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

  • Hamid Zarrabi-Zadeh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5193)

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 substantially improves (for any fixed dimension \(d \geqslant 3\)) the best previous algorithm for this problem that uses O(1/ε d − (3/2)) space, presented by Agarwal and Yu at SoCG’07. Our algorithm immediately improves the space complexity of the best previous streaming algorithms for a number of fundamental geometric optimization problems in fixed dimensions, including width, minimum enclosing cylinder, minimum-width enclosing annulus, minimum-width enclosing cylindrical shell, etc.

Keywords

Cylindrical Shell Space Complexity Input Point Compression Step Maximum Span Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hamid Zarrabi-Zadeh
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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