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1 | <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> |
| 2 | <html> | |
| 3 | <!-- | |
| 4 | Copyright (c) 2005 Trustees of Indiana University | |
| 5 | ||
| 6 | Distributed under the Boost Software License, Version 1.0. | |
| 7 | (See accompanying file LICENSE_1_0.txt or copy at | |
| 8 | http://www.boost.org/LICENSE_1_0.txt) | |
| 9 | --> | |
| 10 | <head> | |
| 11 | <title>Boost Graph Library: Sequential Vertex Coloring</title> | |
| 12 | </head> | |
| 13 | ||
| 14 | <body> | |
| 15 | <IMG SRC="../../../boost.png" | |
| 16 | ALT="C++ Boost" width="277" height="86"> | |
| 17 | <h1><img src="figs/python.gif" alt="(Python)"/><tt>sequential_vertex_coloring</tt></h1> | |
| 18 | ||
| 19 | <p> | |
| 20 | <pre> | |
| 21 | template<class VertexListGraph, class OrderPA, class ColorMap> | |
| 22 | typename property_traits<ColorMap>::value_type | |
| 23 | sequential_vertex_coloring(const VertexListGraph& g, OrderPA order, | |
| 24 | ColorMap color); | |
| 25 | ||
| 26 | template<class VertexListGraph, class ColorMap> | |
| 27 | typename property_traits<ColorMap>::value_type | |
| 28 | sequential_vertex_coloring(const VertexListGraph& g, ColorMap color); | |
| 29 | </pre> | |
| 30 | ||
| 31 | <p>Computes a <a href="graph_coloring.html">vertex coloring</a> for | |
| 32 | the vertices in the graph, using a simple algorithm [<a | |
| 33 | href="bibliography.html#coleman83">59</a>]. Given vertices | |
| 34 | ordered v<sub>1</sub>, v<sub>2</sub>, ... , v<sub>n</sub>, for k = 1, | |
| 35 | 2, ..., n the algorithm assigns v<sub>k</sub> to the smallest possible | |
| 36 | color. The algorithm does not guarantee an optimum coloring. | |
| 37 | ||
| 38 | <p>Here is the coloring that would be produced on a graph given the | |
| 39 | vertex ordering A, B, C, D, E. | |
| 40 | ||
| 41 | <p><img src="figs/sequential_vertex_coloring.png">, | |
| 42 | ||
| 43 | <h3>Where Defined</h3> | |
| 44 | <a href="../../../boost/graph/sequential_vertex_coloring.hpp"><tt>boost/graph/sequential_vertex_coloring.hpp</tt></a> | |
| 45 | ||
| 46 | <h3>Parameters</h3> | |
| 47 | IN: <tt>const Graph& g</tt> | |
| 48 | <blockquote> | |
| 49 | The graph object on which the algorithm will be applied. The type | |
| 50 | <tt>Graph</tt> must be a model of <a | |
| 51 | href="VertexListGraph.html">Vertex List Graph</a> and <a | |
| 52 | href="AdjacencyGraph.html">Adjacency Graph</a>.<br> | |
| 53 | <b>Python</b>: The parameter is named <tt>graph</tt>. | |
| 54 | </blockquote> | |
| 55 | ||
| 56 | OUT: <tt>ColorMap color</tt> | |
| 57 | <blockquote> | |
| 58 | This property map records the colors of each vertex. It must be a | |
| 59 | model of | |
| 60 | <a href="../../property_map/doc/WritablePropertyMap.html">Writeable | |
| 61 | Property Map</a> whose key type is the same as the vertex descriptor | |
| 62 | type of the graph and whose value type is an integral type that can | |
| 63 | store all values of the graph's <tt>vertices_size_type</tt>.<br> | |
| 64 | <b>Python</b>: Must be an <tt>vertex_int_map</tt> for the graph. | |
| 65 | </blockquote> | |
| 66 | ||
| 67 | IN: <tt>OrderPA order</tt> | |
| 68 | <blockquote> | |
| 69 | A mapping from integers in the range <em>[0, num_vertices(g))</em> | |
| 70 | to the vertices of the graph.<br> | |
| 71 | ||
| 72 | <b>Default:</b> A property map ordering the vertices in the same way | |
| 73 | they are ordered by <tt>vertices(g)</tt>.<br> | |
| 74 | <b>Python</b>: Unsupported parameter. | |
| 75 | </blockquote> | |
| 76 | ||
| 77 | <h3>Complexity</h3> | |
| 78 | ||
| 79 | The time complexity is <em>O(V(d+k))</em>, where <em>V</em> is the | |
| 80 | number of vertices, <em>d</em> is the maximum degree of the vertices | |
| 81 | in the graph, and <em>k</em> is the number of colors used. | |
| 82 | ||
| 83 | <h3>Example</h3> | |
| 84 | <pre> | |
| 85 | typedef adjacency_list<listS, vecS, undirectedS> Graph; | |
| 86 | typedef graph_traits<Graph>::vertex_descriptor vertex_descriptor; | |
| 87 | typedef graph_traits<Graph>::vertices_size_type vertices_size_type; | |
| 88 | typedef property_map<Graph, vertex_index_t>::const_type vertex_index_map; | |
| 89 | ||
| 90 | typedef std::pair<int, int> Edge; | |
| 91 | enum nodes {A, B, C, D, E, n}; | |
| 92 | Edge edge_array[] = { Edge(A, C), Edge(B, B), Edge(B, D), Edge(B, E), | |
| 93 | Edge(C, B), Edge(C, D), Edge(D, E), Edge(E, A), | |
| 94 | Edge(E, B) }; | |
| 95 | int m = sizeof(edge_array) / sizeof(Edge); | |
| 96 | Graph g(edge_array, edge_array + m, n); | |
| 97 | ||
| 98 | <em>// Test with the normal order</em> | |
| 99 | std::vector<vertices_size_type> color_vec(num_vertices(g)); | |
| 100 | iterator_property_map<vertices_size_type*, vertex_index_map> | |
| 101 | color(&color_vec.front(), get(vertex_index, g)); | |
| 102 | <b>vertices_size_type num_colors = sequential_vertex_coloring(g, color);</b> | |
| 103 | </pre> | |
| 104 | ||
| 105 | <hr> | |
| 106 | ||
| 107 | <TABLE> | |
| 108 | <TR valign=top> | |
| 109 | <TD nowrap>Copyright © 1997-2004</TD><TD> | |
| 110 | <A HREF="http://www.osl.iu.edu/~lums">Andrew Lumsdaine</A>, | |
| 111 | Indiana University (<A | |
| 112 | HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)<br> | |
| 113 | <A HREF="http://www.boost.org/people/doug_gregor.html">Douglas Gregor</A>, Indiana University (dgregor -at- cs.indiana.edu)</A>) | |
| 114 | </TD></TR></TABLE> | |
| 115 | </body> | |
| 116 | </html> |