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- Copyright (c) Jeremy Siek 2000
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- Distributed under the Boost Software License, Version 1.0.
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- <Head>
- <Title>Boost Graph Library: Bandwidth</Title>
- <BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
- ALINK="#ff0000">
- <IMG SRC="../../../boost.png"
- ALT="C++ Boost" width="277" height="86">
- <BR Clear>
- <H1><A NAME="sec:bandwidth">
- <TT>bandwidth</TT>
- </H1>
- <pre>
- (1)
- template <typename Graph>
- typename graph_traits<Graph>::vertices_size_type
- bandwidth(const Graph& g)
- (2)
- template <typename Graph, typename VertexIndexMap>
- typename graph_traits<Graph>::vertices_size_type
- bandwidth(const Graph& g, VertexIndexMap index_map)
- </pre>
- The <b><i>bandwidth</i></b> of a graph is the maximum
- distance between two adjacent vertices, with distance measured on a
- line upon which the vertices have been placed at unit intervals. To
- put it another way, if the vertices of a graph
- <i>G=(V,E)</i> are each assigned an index from zero to <i>|V| - 1</i>
- given by <i>index[v]</i>, then the bandwidth of <i>G</i> is<br>
- <br>
- <i>B(G) = max { |index[u] - index[v]| | (u,v) in E }</i><br>
- <h3>Defined in</h3>
- <a href="../../../boost/graph/bandwidth.hpp"><tt>boost/graph/bandwidth.hpp</tt></a>
- <hr>
- <H1><A NAME="sec:ith-bandwidth">
- <TT>ith_bandwidth</TT>
- </H1>
- <pre>
- (1)
- template <typename Graph>
- typename graph_traits<Graph>::vertices_size_type
- ith_bandwidth(typename graph_traits<Graph>::vertex_descriptor i,
- const Graph& g)
- (2)
- template <typename Graph, typename VertexIndexMap>
- typename graph_traits<Graph>::vertices_size_type
- ith_bandwidth(typename graph_traits<Graph>::vertex_descriptor i,
- const Graph& g,
- VertexIndexMap index)
- </pre>
- The <b><i>i-th bandwidth</i></b> a graph is the maximum distance
- between the <i>i-th</i> vertex and any of its neighbors.<br>
- <br>
- <i>B<sub>i</sub>(G) = max { |index[i] - index[j]| | (i,j) in E }</i><br>
- <br>
- So the bandwidth <i>B(G)</i> can be expressed as the maximum
- of the i-th bandwidths <i>B<sub>i</sub>(G)</i>.<br>
- <br>
- <i>B(G) = max { B<sub>i</sub>(G) | i=0...|V|-1 }</i><br>
- <h3>Defined in</h3>
- <a href="../../../boost/graph/bandwidth.hpp"><tt>boost/graph/bandwidth.hpp</tt></a>
- <br>
- <HR>
- <TABLE>
- <TR valign=top>
- <TD nowrap>Copyright © 2000-2001</TD><TD>
- <A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>, Indiana University (<A HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)
- </TD></TR></TABLE>
- </BODY>
- </HTML>
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