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Algorithmica

, Volume 60, Issue 1, pp 46–59 | Cite as

An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions

  • Hamid Zarrabi-Zadeh
Article

Abstract

We present a new streaming algorithm for maintaining an ε-kernel of a point set in ℝ d using O((1/ε (d−1)/2)log (1/ε)) space. The space used by our algorithm is optimal up to a small logarithmic factor. This significantly improves (for any fixed dimension d 3) the best previous algorithm for this problem that uses O(1/ε d−(3/2)) space, presented by Agarwal and Yu. Our algorithm immediately improves the space complexity of the previous streaming algorithms for a number of fundamental geometric optimization problems in fixed dimensions, including width, minimum-volume bounding box, minimum-radius enclosing cylinder, minimum-width enclosing annulus, etc.

Keywords

Approximation algorithms Data streams Geometric optimization problems Coresets 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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