Sharp bounds on geometric permutations of pairwise disjoint balls in R d
Shakhar Smorodinsky, Joseph S. B. Mitchell, Micha Sharir · 1999
We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in IRd, is O(nd-l).This improves substantially the upper bound of O(n2d-2) 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].