1 | namespace lemon { |
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2 | /** |
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3 | |
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4 | \ingroup demos |
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5 | \file graph_orientation.cc |
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6 | \brief Graph orientation with lower bound requirement on the |
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7 | in-degree of the nodes. |
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8 | |
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9 | This demo shows an adaptation of the well-known "preflow push" algorithm to |
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10 | a simple graph orientation problem. |
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11 | |
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12 | The input of the problem is a(n undirected) graph and an integer value |
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13 | <i>f(n)</i> assigned to each node \e n. The task is to find an orientation |
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14 | of the edges for which the number of edge arriving to each node \e n is at |
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15 | least least <i>f(n)</i>. |
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16 | |
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17 | In fact, the algorithm reads a directed graph and computes a set of edges to |
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18 | be reversed in order to achieve the in-degree requirement. |
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19 | This input is given using |
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20 | \ref graph-io-page ".lgf (Lemon Graph Format)" file. It should contain |
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21 | three node maps. The one called "f" contains the in-degree requirements, while |
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22 | "coordinate_x" and "coordinate_y" indicate the position of the nodes. These |
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23 | latter ones are used to generate the output, which is a <tt>.eps</tt> file. |
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24 | |
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25 | |
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26 | \section go-alg-dec The C++ source file |
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27 | |
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28 | Here you find how to solve the problem above using lemon. |
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29 | |
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30 | \subsection go-alg-head Headers and convenience typedefs |
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31 | |
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32 | First we include some important headers. |
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33 | |
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34 | The first one defines \ref lemon::ListGraph "ListGraph", |
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35 | the "Swiss army knife" graph implementation. |
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36 | \dontinclude graph_orientation.cc |
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37 | \skipline list_graph |
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38 | |
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39 | The next is to read a \ref graph-io-page ".lgf" (Lemon Graph Format) file. |
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40 | \skipline reader |
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41 | |
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42 | This provides us with some special purpose graph \ref maps "maps". |
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43 | \skipline iterable |
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44 | |
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45 | The following header defines a simple data structure to store and manipulate |
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46 | planar coordinates. It will be used to draw the result. |
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47 | \skipline xy |
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48 | |
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49 | And finally, this header contains a simple graph drawing utility. |
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50 | \skipline eps |
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51 | |
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52 | As we don't want to type in \ref lemon "lemon::" million times, the |
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53 | following line seems to be useful. |
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54 | \skipline namespace |
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55 | |
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56 | The following <tt>typedef</tt>s will also save a lot of typing. |
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57 | \skip typedef |
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58 | \until InEdgeIt |
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59 | |
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60 | \subsection go-alg-main The main() function |
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61 | |
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62 | Well, we are ready to start <tt>main()</tt>. |
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63 | \skip main |
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64 | \until { |
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65 | |
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66 | First we check whether the program is called with exactly one parameter. |
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67 | If it isn't, we print a short help message end exit. |
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68 | The vast majority of people would probably skip this block. |
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69 | \skip if |
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70 | \until } |
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71 | |
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72 | Now, we read a graph \c g, and a map \c f containing |
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73 | the in-deg requirements from a \ref graph-io-page ".lgf (Lemon Graph Format)" |
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74 | file. To generate the output picture, we also read the node titles (\c label) |
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75 | and |
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76 | coordinates (\c coords). |
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77 | So, first we create the graph |
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78 | \skipline ListGraph |
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79 | and the corresponding NodeMaps. |
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80 | \skipline NodeMap |
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81 | \until coords |
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82 | \note The graph must be given to the maps' constructor. |
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83 | |
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84 | Then, the following block will read these data from the file, or exit if |
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85 | the file is missing or corrupt. |
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86 | \skip try |
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87 | \until } |
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88 | \until } |
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89 | |
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90 | The algorithm needs an integer value assigned to each node. We call this "level" and the nodes are on level 0 at the |
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91 | beginning of the execution. |
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92 | |
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93 | \skipline level |
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94 | |
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95 | The deficiency (\c def) of a node is the in-degree requirement minus the |
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96 | actual in-degree. |
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97 | |
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98 | \skip def |
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99 | \until subMap |
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100 | |
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101 | A node is \e active if its deficiency is positive (i.e. if it doesn't meet |
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102 | the degree requirement). |
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103 | \skip active |
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104 | \until def |
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105 | |
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106 | We also store in a bool map indicating which edges are reverted. |
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107 | Actually this map called \c rev is only |
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108 | used to draw these edges with different color in the output picture. The |
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109 | algorithm updates this map, but will not use it otherwise. |
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110 | \skip rev |
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111 | \until reversed |
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112 | |
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113 | The variable \c nodeNum will refer to the number of nodes. |
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114 | \skipline nodeNum |
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115 | |
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116 | Here comes the algorithms itself. |
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117 | In each iteration we choose an active node (\c act will do it for us). |
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118 | If there is |
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119 | no such a node, then the orientation is feasible so we are done. |
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120 | \skip act |
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121 | \until while |
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122 | |
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123 | Then we check if there exists an edge leaving this node that steps down exactly |
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124 | one level. |
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125 | \skip OutEdge |
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126 | \until while |
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127 | |
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128 | If there exists, we decrease the "activity" of the node \c act by reverting |
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129 | this egde. |
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130 | Fortunately, \ref lemon::ListGraph "ListGraph" |
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131 | has a special function \ref lemon::ListGraph::reverseEdge() "reverseEdge()" |
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132 | that makes this easy. |
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133 | We also have to update the maps \c def and |
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134 | \c rev. |
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135 | \skipline if |
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136 | \skip if |
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137 | \until } |
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138 | Otherwise (i.e. if there is no edge stepping down one level). We lift up the |
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139 | current active node \c act. If it reaches level \c nodeNum, then there |
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140 | exists no appropriate orientation so we stop. |
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141 | \skipline else |
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142 | \skipline if |
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143 | \skipline return |
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144 | \until } |
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145 | \until } |
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146 | \until } |
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147 | |
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148 | Believe it or not, this algorithm works and runs fast. |
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149 | |
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150 | Finally, we print the obtained orientation. Note, how the different |
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151 | \c bool values of |
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152 | \c rev are transformed into different \ref lemon::Color "RGB color"s |
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153 | using the class |
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154 | \ref lemon::ColorSet "ColorSet" |
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155 | and the \ref map_adaptors "map adaptor" called |
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156 | \ref lemon::ComposeMap "composeMap". |
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157 | |
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158 | \skip graphToEps |
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159 | \until run |
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160 | |
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161 | |
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162 | \until end of main |
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163 | |
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164 | Finally here are again the list of the used include files (because I can't turn |
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165 | this section off.) |
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166 | |
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167 | */ |
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168 | |
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169 | } |
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