trianglnqlty.html

来自「数据结构词典（英文）」· HTML 代码 · 共 46 行

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<TITLE>triangle inequality</TITLE>
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  content="Definition of triangle inequality,
	possibly with links to more information and implementations.">
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<H1>triangle inequality</H1>
<P>
(definition)

<P>
<strong>Definition:</strong>
The property that a <a href="#complete"><em>complete</em></a> <a href="weightgraph.html" tppabs="http://hissa.nist.gov/dads/HTML/weightgraph.html"><em>weighted graph</em></a> satisfies  weight(u,v)  <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7  width=14 alt="less than or equal to">  weight(u,w) + weight(w,v) for all <a href="vertex.html" tppabs="http://hissa.nist.gov/dads/HTML/vertex.html"><em>vertices</em></a> u, v, w.  Informally, the graph has no short cuts.
<P><em>Note:
This holds for any graph representing points in a metric space.  Many problems involving edge-weighted graphs have better approximation algorithms if the problem is restricted to weights satisfying the triangle inequality. From Algorithms and Theory of Computation Handbook, page 34-17, Copyright &copy; 1999 by CRC Press LLC.</em>
<P>Author: <a href="terms.html#authorCRC-A" tppabs="http://hissa.nist.gov/dads/terms.html#authorCRC-A">CRC-A</a>

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<p>
Entry modified Thu Jun 17 09:56:40 1999.<BR>
HTML page formatted Wed Dec 22 09:36:46 1999.

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