Sharp Bounds on Geometric Permutations of Pairwise Disjoint Balls in R^d (1999)
by
Shakhar Smorodinsky
,
Joseph S. B. Mitchell
,
Micha Sharir
| Citations: | 13 - 2 self |
BibTeX
@MISC{Smorodinsky99sharpbounds,
author = {Shakhar Smorodinsky and Joseph S. B. Mitchell and Micha Sharir},
title = {Sharp Bounds on Geometric Permutations of Pairwise Disjoint Balls in R^d},
year = {1999}
}
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Abstract
We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in IR d , is \Theta(n d\Gamma1 ). This improves substantially the upper bound of O(n 2d\Gamma2 ) known for general convex sets [9]. We show that the maximum number of geometric permutations of a sufficiently large collection of pairwise disjoint unit discs in the plane is 2, improving the previous upper bound of 3 given in [5].
