1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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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 | /** |
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20 | @defgroup datas Data Structures |
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21 | This group describes the several data structures implemented in LEMON. |
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22 | */ |
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23 | |
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24 | /** |
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25 | @defgroup graphs Graph Structures |
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26 | @ingroup datas |
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27 | \brief Graph structures implemented in LEMON. |
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28 | |
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29 | The implementation of combinatorial algorithms heavily relies on |
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30 | efficient graph implementations. LEMON offers data structures which are |
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31 | planned to be easily used in an experimental phase of implementation studies, |
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32 | and thereafter the program code can be made efficient by small modifications. |
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33 | |
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34 | The most efficient implementation of diverse applications require the |
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35 | usage of different physical graph implementations. These differences |
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36 | appear in the size of graph we require to handle, memory or time usage |
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37 | limitations or in the set of operations through which the graph can be |
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38 | accessed. LEMON provides several physical graph structures to meet |
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39 | the diverging requirements of the possible users. In order to save on |
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40 | running time or on memory usage, some structures may fail to provide |
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41 | some graph features like arc/edge or node deletion. |
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42 | |
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43 | Alteration of standard containers need a very limited number of |
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44 | operations, these together satisfy the everyday requirements. |
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45 | In the case of graph structures, different operations are needed which do |
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46 | not alter the physical graph, but gives another view. If some nodes or |
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47 | arcs have to be hidden or the reverse oriented graph have to be used, then |
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48 | this is the case. It also may happen that in a flow implementation |
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49 | the residual graph can be accessed by another algorithm, or a node-set |
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50 | is to be shrunk for another algorithm. |
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51 | LEMON also provides a variety of graphs for these requirements called |
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52 | \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only |
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53 | in conjunction with other graph representations. |
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54 | |
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55 | You are free to use the graph structure that fit your requirements |
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56 | the best, most graph algorithms and auxiliary data structures can be used |
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57 | with any graph structure. |
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58 | |
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59 | <b>See also:</b> \ref graph_concepts "Graph Structure Concepts". |
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60 | */ |
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61 | |
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62 | /** |
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63 | @defgroup semi_adaptors Semi-Adaptor Classes for Graphs |
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64 | @ingroup graphs |
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65 | \brief Graph types between real graphs and graph adaptors. |
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66 | |
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67 | This group describes some graph types between real graphs and graph adaptors. |
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68 | These classes wrap graphs to give new functionality as the adaptors do it. |
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69 | On the other hand they are not light-weight structures as the adaptors. |
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70 | */ |
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71 | |
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72 | /** |
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73 | @defgroup maps Maps |
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74 | @ingroup datas |
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75 | \brief Map structures implemented in LEMON. |
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76 | |
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77 | This group describes the map structures implemented in LEMON. |
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78 | |
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79 | LEMON provides several special purpose maps and map adaptors that e.g. combine |
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80 | new maps from existing ones. |
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81 | |
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82 | <b>See also:</b> \ref map_concepts "Map Concepts". |
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83 | */ |
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84 | |
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85 | /** |
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86 | @defgroup graph_maps Graph Maps |
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87 | @ingroup maps |
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88 | \brief Special graph-related maps. |
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89 | |
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90 | This group describes maps that are specifically designed to assign |
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91 | values to the nodes and arcs of graphs. |
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92 | */ |
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93 | |
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94 | /** |
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95 | \defgroup map_adaptors Map Adaptors |
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96 | \ingroup maps |
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97 | \brief Tools to create new maps from existing ones |
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98 | |
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99 | This group describes map adaptors that are used to create "implicit" |
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100 | maps from other maps. |
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101 | |
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102 | Most of them are \ref lemon::concepts::ReadMap "read-only maps". |
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103 | They can make arithmetic and logical operations between one or two maps |
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104 | (negation, shifting, addition, multiplication, logical 'and', 'or', |
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105 | 'not' etc.) or e.g. convert a map to another one of different Value type. |
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106 | |
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107 | The typical usage of this classes is passing implicit maps to |
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108 | algorithms. If a function type algorithm is called then the function |
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109 | type map adaptors can be used comfortable. For example let's see the |
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110 | usage of map adaptors with the \c graphToEps() function. |
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111 | \code |
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112 | Color nodeColor(int deg) { |
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113 | if (deg >= 2) { |
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114 | return Color(0.5, 0.0, 0.5); |
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115 | } else if (deg == 1) { |
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116 | return Color(1.0, 0.5, 1.0); |
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117 | } else { |
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118 | return Color(0.0, 0.0, 0.0); |
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119 | } |
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120 | } |
