New constructions of SSPDs and their applications

Authors:
Mohammad A. Abam;Sariel Har-Peled
Affiliations:
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran;Department of Computer Science, University of Illinois, 201 N. Goodwin Avenue, Urbana, IL 61801, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2012

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Abstract

We present a new optimal construction of a semi-separated pair decomposition (i.e., SSPD) for a set of n points in R^d. 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 t1, we present a new construction of a t-spanner with O(n) edges and maximum degree O(log^2n) that has a separator of size O(n^1^-^1^/^d).