An optimal generalization of the centerpoint theorem, and its extensions

Nabil Mustafa, Saurabh Ray

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

Abstract

We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the plane, there exist two points (not necessarily among input points) that hit allconvex objects containingmore than 4n/7 points of P. We further prove that this bound is tight. We get this bound as part of a more general procedure forfinding small number of points hitting convex sets over P, yieldingseveral improvements over previous results.

Original languageEnglish (US)
Title of host publicationProceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07
Pages138-141
Number of pages4
DOIs
StatePublished - Oct 22 2007
Event23rd Annual Symposium on Computational Geometry, SCG'07 - Gyeongju, Korea, Republic of
Duration: Jun 6 2007Jun 8 2007

Other

Other23rd Annual Symposium on Computational Geometry, SCG'07
CountryKorea, Republic of
CityGyeongju
Period6/6/076/8/07

Fingerprint

Theorem
Hitting Set
Hits
Convex Sets
Generalization
Object

Keywords

  • Centerpoint theorem
  • Combinatorial geometry
  • Discrete geometry
  • Extremal methods
  • Hitting convex sets
  • Weak -nets

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Mustafa, N., & Ray, S. (2007). An optimal generalization of the centerpoint theorem, and its extensions. In Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07 (pp. 138-141) https://doi.org/10.1145/1247069.1247097

An optimal generalization of the centerpoint theorem, and its extensions. / Mustafa, Nabil; Ray, Saurabh.

Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07. 2007. p. 138-141.

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

Mustafa, N & Ray, S 2007, An optimal generalization of the centerpoint theorem, and its extensions. in Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07. pp. 138-141, 23rd Annual Symposium on Computational Geometry, SCG'07, Gyeongju, Korea, Republic of, 6/6/07. https://doi.org/10.1145/1247069.1247097
Mustafa N, Ray S. An optimal generalization of the centerpoint theorem, and its extensions. In Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07. 2007. p. 138-141 https://doi.org/10.1145/1247069.1247097
Mustafa, Nabil ; Ray, Saurabh. / An optimal generalization of the centerpoint theorem, and its extensions. Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07. 2007. pp. 138-141
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