An optimal extension of the centerpoint theorem

Nabil H. Mustafa; Saurabh Ray

doi:10.1016/j.comgeo.2007.10.004

An optimal extension of the centerpoint theorem

Nabil H. Mustafa, Saurabh Ray

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We prove an optimal extension 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 all convex sets containing more than 47n points of P. We further prove that this bound is tight. We get this bound as part of a more general procedure for finding small number of points hitting convex sets over P, yielding several improvements over previous results.

Original language	English (US)
Pages (from-to)	505-510
Number of pages	6
Journal	Computational Geometry: Theory and Applications
Volume	42
Issue number	6-7
DOIs	https://doi.org/10.1016/j.comgeo.2007.10.004
State	Published - Aug 2009

Keywords

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

ASJC Scopus subject areas

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.comgeo.2007.10.004

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AB - We prove an optimal extension 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 all convex sets containing more than 47n points of P. We further prove that this bound is tight. We get this bound as part of a more general procedure for finding small number of points hitting convex sets over P, yielding several improvements over previous results.

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KW - Combinatorial geometry

KW - Discrete geometry

KW - Extremal methods

KW - Hitting convex sets

KW - Weak -nets

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An optimal extension of the centerpoint theorem

Abstract

Keywords

ASJC Scopus subject areas

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