TY - GEN

T1 - Streaming and dynamic algorithms for minimum enclosing balls in high dimensions

AU - Chan, Timothy M.

AU - Pathak, Vinayak

PY - 2011

Y1 - 2011

N2 - 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 logn) expected amortized time per insertion/deletion.

AB - 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 logn) expected amortized time per insertion/deletion.

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U2 - 10.1007/978-3-642-22300-6_17

DO - 10.1007/978-3-642-22300-6_17

M3 - Conference contribution

AN - SCOPUS:80052118924

SN - 9783642222993

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 195

EP - 206

BT - Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings

T2 - 12th International Symposium on Algorithms and Data Structures, WADS 2011

Y2 - 15 August 2011 through 17 August 2011

ER -