Improved bounds for geometric permutations

Natan Rubin; Haim Kaplan; Micha Sharir

doi:10.1109/FOCS.2010.41

Improved bounds for geometric permutations

Natan Rubin, Haim Kaplan, Micha Sharir

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We show that the number of geometric permutations of an arbitrary collection of n pairwise disjoint convex sets in double-struck R^d, for d ≥ 3, is O(n^2d-3 log n), improving Wenger's 20 years old bound of O(n^2d-2).

Original language	English
Title of host publication	Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
Publisher	Institute of Electrical and Electronics Engineers
Pages	355-364
Number of pages	10
ISBN (Print)	9780769542447
DOIs	https://doi.org/10.1109/FOCS.2010.41
State	Published - 1 Jan 2010
Externally published	Yes
Event	2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 - Las Vegas, United States Duration: 23 Oct 2010 → 26 Oct 2010

Publication series

Name	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)	0272-5428

Conference

Conference	2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
Country/Territory	United States
City	Las Vegas
Period	23/10/10 → 26/10/10

Keywords

Arrangements
Convex sets
Geometric permutations
Line transversals

ASJC Scopus subject areas

General Computer Science

Access to Document

10.1109/FOCS.2010.41

Cite this

Rubin, N., Kaplan, H., & Sharir, M. (2010). Improved bounds for geometric permutations. In Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 (pp. 355-364). Article 5671203 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/FOCS.2010.41

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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 double-struck Rd, for d ≥ 3, is O(n2d-3 log n), improving Wenger's 20 years old bound of O(n2d-2).",

keywords = "Arrangements, Convex sets, Geometric permutations, Line transversals",

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

year = "2010",

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doi = "10.1109/FOCS.2010.41",

language = "English",

isbn = "9780769542447",

series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",

publisher = "Institute of Electrical and Electronics Engineers",

pages = "355--364",

booktitle = "Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010",

address = "United States",

note = "2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 ; Conference date: 23-10-2010 Through 26-10-2010",

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Rubin, N, Kaplan, H & Sharir, M 2010, Improved bounds for geometric permutations. in Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010., 5671203, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, Institute of Electrical and Electronics Engineers, pp. 355-364, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010, Las Vegas, United States, 23/10/10. https://doi.org/10.1109/FOCS.2010.41

Improved bounds for geometric permutations. / Rubin, Natan; Kaplan, Haim; Sharir, Micha.
Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010. Institute of Electrical and Electronics Engineers, 2010. p. 355-364 5671203 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Kaplan, Haim

AU - Sharir, Micha

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N2 - We show that the number of geometric permutations of an arbitrary collection of n pairwise disjoint convex sets in double-struck Rd, for d ≥ 3, is O(n2d-3 log n), improving Wenger's 20 years old bound of O(n2d-2).

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

KW - Arrangements

KW - Convex sets

KW - Geometric permutations

KW - Line transversals

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DO - 10.1109/FOCS.2010.41

M3 - Conference contribution

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BT - Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010

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ER -

Improved bounds for geometric permutations

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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