ceph/src/boost/libs/graph/doc/bandwidth.html

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   9 <Head>
  10 <Title>Boost Graph Library: Bandwidth</Title>
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  18 <H1><A NAME="sec:bandwidth">
  19 <TT>bandwidth</TT>
  20 </H1>
  21
  22 <pre>
  23   (1)
  24   template &lt;typename Graph&gt;
  25   typename graph_traits&lt;Graph&gt;::vertices_size_type
  26   bandwidth(const Graph& g)
  27
  28   (2)
  29   template &lt;typename Graph, typename VertexIndexMap&gt;
  30   typename graph_traits&lt;Graph&gt;::vertices_size_type
  31   bandwidth(const Graph& g, VertexIndexMap index_map)
  32 </pre>
  33
  34 The <b><i>bandwidth</i></b> of a 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 a 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]|&nbsp;&nbsp;| (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 &lt;typename Graph&gt;
  58   typename graph_traits&lt;Graph&gt;::vertices_size_type
  59   ith_bandwidth(typename graph_traits&lt;Graph&gt;::vertex_descriptor i,
  60                 const Graph&amp; g)
  61
  62   (2)
  63   template &lt;typename Graph, typename VertexIndexMap&gt;
  64   typename graph_traits&lt;Graph&gt;::vertices_size_type
  65   ith_bandwidth(typename graph_traits&lt;Graph&gt;::vertex_descriptor i,
  66                 const Graph&amp; 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]|&nbsp;&nbsp;| (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) &nbsp;&nbsp;| 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 &copy; 2000-2001</TD><TD>
  89 <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>)
  90 </TD></TR></TABLE>
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