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) 2003-2008 |
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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_MIN_MEAN_CYCLE_H |
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20 | #define LEMON_MIN_MEAN_CYCLE_H |
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21 | |
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22 | /// \ingroup shortest_path |
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23 | /// |
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24 | /// \file |
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25 | /// \brief Karp's algorithm for finding a minimum mean (directed) cycle. |
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26 | |
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27 | #include <vector> |
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28 | #include <lemon/graph_utils.h> |
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29 | #include <lemon/topology.h> |
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30 | #include <lemon/path.h> |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | /// \addtogroup shortest_path |
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35 | /// @{ |
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36 | |
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37 | /// \brief Implementation of Karp's algorithm for finding a |
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38 | /// minimum mean (directed) cycle. |
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39 | /// |
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40 | /// The \ref lemon::MinMeanCycle "MinMeanCycle" implements Karp's |
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41 | /// algorithm for finding a minimum mean (directed) cycle. |
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42 | /// |
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43 | /// \param Graph The directed graph type the algorithm runs on. |
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44 | /// \param LengthMap The type of the length (cost) map. |
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45 | /// |
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46 | /// \author Peter Kovacs |
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47 | |
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48 | template <typename Graph, |
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49 | typename LengthMap = typename Graph::template EdgeMap<int> > |
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50 | class MinMeanCycle |
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51 | { |
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52 | typedef typename Graph::Node Node; |
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53 | typedef typename Graph::NodeIt NodeIt; |
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54 | typedef typename Graph::Edge Edge; |
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55 | typedef typename Graph::EdgeIt EdgeIt; |
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56 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
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57 | |
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58 | typedef typename LengthMap::Value Length; |
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59 | |
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60 | typedef typename Graph::template NodeMap<int> IntNodeMap; |
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61 | typedef typename Graph::template NodeMap<Edge> PredNodeMap; |
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62 | typedef Path<Graph> Path; |
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63 | typedef std::vector<Node> NodeVector; |
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64 | |
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65 | protected: |
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66 | |
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67 | /// \brief Data structure for path data. |
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68 | struct PathData |
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69 | { |
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70 | bool found; |
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71 | Length dist; |
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72 | Edge pred; |
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73 | PathData(bool _found = false, Length _dist = 0) : |
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74 | found(_found), dist(_dist), pred(INVALID) {} |
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75 | PathData(bool _found, Length _dist, Edge _pred) : |
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76 | found(_found), dist(_dist), pred(_pred) {} |
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77 | }; |
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78 | |
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79 | private: |
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80 | |
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81 | typedef typename Graph::template NodeMap<std::vector<PathData> > |
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82 | PathDataNodeMap; |
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83 | |
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84 | protected: |
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85 | |
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86 | /// \brief Node map for storing path data. |
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87 | /// |
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88 | /// Node map for storing path data of all nodes in the current |
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89 | /// component. dmap[v][k] is the length of a shortest directed walk |
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90 | /// to node v from the starting node containing exactly k edges. |
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91 | PathDataNodeMap dmap; |
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92 | |
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93 | /// \brief The directed graph the algorithm runs on. |
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94 | const Graph &graph; |
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95 | /// \brief The length of the edges. |
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96 | const LengthMap &length; |
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97 | |
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98 | /// \brief The total length of the found cycle. |
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99 | Length cycle_length; |
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100 | /// \brief The number of edges in the found cycle. |
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101 | int cycle_size; |
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102 | /// \brief A node for obtaining a minimum mean cycle. |
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103 | Node cycle_node; |
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104 | |
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105 | /// \brief The found cycle. |
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106 | Path *cycle_path; |
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107 | /// \brief The algorithm uses local \ref lemon::Path "Path" |
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108 | /// structure to store the found cycle. |
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109 | bool local_path; |
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110 | |
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111 | /// \brief Node map for identifying strongly connected components. |
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112 | IntNodeMap comp; |
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113 | /// \brief The number of strongly connected components. |
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114 | int comp_num; |
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115 | /// \brief Counter for identifying the current component. |
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116 | int comp_cnt; |
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117 | /// \brief Nodes of the current component. |
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118 | NodeVector nodes; |
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119 | /// \brief The processed nodes in the last round. |
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120 | NodeVector process; |
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121 | |
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122 | public : |
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123 | |
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124 | /// \brief The constructor of the class. |
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125 | /// |
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126 | /// The constructor of the class. |
