Journey to the center of the point set

Sariel Har-Peled, Mitchell Jones

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

Abstract

We revisit an algorithm of Clarkson et al. [1], that computes (roughly) a 1/(4d2)-centerpoint in Õ(d9) time, for a point set in ℝd, where Õ hides polylogarithmic terms. We present an improved algorithm that computes (roughly) a 1/d2-centerpoint with running time Õ(d7). While the improvements are (arguably) mild, it is the first progress on this well known problem in over twenty years. The new algorithm is simpler, and the running time bound follows by a simple random walk argument, which we believe to be of independent interest. We also present several new applications of the improved centerpoint algorithm.

Original languageEnglish (US)
Title of host publication35th International Symposium on Computational Geometry, SoCG 2019
EditorsGill Barequet, Yusu Wang
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771047
DOIs
StatePublished - Jun 1 2019
Event35th International Symposium on Computational Geometry, SoCG 2019 - Portland, United States
Duration: Jun 18 2019Jun 21 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume129
ISSN (Print)1868-8969

Conference

Conference35th International Symposium on Computational Geometry, SoCG 2019
CountryUnited States
CityPortland
Period6/18/196/21/19

Keywords

  • Centerpoints
  • Computational geometry
  • Random walks

ASJC Scopus subject areas

  • Software

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  • Cite this

    Har-Peled, S., & Jones, M. (2019). Journey to the center of the point set. In G. Barequet, & Y. Wang (Eds.), 35th International Symposium on Computational Geometry, SoCG 2019 [41] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 129). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SoCG.2019.41