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121 | |
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122 | Digraph::NodeMap<int> degree_map(graph); |
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123 | |
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124 | graphToEps(graph, "graph.eps") |
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125 | .coords(coords).scaleToA4().undirected() |
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126 | .nodeColors(composeMap(functorToMap(nodeColor), degree_map)) |
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127 | .run(); |
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128 | \endcode |
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129 | The \c functorToMap() function makes an \c int to \c Color map from the |
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130 | \c nodeColor() function. The \c composeMap() compose the \c degree_map |
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131 | and the previously created map. The composed map is a proper function to |
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132 | get the color of each node. |
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133 | |
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134 | The usage with class type algorithms is little bit harder. In this |
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135 | case the function type map adaptors can not be used, because the |
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136 | function map adaptors give back temporary objects. |
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137 | \code |
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138 | Digraph graph; |
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139 | |
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140 | typedef Digraph::ArcMap<double> DoubleArcMap; |
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141 | DoubleArcMap length(graph); |
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142 | DoubleArcMap speed(graph); |
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143 | |
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144 | typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap; |
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145 | TimeMap time(length, speed); |
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146 | |
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147 | Dijkstra<Digraph, TimeMap> dijkstra(graph, time); |
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148 | dijkstra.run(source, target); |
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149 | \endcode |
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150 | We have a length map and a maximum speed map on the arcs of a digraph. |
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151 | The minimum time to pass the arc can be calculated as the division of |
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152 | the two maps which can be done implicitly with the \c DivMap template |
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153 | class. We use the implicit minimum time map as the length map of the |
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154 | \c Dijkstra algorithm. |
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155 | */ |
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156 | |
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157 | /** |
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158 | @defgroup matrices Matrices |
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159 | @ingroup datas |
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160 | \brief Two dimensional data storages implemented in LEMON. |
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161 | |
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162 | This group describes two dimensional data storages implemented in LEMON. |
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163 | */ |
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164 | |
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165 | /** |
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166 | @defgroup paths Path Structures |
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167 | @ingroup datas |
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168 | \brief %Path structures implemented in LEMON. |
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169 | |
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170 | This group describes the path structures implemented in LEMON. |
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171 | |
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172 | LEMON provides flexible data structures to work with paths. |
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173 | All of them have similar interfaces and they can be copied easily with |
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174 | assignment operators and copy constructors. This makes it easy and |
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175 | efficient to have e.g. the Dijkstra algorithm to store its result in |
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176 | any kind of path structure. |
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177 | |
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178 | \sa lemon::concepts::Path |
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179 | */ |
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180 | |
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181 | /** |
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182 | @defgroup auxdat Auxiliary Data Structures |
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183 | @ingroup datas |
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184 | \brief Auxiliary data structures implemented in LEMON. |
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185 | |
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186 | This group describes some data structures implemented in LEMON in |
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187 | order to make it easier to implement combinatorial algorithms. |
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188 | */ |
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189 | |
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190 | /** |
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191 | @defgroup algs Algorithms |
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192 | \brief This group describes the several algorithms |
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193 | implemented in LEMON. |
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194 | |
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195 | This group describes the several algorithms |
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196 | implemented in LEMON. |
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197 | */ |
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198 | |
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199 | /** |
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200 | @defgroup search Graph Search |
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201 | @ingroup algs |
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202 | \brief Common graph search algorithms. |
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203 | |
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204 | This group describes the common graph search algorithms like |
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205 | Breadth-First Search (BFS) and Depth-First Search (DFS). |
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206 | */ |
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207 | |
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208 | /** |
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209 | @defgroup shortest_path Shortest Path Algorithms |
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210 | @ingroup algs |
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211 | \brief Algorithms for finding shortest paths. |
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212 | |
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213 | This group describes the algorithms for finding shortest paths in graphs. |
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214 | */ |
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215 | |
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216 | /** |
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217 | @defgroup max_flow Maximum Flow Algorithms |
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218 | @ingroup algs |
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219 | \brief Algorithms for finding maximum flows. |
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220 | |
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221 | This group describes the algorithms for finding maximum flows and |
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222 | feasible circulations. |
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223 | |
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224 | The maximum flow problem is to find a flow between a single source and |
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225 | a single target that is maximum. Formally, there is a \f$G=(V,A)\f$ |
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226 | directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity |
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227 | function and given \f$s, t \in V\f$ source and target node. The |
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228 | maximum flow is the \f$f_a\f$ solution of the next optimization problem: |
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229 | |
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230 | \f[ 0 \le f_a \le c_a \f] |
