Kavitha, Telikepalli (2007) Faster algorithms for allpairs small stretch distances in weighted graphs. In: Proceedings of Foundations of Software Software Technology and Theoretical Computer Science FSTTCS 2007.

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Abstract
Abstract. Let G = (V,E) be a weighted undirected graph, with nonnegative edge weights. We consider the problem of efficiently computing approximate distances between all pairs of vertices in G. While many efficient algorithms are known for this problem in unweighted graphs, not many results are known for this problem in weighted graphs. Zwick [14] showed that for any fixed ε> 0, stretch 1 1 + ε distances between all pairs of vertices in a weighted directed graph on n vertices can be computed in Õ(n ω) time, where ω < 2.376 is the exponent of matrix multiplication and n is the number of vertices. It is known that finding distances of stretch less than 2 between all pairs of vertices in G is at least as hard as Boolean matrix multiplication of two n×n matrices. It is also known that allpairs stretch 3 distances can be computed in Õ(n 2) time and allpairs stretch 7/3 distances can be computed in Õ(n 7/3) time. Here we consider efficient algorithms for the problem of computing allpairs stretch (2+ε) distances in G, for any 0 < ε < 1. We show that all pairs stretch (2 + ε) distances for any fixed ε> 0 in G can be computed in expected time O(n 9/4 logn). This algorithm uses a fast rectangular matrix multiplication subroutine. We also present a combinatorial algorithm (that is, it does not use fast matrix multiplication) with expected running time O(n 9/4) for computing allpairs stretch 5/2 distances in G. 1
Item Type:  Conference Paper 

Department/Centre:  Division of Electrical Sciences > Computer Science & Automation 
Date Deposited:  18 Oct 2011 05:26 
Last Modified:  18 Oct 2011 05:26 
URI:  http://eprints.iisc.ac.in/id/eprint/41497 
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