Planar point sets determine many pairwise crossing segments

János Pach, Natan Rubin, G. Tardos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish
Title of host publicationSTOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
EditorsMoses Charikar, Edith Cohen
PublisherAssociation for Computing Machinery
Pages1158-1166
Number of pages9
ISBN (Electronic)9781450367059
DOIs
Publication statusPublished - Jun 23 2019
Event51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States
Duration: Jun 23 2019Jun 26 2019

Publication series

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

Conference

Conference51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
CountryUnited States
CityPhoenix
Period6/23/196/26/19

Keywords

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

ASJC Scopus subject areas

  • Software

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

Planar point sets determine many pairwise crossing segments. / Pach, János; Rubin, Natan; Tardos, G.

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 proceedingConference contribution

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, 6/23/19. https://doi.org/10.1145/3313276.3316328
Pach J, Rubin N, Tardos G. Planar point sets determine many pairwise crossing segments. In Charikar M, Cohen E, editors, STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery. 2019. p. 1158-1166. (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/3313276.3316328
Pach, János ; Rubin, Natan ; Tardos, G. / Planar point sets determine many pairwise crossing segments. STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. editor / Moses Charikar ; Edith Cohen. Association for Computing Machinery, 2019. pp. 1158-1166 (Proceedings of the Annual ACM Symposium on Theory of Computing).
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