An optimal extension of the centerpoint theorem

Authors:
Nabil H. Mustafa;Saurabh Ray
Affiliations:
Lahore University of Management Sciences, Pakistan;Universität des Saarlandes, Germany
Venue:
Computational Geometry: Theory and Applications
Year:
2009

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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.