New constructions of SSPDs and their applications

Authors:
Mohammad Ali Abam;Sariel Har-Peled
Affiliations:
Technische Universitat, Dortmund, Germany;UIUC, Urbana, IL, USA
Venue:
Proceedings of the twenty-sixth annual symposium on Computational geometry
Year:
2010

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Abstract

We present a new optimal construction of semi-separated pair decomposition (SSPD) for a set of n points in IRd. In the new construction each point participates in a few pairs, and it extends easily to spaces with low doubling dimension. This is the first optimal construction with these properties. As an application of the new construction, for a fixed t 1, we present a new construction of a t-spanner with O(n) edges and maximum degree O(log2 n) that has a separator of size O(n1-1/d).