Geometric permutations of balls with bounded size disparity

We study combinatorial bounds for geometric permutations of balls with bounded size disparity in d-space. Our main contribution is the following theorem: given a set S of n disjoint balls in Rd , if n is sufficiently large and the radius ratio between the largest and smallest balls of S is , then the maximum number of geometric permutations of S is O(log ). When d = 2, we are able to prove the tight bound of 2 on the number of geometric permutations for S, which is the

• Type: Conference
• Year: 2001
• Where: CCCG
• Authors: Yunhong Zhou, Subhash Suri
• Keywords: CCCG 2001, CCCG 2007, Combinatorial Bounds, Disjoint Balls, Geometric Permutations