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231 | \f[ \sum_{v\in\delta^{-}(u)}f_{vu}=\sum_{v\in\delta^{+}(u)}f_{uv} |
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232 | \qquad \forall u \in V \setminus \{s,t\}\f] |
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233 | \f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f] |
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234 | |
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235 | LEMON contains several algorithms for solving maximum flow problems: |
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236 | - \ref lemon::EdmondsKarp "Edmonds-Karp" |
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237 | - \ref lemon::Preflow "Goldberg's Preflow algorithm" |
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238 | - \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic trees" |
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239 | - \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees" |
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240 | |
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241 | In most cases the \ref lemon::Preflow "Preflow" algorithm provides the |
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242 | fastest method to compute the maximum flow. All impelementations |
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243 | provides functions to query the minimum cut, which is the dual linear |
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244 | programming problem of the maximum flow. |
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245 | */ |
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246 | |
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247 | /** |
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248 | @defgroup min_cost_flow Minimum Cost Flow Algorithms |
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249 | @ingroup algs |
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250 | |
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251 | \brief Algorithms for finding minimum cost flows and circulations. |
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252 | |
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253 | This group describes the algorithms for finding minimum cost flows and |
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254 | circulations. |
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255 | */ |
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256 | |
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257 | /** |
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258 | @defgroup min_cut Minimum Cut Algorithms |
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259 | @ingroup algs |
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260 | |
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261 | \brief Algorithms for finding minimum cut in graphs. |
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262 | |
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263 | This group describes the algorithms for finding minimum cut in graphs. |
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264 | |
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265 | The minimum cut problem is to find a non-empty and non-complete |
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266 | \f$X\f$ subset of the vertices with minimum overall capacity on |
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267 | outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an |
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268 | \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum |
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269 | cut is the \f$X\f$ solution of the next optimization problem: |
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270 | |
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271 | \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} |
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272 | \sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f] |
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273 | |
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274 | LEMON contains several algorithms related to minimum cut problems: |
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275 | |
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276 | - \ref lemon::HaoOrlin "Hao-Orlin algorithm" to calculate minimum cut |
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277 | in directed graphs |
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278 | - \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" to |
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279 | calculate minimum cut in undirected graphs |
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280 | - \ref lemon::GomoryHuTree "Gomory-Hu tree computation" to calculate all |
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281 | pairs minimum cut in undirected graphs |
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282 | |
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283 | If you want to find minimum cut just between two distinict nodes, |
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284 | please see the \ref max_flow "Maximum Flow page". |
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285 | */ |
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286 | |
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287 | /** |
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288 | @defgroup graph_prop Connectivity and Other Graph Properties |
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289 | @ingroup algs |
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290 | \brief Algorithms for discovering the graph properties |
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291 | |
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292 | This group describes the algorithms for discovering the graph properties |
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293 | like connectivity, bipartiteness, euler property, simplicity etc. |
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294 | |
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295 | \image html edge_biconnected_components.png |
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296 | \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
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297 | */ |
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298 | |
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299 | /** |
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300 | @defgroup planar Planarity Embedding and Drawing |
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301 | @ingroup algs |
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302 | \brief Algorithms for planarity checking, embedding and drawing |
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303 | |
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304 | This group describes the algorithms for planarity checking, |
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305 | embedding and drawing. |
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306 | |
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307 | \image html planar.png |
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308 | \image latex planar.eps "Plane graph" width=\textwidth |
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309 | */ |
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310 | |
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311 | /** |
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312 | @defgroup matching Matching Algorithms |
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313 | @ingroup algs |
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314 | \brief Algorithms for finding matchings in graphs and bipartite graphs. |
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315 | |
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316 | This group contains algorithm objects and functions to calculate |
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317 | matchings in graphs and bipartite graphs. The general matching problem is |
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318 | finding a subset of the arcs which does not shares common endpoints. |
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319 | |
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320 | There are several different algorithms for calculate matchings in |
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321 | graphs. The matching problems in bipartite graphs are generally |
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322 | easier than in general graphs. The goal of the matching optimization |
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323 | can be the finding maximum cardinality, maximum weight or minimum cost |
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324 | matching. The search can be constrained to find perfect or |
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325 | maximum cardinality matching. |
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326 | |
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327 | LEMON contains the next algorithms: |
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328 | - \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" Hopcroft-Karp |
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329 | augmenting path algorithm for calculate maximum cardinality matching in |
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330 | bipartite graphs |
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331 | - \ref lemon::PrBipartiteMatching "PrBipartiteMatching" Push-Relabel |
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332 | algorithm for calculate maximum cardinality matching in bipartite graphs |
