Improved Bounds for Geometric Permutations

Details Improved Bounds for Geometric Permutations Improved Bounds for Geometric Permutations

2010-07-19

arxiv.org/abs/1007.3244v1

Computer Science

Computational Geometry

A preliminary version accepted to FOCS 2010

Scientific paper

We show that the number of geometric permutations of an arbitrary collection
of $n$ pairwise disjoint convex sets in $\mathbb{R}^d$, for $d\geq 3$, is
$O(n^{2d-3}\log n)$, improving Wenger's 20 years old bound of $O(n^{2d-2})$.

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