Improved bounds for geometric permutations

Natan Rubin; Haim Kaplan; Micha Sharir

doi:10.1137/110835918

Improved bounds for geometric permutations

Natan Rubin, Haim Kaplan, Micha Sharir

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

5 Scopus citations

Abstract

We show that the number of geometric permutations of an arbitrary collection of n pairwise disjoint convex sets in Rd, for d = 3, is O(n2d-3 log n), improving Wenger's 20-year-old bound of O(n2d-2).

Original language	English
Pages (from-to)	367-390
Number of pages	24
Journal	SIAM Journal on Computing
Volume	41
Issue number	2
DOIs	https://doi.org/10.1137/110835918
State	Published - 4 Jun 2012
Externally published	Yes

Keywords

Combinatorial complexity
Convex sets
Geometric permutations
Line transversals
Lines in space

ASJC Scopus subject areas

General Computer Science
General Mathematics

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10.1137/110835918

Cite this

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title = "Improved bounds for geometric permutations",

abstract = "We show that the number of geometric permutations of an arbitrary collection of n pairwise disjoint convex sets in Rd, for d = 3, is O(n2d-3 log n), improving Wenger's 20-year-old bound of O(n2d-2).",

keywords = "Combinatorial complexity, Convex sets, Geometric permutations, Line transversals, Lines in space",

author = "Natan Rubin and Haim Kaplan and Micha Sharir",

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doi = "10.1137/110835918",

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AU - Kaplan, Haim

AU - Sharir, Micha

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AB - We show that the number of geometric permutations of an arbitrary collection of n pairwise disjoint convex sets in Rd, for d = 3, is O(n2d-3 log n), improving Wenger's 20-year-old bound of O(n2d-2).

KW - Combinatorial complexity

KW - Convex sets

KW - Geometric permutations

KW - Line transversals

KW - Lines in space

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Improved bounds for geometric permutations

Abstract

Keywords

ASJC Scopus subject areas

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