Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Approximating extent measures of points
Journal of the ACM (JACM)
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Discrete & Computational Geometry - Special Issue: 24th Annual Symposium on Computational Geometry
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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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+@e~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(dlogn) expected amortized time per insertion/deletion.