Smaller core-sets for balls

We prove the existence of small core-sets for solving approximate k-center clustering and related problems. The size of these core-sets is considerably smaller than the previously known bounds, and imply faster algorithms; in particular, we get an algorithm needing O(dn/ + (1/ )5 ) time to compute an -approximate minimum enclosing ball (1-center) of n points in d dimensions. We also give a simple gradientdescent algorithm for computing the minimum enclosing ball in O(dn/ 2 ) time. This algorithm also implies slightly faster algorithms for computing approximately the smallest radius k-flat of a given set of points.

• Type: Conference
• Year: 2003
• Where: SODA
• Authors: Mihai Badoiu, Kenneth L. Clarkson
• Keywords: Algorithms, Approximate K-center Clustering, Faster Algorithms, Minimum Enclosing Ball, SODA 2003