405 research outputs found
An Improved Bound for Weak Epsilon-Nets in the Plane
We show that for any finite set of points in the plane and
there exist
points in , for arbitrary small , that pierce every
convex set with . This is the first improvement
of the bound of that was
obtained in 1992 by Alon, B\'{a}r\'{a}ny, F\"{u}redi and Kleitman for general
point sets in the plane.Comment: A preliminary version to appear in the proceedings of FOCS 201
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