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) 2003-2010 |
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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 | namespace lemon { |
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20 | /** |
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21 | [PAGE]sec_graph_adaptors[PAGE] Graph Adaptors |
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22 | |
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23 | \todo Clarify this section. |
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24 | |
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25 | Alteration of standard containers need a very limited number of |
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26 | operations, these together satisfy the everyday requirements. |
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27 | In the case of graph structures, different operations are needed which do |
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28 | not alter the physical graph, but gives another view. If some nodes or |
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29 | arcs have to be hidden or the reverse oriented graph have to be used, then |
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30 | this is the case. It also may happen that in a flow implementation |
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31 | the residual graph can be accessed by another algorithm, or a node-set |
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32 | is to be shrunk for another algorithm. |
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33 | LEMON also provides a variety of graphs for these requirements called |
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34 | \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only |
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35 | in conjunction with other graph representations. |
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36 | |
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37 | The main parts of LEMON are the different graph structures, generic |
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38 | graph algorithms, graph concepts, which couple them, and graph |
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39 | adaptors. While the previous notions are more or less clear, the |
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40 | latter one needs further explanation. Graph adaptors are graph classes |
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41 | which serve for considering graph structures in different ways. |
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42 | |
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43 | A short example makes this much clearer. Suppose that we have an |
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44 | instance \c g of a directed graph type, say ListDigraph and an algorithm |
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45 | \code |
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46 | template <typename Digraph> |
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47 | int algorithm(const Digraph&); |
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48 | \endcode |
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49 | is needed to run on the reverse oriented graph. It may be expensive |
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50 | (in time or in memory usage) to copy \c g with the reversed |
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51 | arcs. In this case, an adaptor class is used, which (according |
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52 | to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph. |
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53 | The adaptor uses the original digraph structure and digraph operations when |
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54 | methods of the reversed oriented graph are called. This means that the adaptor |
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55 | have minor memory usage, and do not perform sophisticated algorithmic |
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56 | actions. The purpose of it is to give a tool for the cases when a |
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57 | graph have to be used in a specific alteration. If this alteration is |
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58 | obtained by a usual construction like filtering the node or the arc set or |
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59 | considering a new orientation, then an adaptor is worthwhile to use. |
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60 | To come back to the reverse oriented graph, in this situation |
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61 | \code |
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62 | template<typename Digraph> class ReverseDigraph; |
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63 | \endcode |
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64 | template class can be used. The code looks as follows |
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65 | \code |
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66 | ListDigraph g; |
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67 | ReverseDigraph<ListDigraph> rg(g); |
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68 | int result = algorithm(rg); |
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69 | \endcode |
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70 | During running the algorithm, the original digraph \c g is untouched. |
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71 | This techniques give rise to an elegant code, and based on stable |
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72 | graph adaptors, complex algorithms can be implemented easily. |
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73 | |
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74 | In flow, circulation and matching problems, the residual |
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75 | graph is of particular importance. Combining an adaptor implementing |
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76 | this with shortest path algorithms or minimum mean cycle algorithms, |
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77 | a range of weighted and cardinality optimization algorithms can be |
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78 | obtained. For other examples, the interested user is referred to the |
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79 | detailed documentation of particular adaptors. |
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80 | |
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81 | The behavior of graph adaptors can be very different. Some of them keep |
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82 | capabilities of the original graph while in other cases this would be |
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83 | meaningless. This means that the concepts that they meet depend |
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84 | on the graph adaptor, and the wrapped graph. |
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85 | For example, if an arc of a reversed digraph is deleted, this is carried |
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86 | out by deleting the corresponding arc of the original digraph, thus the |
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87 | adaptor modifies the original digraph. |
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88 | However in case of a residual digraph, this operation has no sense. |
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89 | |
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90 | Let us stand one more example here to simplify your work. |
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91 | ReverseDigraph has constructor |
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92 | \code |
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93 | ReverseDigraph(Digraph& digraph); |
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94 | \endcode |
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95 | This means that in a situation, when a <tt>const %ListDigraph&</tt> |
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96 | reference to a graph is given, then it have to be instantiated with |
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97 | <tt>Digraph=const %ListDigraph</tt>. |
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98 | \code |
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99 | int algorithm1(const ListDigraph& g) { |
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100 | ReverseDigraph<const ListDigraph> rg(g); |
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101 | return algorithm2(rg); |
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102 | } |
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103 | \endcode |
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104 | |
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105 | <hr> |
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106 | |
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107 | The LEMON graph adaptor classes serve for considering graphs in |
