1 | // -*- c++ -*- |
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2 | #ifndef HUGO_MINLENGTHPATHS_H |
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3 | #define HUGO_MINLENGTHPATHS_H |
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4 | |
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5 | ///\file |
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6 | ///\brief An algorithm for finding k paths of minimal total length. |
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7 | |
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8 | #include <iostream> |
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9 | #include <dijkstra.h> |
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10 | #include <graph_wrapper.h> |
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11 | #include <maps.h> |
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12 | #include <vector> |
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13 | |
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14 | |
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15 | namespace hugo { |
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16 | |
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17 | |
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18 | |
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19 | ///\brief Implementation of an algorithm for finding k paths between 2 nodes |
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20 | /// of minimal total length |
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21 | /// |
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22 | /// The class \ref hugo::MinLengthPaths "MinLengthPaths" implements |
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23 | /// an algorithm which finds k edge-disjoint paths |
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24 | /// from a given source node to a given target node in an |
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25 | /// edge-weighted directed graph having minimal total weigth (length). |
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26 | |
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27 | template <typename Graph, typename LengthMap> |
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28 | class MinLengthPaths { |
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29 | |
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30 | typedef typename LengthMap::ValueType Length; |
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31 | |
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32 | typedef typename Graph::Node Node; |
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33 | typedef typename Graph::NodeIt NodeIt; |
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34 | typedef typename Graph::Edge Edge; |
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35 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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36 | typedef typename Graph::EdgeMap<int> EdgeIntMap; |
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37 | |
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38 | typedef ConstMap<Edge,int> ConstMap; |
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39 | |
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40 | typedef ResGraphWrapper<const Graph,int,EdgeIntMap,ConstMap> ResGraphType; |
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41 | |
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42 | |
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43 | class ModLengthMap { |
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44 | typedef typename ResGraphType::NodeMap<Length> NodeMap; |
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45 | const ResGraphType& G; |
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46 | const EdgeIntMap& rev; |
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47 | const LengthMap &ol; |
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48 | const NodeMap &pot; |
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49 | public : |
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50 | typedef typename LengthMap::KeyType KeyType; |
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51 | typedef typename LengthMap::ValueType ValueType; |
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52 | |
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53 | ValueType operator[](typename ResGraphType::Edge e) const { |
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54 | //if ( (1-2*rev[e])*ol[e]-(pot[G.head(e)]-pot[G.tail(e)] ) <0 ){ |
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55 | // std::cout<<"Negative length!!"<<std::endl; |
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56 | //} |
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57 | return (1-2*rev[e])*ol[e]-(pot[G.head(e)]-pot[G.tail(e)]); |
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58 | } |
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59 | |
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60 | ModLengthMap(const ResGraphType& _G, const EdgeIntMap& _rev, |
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61 | const LengthMap &o, const NodeMap &p) : |
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62 | G(_G), rev(_rev), ol(o), pot(p){}; |
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63 | }; |
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64 | |
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65 | |
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66 | const Graph& G; |
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67 | const LengthMap& length; |
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68 | |
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69 | //auxiliary variables |
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70 | |
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71 | //The value is 1 iff the edge is reversed. |
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72 | //If the algorithm has finished, the edges of the seeked paths are |
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73 | //exactly those that are reversed |
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74 | EdgeIntMap reversed; |
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75 | |
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76 | //Container to store found paths |
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77 | std::vector< std::vector<Edge> > paths; |
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78 | |
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79 | public : |
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80 | |
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81 | |
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82 | MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G), |
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83 | length(_length), reversed(_G)/*, dijkstra_dist(_G)*/{ } |
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84 | |
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85 | |
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86 | ///Runs the algorithm |
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87 | ///Returns k if there are at least k edge-disjoint paths from s to t. |
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88 | ///Otherwise it returns the number of edge-disjoint paths from s to t. |
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89 | int run(Node s, Node t, int k) { |
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90 | ConstMap const1map(1); |
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91 | |
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92 | //We need a residual graph, in which some of the edges are reversed |
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93 | ResGraphType res_graph(G, reversed, const1map); |
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94 | |
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95 | //Initialize the copy of the Dijkstra potential to zero |
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96 | typename ResGraphType::NodeMap<Length> dijkstra_dist(res_graph); |
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97 | ModLengthMap mod_length(res_graph, reversed, length, dijkstra_dist); |
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98 | |
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99 | Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length); |
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100 | |
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101 | int i; |
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102 | for (i=0; i<k; ++i){ |
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103 | dijkstra.run(s); |
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104 | if (!dijkstra.reached(t)){ |
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105 | //There are no k paths from s to t |
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106 | break; |
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107 | }; |
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108 | |
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109 | { |
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110 | //We have to copy the potential |
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111 | typename ResGraphType::NodeIt n; |
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112 | for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) { |
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113 | dijkstra_dist[n] += dijkstra.distMap()[n]; |
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114 | } |
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115 | } |
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116 | |
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117 | |
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118 | //Reversing the sortest path |
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119 | Node n=t; |
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120 | Edge e; |
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121 | while (n!=s){ |
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122 | e = dijkstra.pred(n); |
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123 | n = dijkstra.predNode(n); |
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124 | reversed[e] = 1-reversed[e]; |
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125 | } |
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126 | |
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127 | |
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128 | } |
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129 | |
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130 | //Let's find the paths |
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131 | //We put the paths into vectors (just for now). In the meantime we lose |
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132 | //the information stored in 'reversed' |
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133 | //We suppose the lengths to be positive now. |
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134 | paths.clear(); |
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135 | paths.resize(k); |
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136 | for (int j=0; j<i; ++j){ |
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137 | Node n=s; |
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138 | OutEdgeIt e; |
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139 | |
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140 | while (n!=t){ |
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141 | |
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142 | |
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143 | G.first(e,n); |
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144 | |
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145 | while (!reversed[e]){ |
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146 | G.next(e); |
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147 | } |
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148 | n = G.head(e); |
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149 | paths[j].push_back(e); |
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150 | reversed[e] = 1-reversed[e]; |
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151 | } |
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152 | |
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153 | } |
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154 | |
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155 | return i; |
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156 | } |
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157 | |
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158 | |
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159 | }; //class MinLengthPaths |
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160 | |
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161 | |
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162 | } //namespace hugo |
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163 | |
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164 | #endif //HUGO_MINLENGTHPATHS_H |
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