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<HTML><HEAD><TITLE>Boost Graph Library: Cuthill-Mckee Ordering</TITLE>
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<H1><A name=sec:bfs></a><tt>sloan_start_end_vertices</tt></H1>
<P>
<DIV align=left>
<TABLE cellPadding=3 border=1>
<TBODY>
<TR>
<TH align=left><B>Graphs:</B></TH>
<TD align=left>undirected</TD></TR>
<TR>
<TH align=left><B>Properties:</B></TH>
<TD align=left>color, degree</TD>
</TR>
<TR>
<TH align=left><B>Complexity:</B></TH>
<TD align=left> </TD>
</TR></TBODY></TABLE></DIV>
<PRE> (1)
template <class Graph, class ColorMap, class DegreeMap>
typename graph_traits<Graph>::vertex_descriptor
sloan_start_end_vertices(Graph& G,
typename graph_traits<Graph>::vertex_descriptor &s,
ColorMap color,
DegreeMap degree )
</PRE>
<p>The goal of the sloan_start_end_vertices algorithm[1, 2] is to find good start-
and end-vertices for the profile and wavefront reduction algorithm sloan_ordering.
The algorithm is similar to pseudo_peripheral_pair and also based on breadth_first_search.
With this breadth_first_search function a so-called rooted level structure (RLS)
is formed, where the vertices with the same distance to the starting vertex
are grouped together. The maximum number of vertices in one group is called
the width of the RLS. Sloan_start_end_vertices tries to find a pseudoperipheral
pair with a minimum RLS-width.</p>
<H3>Parameters</H3>
For version 1:
<UL>
<LI><TT>Graph& g</TT> (IN) <BR>
An undirected graph. The graph's type must be a model of <A
href="http://www.boost.org/libs/graph/doc/IncidenceGraph.html">IncidenceGraph</A>.
<LI><TT>vertex_descriptor s</TT> (IN) <BR>
The starting vertex.
<LI><TT>ColorMap color_map</TT> (WORK) <BR>
Used internally to keep track of the progress of the algorithm (to avoid visiting
the same vertex twice).
<LI><TT>DegreeMap degree_map</TT> (IN) <BR>
This must map vertices to their degree. </LI>
</UL>
<p> </p>
<H3>Example</H3>
See <A
href="http://www.boost.org/libs/graph/example/cuthill_mckee_ordering.cpp"><TT>example/sloan_ordering.cpp</TT></A>.
<H3>See Also</H3>
<p><a href="http://www.boost.org/libs/graph/doc/sloan_start_end_vertices.htm">sloan_start_end_vertices</a>,
<A
href="http://www.boost.org/libs/graph/doc/bandwidth.html">bandwidth</A>, <a href="http://www.boost.org/libs/graph/doc/profile.htm">profile</a>,
<a href="http://www.boost.org/libs/graph/doc/wavefront.htm">wavefront</a> and
<TT>degree_property_map</TT> in <TT>boost/graph/properties.hpp</TT>. </p>
<p>[1] S. W. Sloan, <i>An algorithm for profile and wavefront reduction of sparse
matrices</i>, Int. j. numer. methods eng., <b>23</b>, 239 - 251 (1986)</p>
<p>[2] S. W. Sloan, <i>A fortran program for profile and wavefront reduction</i>,
Int. j. numer. methods eng., <b>28</b>, 2651 - 2679 (1989)<BR>
</p>
<HR>
<TABLE width="663">
<TBODY>
<TR vAlign=top>
<TD noWrap>Copyright 2001-2002</TD>
<TD>Marc Wintermantel, ETH Zurich(<A
href="mailto:wintermantel@imes.mavt.ethz.ch">wintermantel@imes.mavt.ethz.ch</a>)
</TD>
</TR></TBODY></TABLE></BODY></HTML>
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