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Sharp Bounds on Geometric Permutations of Pairwise Disjoint Balls in R d (2000)

Smorodinsky, S. ; Mitchell, J. S. B. ; Sharir, M.

Springer

Discrete & computational geometry 23 (2000), S. 247-259

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ISSN: 1432-0444

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract. 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 Θ (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].

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/PL00009498

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