Improved Bounds for Geometric Permutations

Natan Rubin, Haim Kaplan, Micha Sharir

Abstract: 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-year-old bound of $O(n^{2d-2})$.