Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs

Baswana, Surender and Kavitha, Telikepalli (2010) Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs. In: SIAM Journal on Computing, 39 (7). pp. 2865-2896.

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Abstract

Let G - (V, E) be a weighted undirected graph having nonnegative edge weights. An estimate (delta) over cap (u, v) of the actual distance d( u, v) between u, v is an element of V is said to be of stretch t if and only if delta(u, v) <= (delta) over cap (u, v) <= t . delta(u, v). Computing all-pairs small stretch distances efficiently ( both in terms of time and space) is a well-studied problem in graph algorithms. We present a simple, novel, and generic scheme for all-pairs approximate shortest paths. Using this scheme and some new ideas and tools, we design faster algorithms for all-pairs t-stretch distances for a whole range of stretch t, and we also answer an open question posed by Thorup and Zwick in their seminal paper [J. ACM, 52 (2005), pp. 1-24].

Item Type:	Journal Article
Publication:	SIAM Journal on Computing
Publisher:	Society for Industrial and Applied Mathematics
Additional Information:	Copyright of this article belongs to Society for Industrial and Applied Mathematics.
Keywords:	Shortest path,distance,approximate distance,oracle, randomization.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	06 Sep 2010 11:28
Last Modified:	19 Sep 2010 06:15
URI:	http://eprints.iisc.ac.in/id/eprint/31965

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