@inproceedings{74e1fa0093a94574beadac45877ef956,
title = "An optimal generalization of the centerpoint theorem, and its extensions",
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.",
keywords = "Centerpoint theorem, Combinatorial geometry, Discrete geometry, Extremal methods, Hitting convex sets, Weak -nets",
author = "Nabil Mustafa and Saurabh Ray",
year = "2007",
month = oct,
day = "22",
doi = "10.1145/1247069.1247097",
language = "English",
isbn = "1595937056",
series = "Proceedings of the Annual Symposium on Computational Geometry",
pages = "138--141",
booktitle = "Proceedings of the Twenty-third Annual Symposium on Computational Geometry, SCG'07",
note = "23rd Annual Symposium on Computational Geometry, SCG'07 ; Conference date: 06-06-2007 Through 08-06-2007",
}