NIST

triangle inequality

(definition)

Definition: The property that a complete weighted graph satisfies weight(u,v) ≤ weight(u,w) + weight(w,v) for all vertices u, v, w. Informally, the graph has no short cuts.

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 © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.

Author: CRC-A


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Entry modified 17 December 2004.
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Cite this as:
Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "triangle inequality", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/trianglnqlty.html