再论半空间的ε-网
Epsilon-Nets for Halfspaces Revisited
摘要：
给定一组$P$的$n$点在$\mathbb{R}^3$，我们表明，对于任何$\varepsilon >0$，存在一个$\varepsilon$-网的$P$的半空间范围，大小为$O(1/\varepsilon)$。我们给出了这个结果的五个证明，可以说比以前的证明\cite{msw-hnlls-90, cv-iaags-07, pr-nepen-08}更简单。我们还考虑了这个结果的几个相关的变体，包括点和伪盘在平面上的情况。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