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127 | /// |
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128 | /// \param _graph The directed graph the algorithm runs on. |
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129 | /// \param _length The length (cost) of the edges. |
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130 | MinMeanCycle( const Graph &_graph, |
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131 | const LengthMap &_length ) : |
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132 | graph(_graph), length(_length), dmap(_graph), comp(_graph), |
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133 | cycle_length(0), cycle_size(-1), cycle_node(INVALID), |
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134 | cycle_path(NULL), local_path(false) |
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135 | { } |
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136 | |
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137 | /// \brief The destructor of the class. |
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138 | ~MinMeanCycle() { |
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139 | if (local_path) delete cycle_path; |
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140 | } |
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141 | |
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142 | protected: |
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143 | |
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144 | /// \brief Initializes the internal data structures for the current |
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145 | /// component. |
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146 | void initCurrent() { |
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147 | nodes.clear(); |
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148 | // Finding the nodes of the current component |
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149 | for (NodeIt v(graph); v != INVALID; ++v) { |
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150 | if (comp[v] == comp_cnt) nodes.push_back(v); |
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151 | } |
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152 | // Creating vectors for all nodes |
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153 | int n = nodes.size(); |
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154 | for (int i = 0; i < n; ++i) { |
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155 | dmap[nodes[i]].resize(n + 1); |
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156 | } |
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157 | } |
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158 | |
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159 | /// \brief Processes all rounds of computing required path data for |
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160 | /// the current component. |
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161 | void processRounds() { |
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162 | dmap[nodes[0]][0] = PathData(true, 0); |
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163 | process.clear(); |
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164 | // Processing the first round |
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165 | for (OutEdgeIt e(graph, nodes[0]); e != INVALID; ++e) { |
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166 | Node v = graph.target(e); |
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167 | if (comp[v] != comp_cnt || v == nodes[0]) continue; |
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168 | dmap[v][1] = PathData(true, length[e], e); |
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169 | process.push_back(v); |
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170 | } |
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171 | // Processing other rounds |
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172 | int n = nodes.size(), k; |
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173 | for (k = 2; k <= n && process.size() < n; ++k) |
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174 | processNextBuildRound(k); |
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175 | for ( ; k <= n; ++k) |
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176 | processNextFullRound(k); |
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177 | } |
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178 | |
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179 | /// \brief Processes one round of computing required path data and |
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180 | /// rebuilds \ref process vector. |
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181 | void processNextBuildRound(int k) { |
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182 | NodeVector next; |
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183 | for (int i = 0; i < process.size(); ++i) { |
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184 | for (OutEdgeIt e(graph, process[i]); e != INVALID; ++e) { |
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185 | Node v = graph.target(e); |
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186 | if (comp[v] != comp_cnt) continue; |
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187 | if (!dmap[v][k].found) { |
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188 | next.push_back(v); |
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189 | dmap[v][k] = PathData(true, dmap[process[i]][k-1].dist + length[e], e); |
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190 | } |
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191 | else if (dmap[process[i]][k-1].dist + length[e] < dmap[v][k].dist) { |
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192 | dmap[v][k] = PathData(true, dmap[process[i]][k-1].dist + length[e], e); |
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193 | } |
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194 | } |
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195 | } |
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196 | process.swap(next); |
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197 | } |
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198 | |
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199 | /// \brief Processes one round of computing required path data |
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200 | /// using \ref nodes vector instead of \ref process vector. |
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201 | void processNextFullRound(int k) { |
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202 | for (int i = 0; i < nodes.size(); ++i) { |
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203 | for (OutEdgeIt e(graph, nodes[i]); e != INVALID; ++e) { |
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204 | Node v = graph.target(e); |
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205 | if (comp[v] != comp_cnt) continue; |
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206 | if ( !dmap[v][k].found || |
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207 | dmap[nodes[i]][k-1].dist + length[e] < dmap[v][k].dist ) { |
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208 | dmap[v][k] = PathData(true, dmap[nodes[i]][k-1].dist + length[e], e); |
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209 | } |
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210 | } |
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211 | } |
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212 | } |
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213 | |
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214 | /// \brief Finds the minimum cycle mean value in the current |
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215 | /// component. |
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216 | bool findCurrentMin(Length &min_length, int &min_size, Node &min_node) { |
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217 | bool found_min = false; |
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218 | for (int i = 0; i < nodes.size(); ++i) { |
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219 | int n = nodes.size(); |
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220 | if (!dmap[nodes[i]][n].found) continue; |
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221 | Length len; |
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222 | int size; |
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223 | bool found_one = false; |
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224 | for (int k = 0; k < n; ++k) { |
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225 | if (!dmap[nodes[i]][k].found) continue; |
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226 | Length _len = dmap[nodes[i]][n].dist - dmap[nodes[i]][k].dist; |
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227 | int _size = n - k; |
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228 | if (!found_one || len * _size < _len * size) { |
