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Algorithmica

, Volume 72, Issue 1, pp 83–98 | Cite as

Streaming Algorithms for Extent Problems in High Dimensions

  • Pankaj K. Agarwal
  • R. SharathkumarEmail author
Article

Abstract

We present (single-pass) streaming algorithms for maintaining extent measures of a stream S of n points in \(\mathbb{R} ^{d}\). 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 farthest-point 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.

Keywords

Streaming algorithms Computational geometry Extent problems Minimum enclosing ball Diameter 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.Department of Computer ScienceStanford UniversityStanfordUSA

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