Streaming and dynamic algorithms for minimum enclosing balls in high dimensions

Timothy M. Chan, Vinayak Pathak

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 logn) expected amortized time per insertion/deletion.

Original languageEnglish (US)
Title of host publicationAlgorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings
Pages195-206
Number of pages12
DOIs
StatePublished - Sep 1 2011
Externally publishedYes
Event12th International Symposium on Algorithms and Data Structures, WADS 2011 - New York, NY, United States
Duration: Aug 15 2011Aug 17 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6844 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other12th International Symposium on Algorithms and Data Structures, WADS 2011
CountryUnited States
CityNew York, NY
Period8/15/118/17/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Chan, T. M., & Pathak, V. (2011). Streaming and dynamic algorithms for minimum enclosing balls in high dimensions. In Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings (pp. 195-206). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6844 LNCS). https://doi.org/10.1007/978-3-642-22300-6_17