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<H1>traveling salesman</H1>
<P>
(classic problem)

<P>
<strong>Definition:</strong>
Find a <a href="path.html" tppabs="http://hissa.nist.gov/dads/HTML/path.html"><em>path</em></a> through a <a href="weightgraph.html" tppabs="http://hissa.nist.gov/dads/HTML/weightgraph.html"><em>weighted graph</em></a> which starts and ends at the same <a href="vertex.html" tppabs="http://hissa.nist.gov/dads/HTML/vertex.html"><em>vertex</em></a>, includes every other vertex exactly once, and minimizes the total cost of <a href="edge.html" tppabs="http://hissa.nist.gov/dads/HTML/edge.html"><em>edges</em></a>.
<P><strong>See also</strong>
<a href="btltravsale.html" tppabs="http://hissa.nist.gov/dads/HTML/btltravsale.html"><em>bottleneck traveling salesman</em></a>, <a href="eulercycle.html" tppabs="http://hissa.nist.gov/dads/HTML/eulercycle.html"><em>Euler cycle</em></a>.
<P><em>Note:
Less formally, find a path for a salesman to visit every listed city at the lowest total cost. <P> The above described path is called a <a href="hamilcyc.html" tppabs="http://hissa.nist.gov/dads/HTML/hamilcyc.html"><em>Hamiltonian cycle</em></a> or <em>tour</em>, however a hamiltonian cycle need not be optimal.  The above is the <em>optimization</em> form of the problem.  The <em>decision</em> form asks if there is a tour with a cost less than some given amount. See [CLR, page 969].</em>
<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/traveling-salesman.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/traveling-salesman.shtml'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.sunysb.edu/%7Ealgorith/files/traveling-salesman.shtml">(C, Fortran, Pascal, Mathematica, and C++)</A>

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&nbsp;(<a href="mailto:paul.black@nist.gov">paul.black@nist.gov</a>).

<p>
Entry modified Thu Apr  1 10:45:52 1999.<BR>
HTML page formatted Wed Dec 22 09:36:45 1999.

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This page's URL is
<A href="travelsales.html" tppabs="http://hissa.nist.gov/dads/HTML/travelsales.html">http://hissa.nist.gov/dads/HTML/travelsales.html</A>

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