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New constructions of SSPDs and their applications

Abam, M. A ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.comgeo.2011.12.003
  3. Publisher: 2012
  4. Abstract:
  5. We present a new optimal construction of a semi-separated pair decomposition (i.e., SSPD) for a set of n points in Rd. 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( log2n) that has a separator of size O(n1 -1/d)
  6. Keywords:
  7. Separated pair decomposition ; Doubling dimensions ; Geometric spanner ; Maximum degree ; Optimal construction ; Optimization ; Separators ; Separation
  8. Source: Computational Geometry: Theory and Applications ; Volume 45, Issue 5-6 , 2012 , Pages 200-214 ; 09257721 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0925772111000976