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<H1>NP-complete</H1>
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(definition)
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<strong>Definition:</strong>
The class of problems for which answers can be checked for correctness by an algorithm whose run time is <a href="polynomialtm.html" tppabs="http://hissa.nist.gov/dads/HTML/polynomialtm.html"><em>polynomial</em></a> in the size of the input (it is <a href="np.html" tppabs="http://hissa.nist.gov/dads/HTML/np.html"><em>NP</em></a>) and no other NP problem is more than a polynomial factor harder. Informally, a problem is NP-complete if answers can be verified quickly and a quick algorithm to solve this problem can be used to solve all other NP problems quickly.
<P><strong>See also</strong>
<a href="nphard.html" tppabs="http://hissa.nist.gov/dads/HTML/nphard.html"><em>NP-hard</em></a>, <a href="ap.html" tppabs="http://hissa.nist.gov/dads/HTML/ap.html"><em>AP</em></a>.
<P><em>Note:
A trivial example of NP, but not NP-complete is finding the <strong>AND</strong> of two boolean bits. The problem is NP, since one can quickly verify that the answer is correct, but knowing how to <strong>AND</strong> two bits doesn't help one quickly find, say, a <a href="hamilcyc.html" tppabs="http://hissa.nist.gov/dads/HTML/hamilcyc.html"><em>Hamiltonian cycle</em></a> or tour of a graph. So <strong>AND</strong> is not NP-complete.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>
<H2>More information</H2>
History, definitions, examples, etc. given in <A HREF="javascript:if(confirm('http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.unb.ca/%7Ealopez-o/comp-faq/faq.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://www.cs.unb.ca/%7Ealopez-o/comp-faq/faq.html'" tppabs="http://www.nist.gov/cgi-bin/exit_nist.cgi?url=http://www.cs.unb.ca/%7Ealopez-o/comp-faq/faq.html">Comp.Theory FAQ</A>, scroll down to <strong>P vs. NP</strong>.
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Entry modified Thu Oct 7 12:24:39 1999.<BR>
HTML page formatted Wed Dec 22 09:35:58 1999.
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