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.
+ )-approximation algorithm for MEB; later, Chan and Pathak REF proved that the same algorithm has an approximation ratio less than 1.22.
Streaming and Dynamic Algorithms for Minimum Enclosing Balls in High Dimensions
Comput. Geom.
Comput. Geom.
Mathematics Computer Science