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229 | found_one = true; |
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230 | len = _len; |
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231 | size = _size; |
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232 | } |
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233 | } |
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234 | if ( found_one && |
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235 | (!found_min || len * min_size < min_length * size) ) { |
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236 | found_min = true; |
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237 | min_length = len; |
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238 | min_size = size; |
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239 | min_node = nodes[i]; |
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240 | } |
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241 | } |
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242 | return found_min; |
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243 | } |
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244 | |
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245 | public: |
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246 | |
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247 | /// \brief Runs the algorithm. |
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248 | /// |
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249 | /// Runs the algorithm. |
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250 | /// |
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251 | /// \return \c true if a cycle exists in the graph. |
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252 | /// |
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253 | /// \note Apart from the return value, <tt>m.run()</tt> is just a |
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254 | /// shortcut of the following code. |
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255 | /// \code |
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256 | /// m.init(); |
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257 | /// m.findMinMean(); |
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258 | /// m.findCycle(); |
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259 | /// \endcode |
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260 | bool run() { |
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261 | init(); |
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262 | findMinMean(); |
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263 | return findCycle(); |
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264 | } |
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265 | |
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266 | /// \brief Initializes the internal data structures. |
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267 | /// |
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268 | /// Initializes the internal data structures. |
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269 | /// |
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270 | /// \sa reset() |
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271 | void init() { |
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272 | comp_num = stronglyConnectedComponents(graph, comp); |
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273 | if (!cycle_path) { |
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274 | local_path = true; |
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275 | cycle_path = new Path; |
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276 | } |
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277 | } |
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278 | |
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279 | /// \brief Finds the minimum cycle mean value in the graph. |
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280 | /// |
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281 | /// Computes all the required path data and finds the minimum cycle |
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282 | /// mean value in the graph. |
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283 | /// |
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284 | /// \return \c true if a cycle exists in the graph. |
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285 | /// |
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286 | /// \pre \ref init() must be called before using this function. |
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287 | bool findMinMean() { |
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288 | cycle_node = INVALID; |
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289 | for (comp_cnt = 0; comp_cnt < comp_num; ++comp_cnt) { |
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290 | initCurrent(); |
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291 | processRounds(); |
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292 | |
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293 | Length min_length; |
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294 | int min_size; |
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295 | Node min_node; |
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296 | bool found_min = findCurrentMin(min_length, min_size, min_node); |
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297 | |
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298 | if ( found_min && (cycle_node == INVALID || |
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299 | min_length * cycle_size < cycle_length * min_size) ) { |
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300 | cycle_length = min_length; |
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301 | cycle_size = min_size; |
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302 | cycle_node = min_node; |
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303 | } |
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304 | } |
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305 | return (cycle_node != INVALID); |
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306 | } |
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307 | |
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308 | /// \brief Finds a critical (minimum mean) cycle. |
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309 | /// |
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310 | /// Finds a critical (minimum mean) cycle using the path data |
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311 | /// stored in \ref dmap. |
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312 | /// |
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313 | /// \return \c true if a cycle exists in the graph. |
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314 | /// |
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315 | /// \pre \ref init() and \ref findMinMean() must be called before |
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316 | /// using this function. |
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317 | bool findCycle() { |
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318 | if (cycle_node == INVALID) return false; |
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319 | cycle_length = 0; |
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320 | cycle_size = 0; |
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321 | IntNodeMap reached(graph, -1); |
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322 | int r = reached[cycle_node] = dmap[cycle_node].size() - 1; |
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323 | Node u = graph.source(dmap[cycle_node][r].pred); |
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324 | while (reached[u] < 0) { |
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325 | reached[u] = --r; |
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326 | u = graph.source(dmap[u][r].pred); |
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327 | } |
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328 | r = reached[u]; |
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329 | Edge e = dmap[u][r].pred; |
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330 | cycle_path->addFront(e); |
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331 | cycle_length = cycle_length + length[e]; |
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332 | ++cycle_size; |
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333 | Node v; |
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334 | while ((v = graph.source(e)) != u) { |
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335 | e = dmap[v][--r].pred; |
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336 | cycle_path->addFront(e); |
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337 | cycle_length = cycle_length + length[e]; |
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338 | ++cycle_size; |
