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 | ///\ingroup flowalgs |
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6 | ///\file |
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7 | ///\brief An algorithm for finding k paths of minimal total length. |
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8 | |
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9 | |
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10 | //#include <hugo/dijkstra.h> |
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11 | //#include <hugo/graph_wrapper.h> |
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12 | #include <hugo/maps.h> |
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13 | #include <vector> |
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14 | #include <hugo/mincostflows.h> |
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15 | |
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16 | namespace hugo { |
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17 | |
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18 | /// \addtogroup flowalgs |
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19 | /// @{ |
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20 | |
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21 | ///\brief Implementation of an algorithm for finding k paths between 2 nodes |
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22 | /// of minimal total length |
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23 | /// |
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24 | /// The class \ref hugo::MinLengthPaths "MinLengthPaths" implements |
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25 | /// an algorithm for finding k edge-disjoint paths |
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26 | /// from a given source node to a given target node in an |
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27 | /// edge-weighted directed graph having minimal total weigth (length). |
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28 | /// |
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29 | ///\warning It is assumed that the lengths are positive, since the |
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30 | /// general flow-decomposition is not implemented yet. |
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31 | /// |
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32 | ///\author Attila Bernath |
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33 | template <typename Graph, typename LengthMap> |
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34 | class MinLengthPaths{ |
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35 | |
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36 | |
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37 | typedef typename LengthMap::ValueType Length; |
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38 | |
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39 | typedef typename Graph::Node Node; |
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40 | typedef typename Graph::NodeIt NodeIt; |
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41 | typedef typename Graph::Edge Edge; |
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42 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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43 | typedef typename Graph::template EdgeMap<int> EdgeIntMap; |
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44 | |
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45 | typedef ConstMap<Edge,int> ConstMap; |
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46 | |
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47 | //Input |
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48 | const Graph& G; |
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49 | |
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50 | //Auxiliary variables |
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51 | //This is the capacity map for the mincostflow problem |
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52 | ConstMap const1map; |
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53 | //This MinCostFlows instance will actually solve the problem |
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54 | MinCostFlows<Graph, LengthMap, ConstMap> mincost_flow; |
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55 | |
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56 | //Container to store found paths |
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57 | std::vector< std::vector<Edge> > paths; |
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58 | |
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59 | public : |
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60 | |
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61 | |
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62 | MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G), |
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63 | const1map(1), mincost_flow(_G, _length, const1map){} |
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64 | |
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65 | ///Runs the algorithm. |
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66 | |
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67 | ///Runs the algorithm. |
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68 | ///Returns k if there are at least k edge-disjoint paths from s to t. |
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69 | ///Otherwise it returns the number of found edge-disjoint paths from s to t. |
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70 | int run(Node s, Node t, int k) { |
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71 | |
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72 | int i = mincost_flow.run(s,t,k); |
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73 | |
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74 | |
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75 | |
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76 | //Let's find the paths |
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77 | //We put the paths into stl vectors (as an inner representation). |
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78 | //In the meantime we lose the information stored in 'reversed'. |
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79 | //We suppose the lengths to be positive now. |
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80 | |
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81 | //We don't want to change the flow of mincost_flow, so we make a copy |
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82 | //The name here suggests that the flow has only 0/1 values. |
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83 | EdgeIntMap reversed(G); |
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84 | |
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85 | for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) |
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86 | reversed[e] = mincost_flow.getFlow()[e]; |
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87 | |
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88 | paths.clear(); |
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89 | //total_length=0; |
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90 | paths.resize(k); |
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91 | for (int j=0; j<i; ++j){ |
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92 | Node n=s; |
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93 | OutEdgeIt e; |
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94 | |
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95 | while (n!=t){ |
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96 | |
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97 | |
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98 | G.first(e,n); |
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99 | |
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100 | while (!reversed[e]){ |
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101 | ++e; |
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102 | } |
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103 | n = G.head(e); |
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104 | paths[j].push_back(e); |
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105 | //total_length += length[e]; |
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106 | reversed[e] = 1-reversed[e]; |
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107 | } |
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108 | |
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109 | } |
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110 | return i; |
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111 | } |
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112 | |
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113 | |
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114 | ///This function gives back the total length of the found paths. |
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115 | ///Assumes that \c run() has been run and nothing changed since then. |
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116 | Length totalLength(){ |
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117 | return mincost_flow.totalLength(); |
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118 | } |
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119 | |
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120 | ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must |
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121 | ///be called before using this function. |
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122 | const EdgeIntMap &getFlow() const { return mincost_flow.flow;} |
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123 | |
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124 | ///Returns a const reference to the NodeMap \c potential (the dual solution). |
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125 | /// \pre \ref run() must be called before using this function. |
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126 | const EdgeIntMap &getPotential() const { return mincost_flow.potential;} |
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127 | |
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128 | ///This function checks, whether the given solution is optimal |
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129 | ///Running after a \c run() should return with true |
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130 | ///In this "state of the art" this only checks optimality, doesn't bother with feasibility |
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131 | /// |
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132 | ///\todo Is this OK here? |
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133 | bool checkComplementarySlackness(){ |
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134 | return mincost_flow.checkComplementarySlackness(); |
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135 | } |
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136 | |
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137 | ///This function gives back the \c j-th path in argument p. |
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138 | ///Assumes that \c run() has been run and nothing changed since then. |
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139 | /// \warning It is assumed that \c p is constructed to be a path of graph \c G. If \c j is not less than the result of previous \c run, then the result here will be an empty path (\c j can be 0 as well). |
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140 | template<typename DirPath> |
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141 | void getPath(DirPath& p, size_t j){ |
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142 | |
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143 | p.clear(); |
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144 | if (j>paths.size()-1){ |
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145 | return; |
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146 | } |
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147 | typename DirPath::Builder B(p); |
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148 | for(typename std::vector<Edge>::iterator i=paths[j].begin(); |
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149 | i!=paths[j].end(); ++i ){ |
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150 | B.pushBack(*i); |
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151 | } |
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152 | |
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153 | B.commit(); |
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154 | } |
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155 | |
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156 | }; //class MinLengthPaths |
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157 | |
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158 | ///@} |
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159 | |
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160 | } //namespace hugo |
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161 | |
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162 | #endif //HUGO_MINLENGTHPATHS_H |
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