Streaming and dynamic algorithms for minimum enclosing balls in high dimensions

Authors:
Timothy M. Chan;Vinayak Pathak
Affiliations:
School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada;School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

Citing 10
Cited 1

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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 +√3)/2 + ε ≈ 1.3661. We prove that the same algorithm has approximation factor less than 1.22, which brings us much closer to a (1 +√2)/2 ≈ 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 log n) expected amortized time per insertion/deletion.