Faster core-set constructions and data stream algorithms in fixed dimensions

Research output: Contribution to conferencePaper

Abstract

We speed up previous (1 + ε)-factor approximation algorithms for a number of geometric optimization problems in fixed dimensions: diameter, width, minimum-radius enclosing cylinder, minimum-width annulus, minimum-volume bounding box, minimum-width cylindrical shell, etc. Linear time bounds were known before; we further improve the dependence of the "constants" in terms of ε. We next consider the data stream model and present new (1 + ε)-factor approximation algorithms that need only constant space for all of the above problems in any fixed dimension. Previously, such a result was known only for diameter. Both sets of results are obtained using the core-set framework recently proposed by Agarwal, Har-Peled, and Varadarajan.

Original languageEnglish (US)
Pages152-159
Number of pages8
StatePublished - Sep 29 2004
Externally publishedYes
EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
Duration: Jun 9 2004Jun 11 2004

Other

OtherProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
CountryUnited States
CityBrooklyn, NY
Period6/9/046/11/04

Keywords

  • Approximation algorithms
  • Data streams
  • Geometric optimization problems

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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  • Cite this

    Chan, T. M-Y. (2004). Faster core-set constructions and data stream algorithms in fixed dimensions. 152-159. Paper presented at Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04), Brooklyn, NY, United States.