| 1 | <HTML> |
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| 2 | <!-- |
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| 3 | -- Copyright (c) Jeremy Siek 2000 |
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| 4 | -- |
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| 5 | -- Distributed under the Boost Software License, Version 1.0. |
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| 6 | -- (See accompanying file LICENSE_1_0.txt or copy at |
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| 7 | -- http://www.boost.org/LICENSE_1_0.txt) |
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| 8 | --> |
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| 9 | <Head> |
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| 10 | <Title>Boost Graph Library: Bandwidth</Title> |
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| 11 | <BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b" |
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| 12 | ALINK="#ff0000"> |
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| 13 | <IMG SRC="../../../boost.png" |
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| 14 | ALT="C++ Boost" width="277" height="86"> |
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| 15 | |
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| 16 | <BR Clear> |
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| 17 | |
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| 18 | <H1><A NAME="sec:bandwidth"> |
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| 19 | <TT>bandwidth</TT> |
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| 20 | </H1> |
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| 21 | |
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| 22 | <pre> |
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| 23 | (1) |
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| 24 | template <typename Graph> |
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| 25 | typename graph_traits<Graph>::vertices_size_type |
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| 26 | bandwidth(const Graph& g) |
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| 27 | |
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| 28 | (2) |
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| 29 | template <typename Graph, typename VertexIndexMap> |
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| 30 | typename graph_traits<Graph>::vertices_size_type |
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| 31 | bandwidth(const Graph& g, VertexIndexMap index_map) |
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| 32 | </pre> |
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| 33 | |
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| 34 | The <b><i>bandwidth</i></b> of an undirected graph is the maximum |
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| 35 | distance between two adjacent vertices, with distance measured on a |
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| 36 | line upon which the vertices have been placed at unit intervals. To |
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| 37 | put it another way, if the vertices of an undirected graph |
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| 38 | <i>G=(V,E)</i> are each assigned an index from zero to <i>|V| - 1</i> |
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| 39 | given by <i>index[v]</i>, then the bandwidth of <i>G</i> is<br> |
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| 40 | <br> |
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| 41 | <i>B(G) = max { |index[u] - index[v]| | (u,v) in E }</i><br> |
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| 42 | |
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| 43 | |
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| 44 | <h3>Defined in</h3> |
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| 45 | |
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| 46 | <a href="../../../boost/graph/bandwidth.hpp"><tt>boost/graph/bandwidth.hpp</tt></a> |
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| 47 | |
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| 48 | |
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| 49 | <hr> |
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| 50 | |
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| 51 | <H1><A NAME="sec:ith-bandwidth"> |
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| 52 | <TT>ith_bandwidth</TT> |
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| 53 | </H1> |
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| 54 | |
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| 55 | <pre> |
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| 56 | (1) |
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| 57 | template <typename Graph> |
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| 58 | typename graph_traits<Graph>::vertices_size_type |
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| 59 | ith_bandwidth(typename graph_traits<Graph>::vertex_descriptor i, |
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| 60 | const Graph& g) |
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| 61 | |
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| 62 | (2) |
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| 63 | template <typename Graph, typename VertexIndexMap> |
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| 64 | typename graph_traits<Graph>::vertices_size_type |
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| 65 | ith_bandwidth(typename graph_traits<Graph>::vertex_descriptor i, |
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| 66 | const Graph& g, |
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| 67 | VertexIndexMap index) |
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| 68 | </pre> |
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| 69 | |
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| 70 | The <b><i>i-th bandwidth</i></b> a graph is the maximum distance |
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| 71 | between the <i>i-th</i> vertex and any of its neighbors.<br> |
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| 72 | <br> |
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| 73 | <i>B<sub>i</sub>(G) = max { |index[i] - index[j]| | (i,j) in E }</i><br> |
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| 74 | <br> |
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| 75 | So the bandwidth <i>B(G)</i> can be expressed as the maximum |
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| 76 | of the i-th bandwidths <i>B<sub>i</sub>(G)</i>.<br> |
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| 77 | <br> |
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| 78 | <i>B(G) = max { B<sub>i</sub>(G) | i=0...|V|-1 }</i><br> |
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| 79 | |
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| 80 | <h3>Defined in</h3> |
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| 81 | |
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| 82 | <a href="../../../boost/graph/bandwidth.hpp"><tt>boost/graph/bandwidth.hpp</tt></a> |
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| 83 | |
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| 84 | <br> |
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| 85 | <HR> |
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| 86 | <TABLE> |
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| 87 | <TR valign=top> |
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| 88 | <TD nowrap>Copyright © 2000-2001</TD><TD> |
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| 89 | <A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Indiana University (<A HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>) |
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| 90 | </TD></TR></TABLE> |
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| 91 | |
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| 92 | </BODY> |
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| 93 | </HTML> |
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