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arXiv · 1410.3154

Epsilon-Nets for Halfspaces Revisited

Sariel Har-Peled·Haim Kaplan·Micha Sharir·Shakhar Smorodinsky
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Abstract

Given a set $P$ of $n$ points in $\mathbb{R}^3$, we show that, for any $\varepsilon >0$, there exists an $\varepsilon$-net of $P$ for halfspace ranges, of size $O(1/\varepsilon)$. We give five proofs of this result, which are arguably simpler than previous proofs \cite{msw-hnlls-90, cv-iaags-07, pr-nepen-08}. We also consider several related variants of this result, including the case of points and pseudo-disks in the plane.

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Sariel Har-Peled, Haim Kaplan, Micha Sharir, Shakhar Smorodinsky. 2014-10-12. Epsilon-Nets for Halfspaces Revisited. https://arxiv.org/abs/1410.3154

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