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333 | - \ref lemon::MaxWeightedBipartiteMatching "MaxWeightedBipartiteMatching" |
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334 | Successive shortest path algorithm for calculate maximum weighted matching |
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335 | and maximum weighted bipartite matching in bipartite graph |
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336 | - \ref lemon::MinCostMaxBipartiteMatching "MinCostMaxBipartiteMatching" |
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337 | Successive shortest path algorithm for calculate minimum cost maximum |
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338 | matching in bipartite graph |
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339 | - \ref lemon::MaxMatching "MaxMatching" Edmond's blossom shrinking algorithm |
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340 | for calculate maximum cardinality matching in general graph |
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341 | - \ref lemon::MaxWeightedMatching "MaxWeightedMatching" Edmond's blossom |
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342 | shrinking algorithm for calculate maximum weighted matching in general |
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343 | graph |
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344 | - \ref lemon::MaxWeightedPerfectMatching "MaxWeightedPerfectMatching" |
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345 | Edmond's blossom shrinking algorithm for calculate maximum weighted |
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346 | perfect matching in general graph |
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347 | |
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348 | \image html bipartite_matching.png |
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349 | \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth |
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350 | */ |
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351 | |
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352 | /** |
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353 | @defgroup spantree Minimum Spanning Tree Algorithms |
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354 | @ingroup algs |
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355 | \brief Algorithms for finding a minimum cost spanning tree in a graph. |
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356 | |
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357 | This group describes the algorithms for finding a minimum cost spanning |
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358 | tree in a graph |
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359 | */ |
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360 | |
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361 | /** |
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362 | @defgroup auxalg Auxiliary Algorithms |
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363 | @ingroup algs |
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364 | \brief Auxiliary algorithms implemented in LEMON. |
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365 | |
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366 | This group describes some algorithms implemented in LEMON |
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367 | in order to make it easier to implement complex algorithms. |
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368 | */ |
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369 | |
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370 | /** |
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371 | @defgroup approx Approximation Algorithms |
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372 | @ingroup algs |
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373 | \brief Approximation algorithms. |
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374 | |
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375 | This group describes the approximation and heuristic algorithms |
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376 | implemented in LEMON. |
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377 | */ |
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378 | |
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379 | /** |
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380 | @defgroup gen_opt_group General Optimization Tools |
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381 | \brief This group describes some general optimization frameworks |
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382 | implemented in LEMON. |
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383 | |
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384 | This group describes some general optimization frameworks |
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385 | implemented in LEMON. |
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386 | */ |
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387 | |
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388 | /** |
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389 | @defgroup lp_group Lp and Mip Solvers |
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390 | @ingroup gen_opt_group |
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391 | \brief Lp and Mip solver interfaces for LEMON. |
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392 | |
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393 | This group describes Lp and Mip solver interfaces for LEMON. The |
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394 | various LP solvers could be used in the same manner with this |
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395 | interface. |
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396 | */ |
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397 | |
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398 | /** |
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399 | @defgroup lp_utils Tools for Lp and Mip Solvers |
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400 | @ingroup lp_group |
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401 | \brief Helper tools to the Lp and Mip solvers. |
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402 | |
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403 | This group adds some helper tools to general optimization framework |
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404 | implemented in LEMON. |
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405 | */ |
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406 | |
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407 | /** |
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408 | @defgroup metah Metaheuristics |
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409 | @ingroup gen_opt_group |
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410 | \brief Metaheuristics for LEMON library. |
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411 | |
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412 | This group describes some metaheuristic optimization tools. |
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413 | */ |
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414 | |
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415 | /** |
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416 | @defgroup utils Tools and Utilities |
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417 | \brief Tools and utilities for programming in LEMON |
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418 | |
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419 | Tools and utilities for programming in LEMON. |
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420 | */ |
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421 | |
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422 | /** |
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423 | @defgroup gutils Basic Graph Utilities |
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424 | @ingroup utils |
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425 | \brief Simple basic graph utilities. |
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426 | |
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427 | This group describes some simple basic graph utilities. |
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428 | */ |
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429 | |
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430 | /** |
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431 | @defgroup misc Miscellaneous Tools |
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432 | @ingroup utils |
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433 | \brief Tools for development, debugging and testing. |
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434 | |
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435 | This group describes several useful tools for development, |
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436 | debugging and testing. |
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437 | */ |
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438 | |
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439 | /** |
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440 | @defgroup timecount Time Measuring and Counting |
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441 | @ingroup misc |
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442 | \brief Simple tools for measuring the performance of algorithms. |
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443 | |
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444 | This group describes simple tools for measuring the performance |
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445 | of algorithms. |
