Planar point sets determine many pairwise crossing segments

János Pach; Natan Rubin; Gábor Tardos

doi:10.1145/3313276.3316328

Planar point sets determine many pairwise crossing segments

János Pach, Natan Rubin, Gábor Tardos

Department of Computer Science

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

6 Scopus citations

Abstract

We show that any set of n points in general position in the plane determines n¹−o(1⁾ pairwise crossing segments. The best previously known lower bound, Ω n, was proved more than 25 years ago by Aronov, Erdős, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.

Original language	English
Title of host publication	STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
Editors	Moses Charikar, Edith Cohen
Publisher	Association for Computing Machinery
Pages	1158-1166
Number of pages	9
ISBN (Electronic)	9781450367059
DOIs	https://doi.org/10.1145/3313276.3316328
State	Published - 23 Jun 2019
Event	51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States Duration: 23 Jun 2019 → 26 Jun 2019

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Conference

Conference	51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
Country/Territory	United States
City	Phoenix
Period	23/06/19 → 26/06/19

Keywords

Avoiding edges
Comparability graphs
Computational geometry
Crossing edges
Extremal combinatorics
Geometric graphs
Intersection graphs
Partial orders

ASJC Scopus subject areas

Software

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10.1145/3313276.3316328

Cite this

Pach, J., Rubin, N., & Tardos, G. (2019). Planar point sets determine many pairwise crossing segments. In M. Charikar, & E. Cohen (Eds.), STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (pp. 1158-1166). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3313276.3316328

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title = "Planar point sets determine many pairwise crossing segments",

abstract = "We show that any set of n points in general position in the plane determines n1−o(1) pairwise crossing segments. The best previously known lower bound, Ω n, was proved more than 25 years ago by Aronov, Erd{\H o}s, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.",

keywords = "Avoiding edges, Comparability graphs, Computational geometry, Crossing edges, Extremal combinatorics, Geometric graphs, Intersection graphs, Partial orders",

author = "J{\'a}nos Pach and Natan Rubin and G{\'a}bor Tardos",

note = "Publisher Copyright: {\textcopyright} 2019 Association for Computing Machinery.; 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 ; Conference date: 23-06-2019 Through 26-06-2019",

year = "2019",

month = jun,

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doi = "10.1145/3313276.3316328",

language = "English",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

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editor = "Moses Charikar and Edith Cohen",

booktitle = "STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing",

}

Pach, J, Rubin, N & Tardos, G 2019, Planar point sets determine many pairwise crossing segments. in M Charikar & E Cohen (eds), STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 1158-1166, 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019, Phoenix, United States, 23/06/19. https://doi.org/10.1145/3313276.3316328

Planar point sets determine many pairwise crossing segments. / Pach, János; Rubin, Natan; Tardos, Gábor.
STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. ed. / Moses Charikar; Edith Cohen. Association for Computing Machinery, 2019. p. 1158-1166 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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

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AU - Rubin, Natan

AU - Tardos, Gábor

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N2 - We show that any set of n points in general position in the plane determines n1−o(1) pairwise crossing segments. The best previously known lower bound, Ω n, was proved more than 25 years ago by Aronov, Erdős, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.

AB - We show that any set of n points in general position in the plane determines n1−o(1) pairwise crossing segments. The best previously known lower bound, Ω n, was proved more than 25 years ago by Aronov, Erdős, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.

KW - Avoiding edges

KW - Comparability graphs

KW - Computational geometry

KW - Crossing edges

KW - Extremal combinatorics

KW - Geometric graphs

KW - Intersection graphs

KW - Partial orders

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M3 - Conference contribution

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BT - STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

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ER -

Planar point sets determine many pairwise crossing segments

Abstract

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Keywords

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Access to Document

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