An optimal generalization of the centerpoint theorem, and its extensions

Authors:
Saurabh Ray;Nabil Mustafa
Affiliations:
Universitaet des Saarlandes, Saabruecken, Germany;Lahore University of Management Sciences, Lahore, Pakistan
Venue:
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Year:
2007

Citing 4
Cited 2

Improved bounds on weak &egr;-nets for convex sets

STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Separators for sphere-packings and nearest neighbor graphs

Journal of the ACM (JACM)
A 3-space partition and its applications

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
New Constructions of Weak ε-Nets

Discrete & Computational Geometry

Small weak epsilon-nets

Computational Geometry: Theory and Applications
Centerpoints and Tverberg's technique

Computational Geometry: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

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.