Streaming Algorithms for extent problems in high dimensions

We develop (single-pass) streaming algorithms for maintaining extent measures of a stream S of n points in Rd . We focus on designing streaming algorithms whose working space is polynomial in d (poly(d)) and sub-linear in n. For the problems of computing diameter, width and minimum enclosing ball of S, we obtain lower bounds on the worst-case approximation ratio of any streaming algorithm that uses poly(d) space. On the positive side, we introduce the notion of blurred ball cover and use it for answering approximate farthestpoint queries and maintaining approximate minimum enclosing ball and diameter of S. We describe a streaming algorithm for maintaining a blurred ball cover whose working space is linear in d and independent of n. Work on this paper is supported by NSF under grants CNS-05-40347, CFF-06-35000, and DEB-04-25465, by ARO grants W911NF-04-1-0278 and W911NF-07-1-0376, by an NIH grant 1P50-GM-08183-01, by a DOE grant OEG-P200A070505, and by a grant from the U.S.?Israel Bin...

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Pankaj K Agarwal, R. Sharathkumar
• Keywords: Blurred Ball Cover, Discrete Algorithms, Minimum Enclosing Ball, SODA 2010, Worst-case Approximation Ratio