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446 | */ |
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447 | |
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448 | /** |
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449 | @defgroup exceptions Exceptions |
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450 | @ingroup utils |
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451 | \brief Exceptions defined in LEMON. |
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452 | |
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453 | This group describes the exceptions defined in LEMON. |
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454 | */ |
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455 | |
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456 | /** |
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457 | @defgroup io_group Input-Output |
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458 | \brief Graph Input-Output methods |
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459 | |
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460 | This group describes the tools for importing and exporting graphs |
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461 | and graph related data. Now it supports the \ref lgf-format |
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462 | "LEMON Graph Format", the \c DIMACS format and the encapsulated |
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463 | postscript (EPS) format. |
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464 | */ |
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465 | |
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466 | /** |
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467 | @defgroup lemon_io LEMON Graph Format |
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468 | @ingroup io_group |
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469 | \brief Reading and writing LEMON Graph Format. |
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470 | |
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471 | This group describes methods for reading and writing |
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472 | \ref lgf-format "LEMON Graph Format". |
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473 | */ |
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474 | |
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475 | /** |
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476 | @defgroup eps_io Postscript Exporting |
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477 | @ingroup io_group |
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478 | \brief General \c EPS drawer and graph exporter |
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479 | |
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480 | This group describes general \c EPS drawing methods and special |
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481 | graph exporting tools. |
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482 | */ |
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483 | |
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484 | /** |
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485 | @defgroup nauty_group NAUTY Format |
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486 | @ingroup io_group |
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487 | \brief Read \e Nauty format |
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488 | Tool to read graphs from \e Nauty format data. |
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489 | */ |
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490 | |
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491 | /** |
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492 | @defgroup concept Concepts |
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493 | \brief Skeleton classes and concept checking classes |
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494 | |
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495 | This group describes the data/algorithm skeletons and concept checking |
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496 | classes implemented in LEMON. |
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497 | |
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498 | The purpose of the classes in this group is fourfold. |
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499 | |
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500 | - These classes contain the documentations of the %concepts. In order |
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501 | to avoid document multiplications, an implementation of a concept |
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502 | simply refers to the corresponding concept class. |
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503 | |
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504 | - These classes declare every functions, <tt>typedef</tt>s etc. an |
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505 | implementation of the %concepts should provide, however completely |
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506 | without implementations and real data structures behind the |
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507 | interface. On the other hand they should provide nothing else. All |
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508 | the algorithms working on a data structure meeting a certain concept |
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509 | should compile with these classes. (Though it will not run properly, |
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510 | of course.) In this way it is easily to check if an algorithm |
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511 | doesn't use any extra feature of a certain implementation. |
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512 | |
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513 | - The concept descriptor classes also provide a <em>checker class</em> |
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514 | that makes it possible to check whether a certain implementation of a |
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515 | concept indeed provides all the required features. |
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516 | |
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517 | - Finally, They can serve as a skeleton of a new implementation of a concept. |
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518 | */ |
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519 | |
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520 | /** |
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521 | @defgroup graph_concepts Graph Structure Concepts |
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522 | @ingroup concept |
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523 | \brief Skeleton and concept checking classes for graph structures |
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524 | |
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525 | This group describes the skeletons and concept checking classes of LEMON's |
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526 | graph structures and helper classes used to implement these. |
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527 | */ |
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528 | |
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529 | /** |
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530 | @defgroup map_concepts Map Concepts |
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531 | @ingroup concept |
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532 | \brief Skeleton and concept checking classes for maps |
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533 | |
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534 | This group describes the skeletons and concept checking classes of maps. |
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535 | */ |
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536 | |
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537 | /** |
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538 | \anchor demoprograms |
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539 | |
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540 | @defgroup demos Demo programs |
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541 | |
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542 | Some demo programs are listed here. Their full source codes can be found in |
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543 | the \c demo subdirectory of the source tree. |
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544 | |
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545 | It order to compile them, use <tt>--enable-demo</tt> configure option when |
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546 | build the library. |
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547 | */ |
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548 | |
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549 | /** |
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550 | @defgroup tools Standalone utility applications |
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551 | |
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552 | Some utility applications are listed here. |
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553 | |
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554 | The standard compilation procedure (<tt>./configure;make</tt>) will compile |
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555 | them, as well. |
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556 | */ |
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557 | |
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