<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<!--
     Copyright (c) 2005 Trustees of Indiana University
    
     Distributed under the Boost Software License, Version 1.0.
     (See accompanying file LICENSE_1_0.txt or copy at
     http://www.boost.org/LICENSE_1_0.txt)
  -->
  <head>
    <title>Boost Graph Library: Sequential Vertex Coloring</title>
  </head>

  <body>
    <IMG SRC="../../../boost.png" 
     ALT="C++ Boost" width="277" height="86"> 
<h1><img src="figs/python.gif" alt="(Python)"/><tt>sequential_vertex_coloring</tt></h1>

    <p>
    <pre>
template&lt;class VertexListGraph, class OrderPA, class ColorMap&gt;
typename property_traits&lt;ColorMap&gt;::value_type
sequential_vertex_coloring(const VertexListGraph&amp; g, OrderPA order, 
                           ColorMap color);

template&lt;class VertexListGraph, class ColorMap&gt;
typename property_traits&lt;ColorMap&gt;::value_type
sequential_vertex_coloring(const VertexListGraph&amp; g, ColorMap color);
    </pre>

<p>Computes a <a href="graph_coloring.html">vertex coloring</a> for
the vertices in the graph, using a simple algorithm [<a
href="bibliography.html#coleman83">59</a>]. Given vertices 
ordered v<sub>1</sub>, v<sub>2</sub>, ... , v<sub>n</sub>, for k = 1,
2, ..., n the algorithm assigns v<sub>k</sub> to the smallest possible
color. The algorithm does not guarantee an optimum coloring.

<p>Here is the coloring that would be produced on a graph given the
vertex ordering A, B, C, D, E.

<p><img src="figs/sequential_vertex_coloring.png">,

<h3>Where Defined</h3>
<a href="../../../boost/graph/sequential_vertex_coloring.hpp"><tt>boost/graph/sequential_vertex_coloring.hpp</tt></a>

<h3>Parameters</h3>
IN: <tt>const Graph&amp; g</tt>
<blockquote>
  The graph object on which the algorithm will be applied.  The type
  <tt>Graph</tt> must be a model of <a
  href="VertexListGraph.html">Vertex List Graph</a> and <a
  href="AdjacencyGraph.html">Adjacency Graph</a>.<br>
<b>Python</b>: The parameter is named <tt>graph</tt>.
</blockquote>
    
OUT: <tt>ColorMap color</tt> 
<blockquote>
  This property map records the colors of each vertex. It must be a
  model of
  <a href="../../property_map/doc/WritablePropertyMap.html">Writeable
  Property Map</a> whose key type is the same as the vertex descriptor
  type of the graph and whose value type is an integral type that can
  store all values of the graph's <tt>vertices_size_type</tt>.<br>
  <b>Python</b>: Must be an <tt>vertex_int_map</tt> for the graph.
</blockquote>

IN: <tt>OrderPA order</tt> 
<blockquote>
  A mapping from integers in the range <em>[0, num_vertices(g))</em>
  to the vertices of the graph.<br>

  <b>Default:</b> A property map ordering the vertices in the same way
  they are ordered by <tt>vertices(g)</tt>.<br>
  <b>Python</b>: Unsupported parameter.
</blockquote>

<h3>Complexity</h3>

The time complexity is <em>O(V(d+k))</em>, where <em>V</em> is the
number of vertices, <em>d</em> is the maximum degree of the vertices
in the graph, and <em>k</em> is the number of colors used.

<h3>Example</h3>
<pre>
  typedef adjacency_list&lt;listS, vecS, undirectedS&gt; Graph;
  typedef graph_traits&lt;Graph&gt;::vertex_descriptor vertex_descriptor;
  typedef graph_traits&lt;Graph&gt;::vertices_size_type vertices_size_type;
  typedef property_map&lt;Graph, vertex_index_t&gt;::const_type vertex_index_map;

  typedef std::pair&lt;int, int&gt; Edge;
  enum nodes {A, B, C, D, E, n};
  Edge edge_array[] = { Edge(A, C), Edge(B, B), Edge(B, D), Edge(B, E), 
                        Edge(C, B), Edge(C, D), Edge(D, E), Edge(E, A), 
                        Edge(E, B) };
  int m = sizeof(edge_array) / sizeof(Edge);
  Graph g(edge_array, edge_array + m, n);

  <em>// Test with the normal order</em>
  std::vector&lt;vertices_size_type&gt; color_vec(num_vertices(g));
  iterator_property_map&lt;vertices_size_type*, vertex_index_map&gt;
    color(&amp;color_vec.front(), get(vertex_index, g));
  <b>vertices_size_type num_colors = sequential_vertex_coloring(g, color);</b>
</pre>

    <hr>

<TABLE>
<TR valign=top>
<TD nowrap>Copyright &copy; 1997-2004</TD><TD>
<A HREF="http://www.osl.iu.edu/~lums">Andrew Lumsdaine</A>,
Indiana University (<A
HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)<br>
<A HREF="http://www.boost.org/people/doug_gregor.html">Douglas Gregor</A>, Indiana University (dgregor -at- cs.indiana.edu)</A>)
</TD></TR></TABLE>
  </body>
</html>