shortestpath.html
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<TITLE>shortest path</TITLE>
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possibly with links to more information and implementations.">
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<H1>shortest path</H1>
<P>
(classic problem)
<P>
<strong>Definition:</strong>
The problem of finding the shortest <a href="path.html" tppabs="http://hissa.nist.gov/dads/HTML/path.html"><em>path</em></a> from one <a href="vertex.html" tppabs="http://hissa.nist.gov/dads/HTML/vertex.html"><em>vertex</em></a> in a <a href="graph.html" tppabs="http://hissa.nist.gov/dads/HTML/graph.html"><em>graph</em></a> to another vertex. "Shortest" may be least number of <a href="edge.html" tppabs="http://hissa.nist.gov/dads/HTML/edge.html"><em>edges</em></a>, least total weight, etc.
<P><strong>See also</strong>
<a href="dijkstraalgo.html" tppabs="http://hissa.nist.gov/dads/HTML/dijkstraalgo.html"><em>Dijkstra's algorithm</em></a>, <a href="bellmanford.html" tppabs="http://hissa.nist.gov/dads/HTML/bellmanford.html"><em>Bellman-Ford algorithm</em></a>, <a href="allpairsshrt.html" tppabs="http://hissa.nist.gov/dads/HTML/allpairsshrt.html"><em>all pairs shortest path</em></a>.
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>
<H2>Implementation</H2>
<A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.sunysb.edu/%7Ealgorith/files/shortest-path.shtml \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.sunysb.edu/%7Ealgorith/files/shortest-path.shtml'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.sunysb.edu/%7Ealgorith/files/shortest-path.shtml">(C, C++, Pascal, Fortran, and Mathematica)</A>
<H2>More information</H2>
OR-Notes on network flow, including <A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://mscmga.ms.ic.ac.uk/jeb/or/netflow.html \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://mscmga.ms.ic.ac.uk/jeb/or/netflow.html'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://mscmga.ms.ic.ac.uk/jeb/or/netflow.html">shortest path</A>.
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<a href="javascript:if(confirm('http://hissa.nist.gov/~black/black.html \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://hissa.nist.gov/~black/black.html'" tppabs="http://hissa.nist.gov/~black/black.html">Paul E. Black</a>
(<a href="mailto:paul.black@nist.gov">paul.black@nist.gov</a>).
<p>
Entry modified Thu Jul 1 08:58:49 1999.<BR>
HTML page formatted Wed Dec 22 09:36:29 1999.
<P>
This page's URL is
<A href="shortestpath.html" tppabs="http://hissa.nist.gov/dads/HTML/shortestpath.html">http://hissa.nist.gov/dads/HTML/shortestpath.html</A>
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