A tight bound on the number of geometric permutations of convex fat objects in ℝd

M. J. Katz; K. R. Varadarajan

doi:10.1007/s00454-001-0044-9

A tight bound on the number of geometric permutations of convex fat objects in ℝ^d

M. J. Katz, K. R. Varadarajan

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We show that the maximum number of geometric permutations of a set of n pairwise-disjoint convex and fat objects in ℝ^d is O(n^d-1). This generalizes the bound of Θ (n^d-1) obtained by Smorodinsky et al. [5] on the number of geometric permutations of n pairwise-disjoint balls.

Original language	English
Pages (from-to)	543-548
Number of pages	6
Journal	Discrete and Computational Geometry
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/s00454-001-0044-9
State	Published - 1 Jan 2001

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-001-0044-9

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abstract = "We show that the maximum number of geometric permutations of a set of n pairwise-disjoint convex and fat objects in ℝd is O(nd-1). This generalizes the bound of Θ (nd-1) obtained by Smorodinsky et al. [5] on the number of geometric permutations of n pairwise-disjoint balls.",

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N2 - We show that the maximum number of geometric permutations of a set of n pairwise-disjoint convex and fat objects in ℝd is O(nd-1). This generalizes the bound of Θ (nd-1) obtained by Smorodinsky et al. [5] on the number of geometric permutations of n pairwise-disjoint balls.

AB - We show that the maximum number of geometric permutations of a set of n pairwise-disjoint convex and fat objects in ℝd is O(nd-1). This generalizes the bound of Θ (nd-1) obtained by Smorodinsky et al. [5] on the number of geometric permutations of n pairwise-disjoint balls.

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A tight bound on the number of geometric permutations of convex fat objects in ℝ^d

Abstract

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