An Improved Bound for Weak Epsilon-nets in the Plane
Author: 
Natan RubinAuthors Info & Claims
Natan RubinAuthors Info & ClaimsArticle No.: 32, Pages 1 - 35
Abstract
We show that for any finite point set P in the plane and ϵ > 0 there exist \(O(\tfrac{1}{{\epsilon }^{3/2+\gamma }})\) points in ℝ2, for arbitrary small γ > 0, that pierce every convex set K with |K∩ P|> ϵ |P|. This is the first improvement of the bound of \(O(\tfrac{1}{{\epsilon }^2})\) that was obtained in 1992 by Alon, Bárány, Füredi, and Kleitman for general point sets in the plane.
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- An Improved Bound for Weak Epsilon-nets in the Plane
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Published In
October 2022
420 pages
ISSN:0004-5411
EISSN:1557-735X
DOI:10.1145/3563903
- Editor:
- Venkatesan Guruswami
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Publication History
Published: 27 October 2022
Online AM: 10 August 2022
Accepted: 31 May 2022
Revised: 21 March 2022
Received: 02 January 2020
Published in JACM Volume 69, Issue 5
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