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339 | } |
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340 | return true; |
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341 | } |
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342 | |
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343 | /// \brief Resets the internal data structures. |
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344 | /// |
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345 | /// Resets the internal data structures so that \ref findMinMean() |
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346 | /// and \ref findCycle() can be called again (e.g. when the |
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347 | /// underlaying graph has been modified). |
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348 | /// |
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349 | /// \sa init() |
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350 | void reset() { |
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351 | for (NodeIt u(graph); u != INVALID; ++u) |
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352 | dmap[u].clear(); |
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353 | cycle_node = INVALID; |
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354 | if (cycle_path) cycle_path->clear(); |
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355 | comp_num = stronglyConnectedComponents(graph, comp); |
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356 | } |
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357 | |
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358 | /// \brief Returns the total length of the found cycle. |
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359 | /// |
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360 | /// Returns the total length of the found cycle. |
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361 | /// |
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362 | /// \pre \ref run() or \ref findCycle() must be called before |
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363 | /// using this function. If only \ref findMinMean() is called, |
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364 | /// the return value is not valid. |
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365 | Length cycleLength() const { |
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366 | return cycle_length; |
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367 | } |
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368 | |
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369 | /// \brief Returns the number of edges in the found cycle. |
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370 | /// |
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371 | /// Returns the number of edges in the found cycle. |
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372 | /// |
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373 | /// \pre \ref run() or \ref findCycle() must be called before |
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374 | /// using this function. If only \ref findMinMean() is called, |
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375 | /// the return value is not valid. |
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376 | int cycleEdgeNum() const { |
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377 | return cycle_size; |
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378 | } |
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379 | |
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380 | /// \brief Returns the mean length of the found cycle. |
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381 | /// |
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382 | /// Returns the mean length of the found cycle. |
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383 | /// |
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384 | /// \pre \ref run() or \ref findMinMean() must be called before |
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385 | /// using this function. |
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386 | /// |
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387 | /// \warning LengthMap::Value must be convertible to double. |
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388 | /// |
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389 | /// \note <tt>m.minMean()</tt> is just a shortcut of the following |
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390 | /// code. |
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391 | /// \code |
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392 | /// return m.cycleLength() / double(m.cycleEdgeNum()); |
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393 | /// \endcode |
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394 | /// However if only \ref findMinMean() is called before using this |
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395 | /// function, <tt>m.cycleLength()</tt> and <tt>m.cycleEdgeNum()</tt> |
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396 | /// are not valid alone, only their ratio is valid. |
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397 | double minMean() const { |
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398 | return cycle_length / (double)cycle_size; |
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399 | } |
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400 | |
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401 | /// \brief Returns a const reference to the \ref lemon::Path "Path" |
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402 | /// structure of the found cycle. |
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403 | /// |
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404 | /// Returns a const reference to the \ref lemon::Path "Path" |
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405 | /// structure of the found cycle. |
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406 | /// |
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407 | /// \pre \ref run() must be called before using this function. |
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408 | /// |
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409 | /// \sa \ref cyclePath() |
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410 | const Path& cycle() const { |
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411 | return *cycle_path; |
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412 | } |
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413 | |
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414 | /// \brief Sets the \ref lemon::Path "Path" structure storing the |
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415 | /// found cycle. |
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416 | /// |
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417 | /// Sets the \ref lemon::Path "Path" structure storing the found |
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418 | /// cycle. If you don't use this function before calling |
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419 | /// \ref run(), it will allocate one. The destuctor deallocates |
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420 | /// this automatically allocated map, of course. |
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421 | /// |
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422 | /// \note The algorithm calls only the \ref lemon::Path::addFront() |
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423 | /// "addFront()" method of the given \ref lemon::Path "Path" |
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424 | /// structure. |
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425 | /// |
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426 | /// \return \c (*this) |
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427 | MinMeanCycle& cyclePath(Path &path) { |
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428 | if (local_path) { |
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429 | delete cycle_path; |
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430 | local_path = false; |
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431 | } |
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432 | cycle_path = &path; |
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433 | return *this; |
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434 | } |
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435 | |
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436 | }; //class MinMeanCycle |
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437 | |
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438 | ///@} |
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439 | |
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440 | } //namespace lemon |
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441 | |
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442 | #endif //LEMON_MIN_MEAN_CYCLE_H |
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