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108 | different ways. The adaptors can be used exactly the same as "real" |
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109 | graphs (i.e., they conform to the graph concepts), thus all generic |
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110 | algorithms can be performed on them. However, the adaptor classes use |
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111 | the underlying graph structures and operations when their methods are |
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112 | called, thus they have only negligible memory usage and do not perform |
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113 | sophisticated algorithmic actions. This technique yields convenient and |
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114 | elegant tools for the cases when a graph has to be used in a specific |
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115 | alteration, but copying it would be too expensive (in time or in memory |
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116 | usage) compared to the algorithm that should be executed on it. The |
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117 | following example shows how the \ref ReverseDigraph adaptor can be used |
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118 | to run Dijksta's algorithm on the reverse oriented graph. Note that the |
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119 | maps of the original graph can be used in connection with the adaptor, |
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120 | since the node and arc types of the adaptors convert to the original |
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121 | item types. |
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122 | |
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123 | \code |
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124 | dijkstra(reverseDigraph(g), length).distMap(dist).run(s); |
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125 | \endcode |
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126 | |
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127 | Using \ref ReverseDigraph could be as efficient as working with the |
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128 | original graph, but not all adaptors can be so fast, of course. For |
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129 | example, the subgraph adaptors have to access filter maps for the nodes |
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130 | and/or the arcs, thus their iterators are significantly slower than the |
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131 | original iterators. LEMON also provides some more complex adaptors, for |
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132 | instance, \ref SplitNodes, which can be used for splitting each node in |
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133 | a directed graph and \ref ResidualDigraph for modeling the residual |
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134 | network for flow and matching problems. |
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135 | |
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136 | Therefore, in cases when rather complex algorithms have to be used |
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137 | on a subgraph (e.g. when the nodes and arcs have to be traversed several |
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138 | times), it could worth copying the altered graph into an efficient structure |
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139 | and run the algorithm on it. |
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140 | Note that the adaptor classes can also be used for doing this easily, |
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141 | without having to copy the graph manually, as shown in the following |
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142 | example. |
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143 | |
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144 | \code |
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145 | ListDigraph g; |
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146 | ListDigraph::NodeMap<bool> filter_map(g); |
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147 | // construct the graph and fill the filter map |
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148 | |
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149 | { |
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150 | SmartDigraph temp_graph; |
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151 | ListDigraph::NodeMap<SmartDigraph::Node> node_ref(g); |
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152 | digraphCopy(filterNodes(g, filter_map), temp_graph) |
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153 | .nodeRef(node_ref).run(); |
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154 | |
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155 | // use temp_graph |
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156 | } |
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157 | \endcode |
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158 | |
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159 | <hr> |
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160 | |
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161 | Another interesting adaptor in LEMON is \ref SplitNodes. |
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162 | It can be used for splitting each node into an in-node and an out-node |
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163 | in a directed graph. Formally, the adaptor replaces each node |
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164 | u in the graph with two nodes, namely node u<sub>in</sub> and node |
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165 | u<sub>out</sub>. Each arc (u,c) in the original graph will correspond to an |
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166 | arc (u<sub>out</sub>,v<sub>in</sub>). The adaptor also adds an |
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167 | additional bind arc (u<sub>in</sub>,u<sub>out</sub>) for each node u |
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168 | of the original digraph. |
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169 | |
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170 | The aim of this class is to assign costs to the nodes when using |
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171 | algorithms which would otherwise consider arc costs only. |
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172 | For example, let us suppose that we have a directed graph with costs |
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173 | given for both the nodes and the arcs. |
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174 | Then Dijkstra's algorithm can be used in connection with \ref SplitNodes |
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175 | as follows. |
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176 | |
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177 | \code |
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178 | typedef SplitNodes<ListDigraph> SplitGraph; |
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179 | SplitGraph sg(g); |
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180 | SplitGraph::CombinedArcMap<NodeCostMap, ArcCostMap> |
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181 | combined_cost(node_cost, arc_cost); |
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182 | SplitGraph::NodeMap<double> dist(sg); |
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183 | dijkstra(sg, combined_cost).distMap(dist).run(sg.outNode(u)); |
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184 | \endcode |
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185 | |
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186 | Note that this problem can be solved more efficiently with |
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187 | map adaptors. |
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188 | |
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189 | These techniques help writing compact and elegant code, and makes it possible |
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190 | to easily implement complex algorithms based on well tested standard components. |
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191 | For instance, in flow and matching problems the residual graph is of |
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192 | particular importance. |
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193 | Combining \ref ResidualDigraph adaptor with various algorithms, a |
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194 | range of weighted and cardinality optimization methods can be obtained |
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195 | directly. |
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196 | |
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197 | [TRAILER] |
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198 | */ |
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199 | } |
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