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COMPGEOM
2007
ACM

An optimal generalization of the centerpoint theorem, and its extensions

9 years 3 months ago
An optimal generalization of the centerpoint theorem, and its extensions
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 all convex objects containing more 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 for finding small number of points hitting convex sets over P, yielding several improvements over previous results. Categories and Subject Descriptors G.2 [Combinatorics]: Discrete Geometry General Terms Algorithms, Theory Keywords Combinatorial geometry, weak -nets, centerpoint theorem, discrete geometry, extremal methods, hitting convex sets
Saurabh Ray, Nabil H. Mustafa
Added 14 Aug 2010
Updated 14 Aug 2010
Type Conference
Year 2007
Where COMPGEOM
Authors Saurabh Ray, Nabil H. Mustafa
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