Geometric permutations of high dimensional spheres

Authors:
Yingping Huang;Jinhui Xu;Danny Z. Chen
Affiliations:
Dept. of Comp. Sci. & Eng., Univ. of Notre Dame, Notre Dame, IN;Dept. of Comp. Sci. & Eng., State Univ. of New York at Buffalo, 226 Bell Hall, Buffalo, NY;Dept. of Comp. Sci. & Eng., Univ. of Notre Dame, Notre Dame, IN
Venue:
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Year:
2001

Citing 3
Cited 6

The maximum number of ways to stab n convex nonintersecting sets in the plane is 2n - 2

Discrete & Computational Geometry
Permutations for convex sets

Discrete & Computational Geometry
The different ways of stabbing disjoint convex sets

Discrete & Computational Geometry

A tight bound on the number of geometric permutations of convex fat objects in {\huge $\mathbf{\reals^d}$}

SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Computational geometry column 41

ACM SIGACT News
Geometric permutations of higher dimensional spheres

Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
Geometric permutations of disjoint unit spheres

Computational Geometry: Theory and Applications
Geometric permutations of disjoint unit spheres

Computational Geometry: Theory and Applications
Improved Bounds for Geometric Permutations

SIAM Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove the maximum number of geometric permutations, induced by line transversals to a set of n pairwise disjoint congruent spheres in Rd with d ⪈ 3, is no more than 4 when n is sufficiently large, achieving the best known upper bound for this problem. We also prove the maximum number of geometric permutations of a set of n noncongruent spheres of bounded radius ratio in Rd, d ⪈ 3, is at most 2[√2M]+1, where M is the ratio or the largest radius and the smallest radius. Our result settles a conjecture in combinatorial geometry.