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Streaming and Dynamic Algorithms for Minimum Enclosing Balls in High Dimensions

  • Timothy M. Chan
  • Vinayak Pathak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)

Abstract

At SODA’10, Agarwal and Sharathkumar presented a streaming algorithm for approximating the minimum enclosing ball of a set of points in d-dimensional Euclidean space. Their algorithm requires one pass, uses O(d) space, and was shown to have approximation factor at most \((1+\sqrt{3})/2 +\varepsilon \approx 1.3661\). We prove that the same algorithm has approximation factor less than 1.22, which brings us much closer to a \((1+\sqrt{2})/2 \approx 1.207\) lower bound given by Agarwal and Sharathkumar.

We also apply this technique to the dynamic version of the minimum enclosing ball problem (in the non-streaming setting). We give an O(dn)-space data structure that can maintain a 1.22-approximate minimum enclosing ball in O(d logn) expected amortized time per insertion/deletion.

Keywords

Anchor Point Priority Queue Approximation Factor Dynamic Algorithm Quadratic Inequality 
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 2011

Authors and Affiliations

  • Timothy M. Chan
    • 1
  • Vinayak Pathak
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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