Streaming algorithms for extent problems in high dimensions


Journal Article

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 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. Copyright © by SIAM.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Sharathkumar, R

Published Date

  • January 1, 2010

Published In

  • Proceedings of the Annual Acm Siam Symposium on Discrete Algorithms

Start / End Page

  • 1481 - 1489

Digital Object Identifier (DOI)

  • 10.1137/1.9781611973075.120

Citation Source

  • Scopus