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