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Title:
An Application of the Universality Theorem for Tverberg Partitions
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Abstract:
We show that, as a consequence of a remarkable new result of
Attila P\'or on universal Tverberg partitions, any large-enough set
$P$ of points in $\Re^d$ has a $(d+2)$-sized subset whose Radon point
has half-space depth at least $c_d \cdot |P|$, where $c_d \in (0, 1)$
depends only on $d$. We then give an application of this result to
computing weak $\eps$-nets by random sampling. Joint work with Nabil
Mustafa.
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