |
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289 | bool terminal(Node n){ |
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290 | return _dijkstra.reached(n) && (*_pred)[n] == INVALID; |
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291 | } |
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292 | |
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293 | /// \brief The total cost of the tree |
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294 | /// |
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295 | /// The total cost of the constructed tree. The calculated value does |
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296 | /// not exceed the double of the optimal value. |
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297 | Value treeValue() const { |
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298 | return _value; |
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299 | } |
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300 | |
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301 | }; |
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302 | |
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303 | } //END OF NAMESPACE LEMON |
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304 | |
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305 | #endif |
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