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One-sided epsilon-approximants Bukh, Boris


Suppose $A$ and $P$ are sets in $\mathbb{R}^d$ such that every convex set containing α-fraction of points P contains at least $(\alpha -\epsilon)$-fraction of points of $A$, for every $\alpha$. In such a case, set $A$ is called a one-sided $\epsilon$-approximant to $P$. We show that every $P$ admits a one-sided $\epsilon$-approximant of size depending only on $\epsilon$ and on $d$. (Joint work with Gariel Nivasch.)

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