[1678] | 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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[1684] | 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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[1678] | 11 | |
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[1684] | 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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[1678] | 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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[1684] | 60 | \subsection go-alg-main The main() function |
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| 61 | |
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[1678] | 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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[1953] | 66 | First we check whether the program is called with exactly one parameter. |
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[1678] | 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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[1684] | 73 | the in-deg requirements from a \ref graph-io-page ".lgf (Lemon Graph Format)" |
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[1953] | 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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[1678] | 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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[1953] | 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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[1678] | 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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[1953] | 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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[1678] | 108 | used to draw these edges with different color in the output picture. The |
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[1953] | 109 | algorithm updates this map, but will not use it otherwise. |
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[1678] | 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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[1953] | 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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[1678] | 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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