Sharp bounds on geometric permutations of pairwise disjoint balls in Rd

Shakhar Smorodinsky, Joseph S. B. Mitchell, Micha Sharir
1999 Proceedings of the fifteenth annual symposium on Computational geometry - SCG '99  
We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in R d , is (n d−1 ). This improves substantially the upper bound of O(n 2d−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 disks in the plane is two, improving the previous upper bound of three given in [5] .
doi:10.1145/304893.304994 dblp:conf/compgeom/SmorodinskyMS99 fatcat:3z6ibi7p6zdqve5srhmqxeh7ye