Crossing families

Boris Aronov, Paul Erdos, Wayne Goddard, Daniel J. Kleitman, Michael Klugerman, János Pach, Leonard J. Schulman

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

    Abstract

    Given n points in the plane, a crossing family is a collection of line segments, each joining two of the points, suck that any two line segments intersect internally. We show that any n points in general position possess a crossing family of size at least √n/12, and describe an O(n logn)-time algorithm for finding one.

    Original languageEnglish (US)
    Title of host publicationProceedings of the Annual Symposium on Computational Geometry
    PublisherAssociation for Computing Machinery
    Pages351-356
    Number of pages6
    VolumePart F129851
    ISBN (Print)0897914260
    DOIs
    StatePublished - Jun 1 1991
    Event7th Annual Symposium on Computational Geometry, SCG 1991 - North Conway, United States
    Duration: Jun 10 1991Jun 12 1991

    Other

    Other7th Annual Symposium on Computational Geometry, SCG 1991
    CountryUnited States
    CityNorth Conway
    Period6/10/916/12/91

    Fingerprint

    Joining
    Line segment
    Intersect
    Family

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Computational Mathematics

    Cite this

    Aronov, B., Erdos, P., Goddard, W., Kleitman, D. J., Klugerman, M., Pach, J., & Schulman, L. J. (1991). Crossing families. In Proceedings of the Annual Symposium on Computational Geometry (Vol. Part F129851, pp. 351-356). Association for Computing Machinery. https://doi.org/10.1145/109648.109687

    Crossing families. / Aronov, Boris; Erdos, Paul; Goddard, Wayne; Kleitman, Daniel J.; Klugerman, Michael; Pach, János; Schulman, Leonard J.

    Proceedings of the Annual Symposium on Computational Geometry. Vol. Part F129851 Association for Computing Machinery, 1991. p. 351-356.

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

    Aronov, B, Erdos, P, Goddard, W, Kleitman, DJ, Klugerman, M, Pach, J & Schulman, LJ 1991, Crossing families. in Proceedings of the Annual Symposium on Computational Geometry. vol. Part F129851, Association for Computing Machinery, pp. 351-356, 7th Annual Symposium on Computational Geometry, SCG 1991, North Conway, United States, 6/10/91. https://doi.org/10.1145/109648.109687
    Aronov B, Erdos P, Goddard W, Kleitman DJ, Klugerman M, Pach J et al. Crossing families. In Proceedings of the Annual Symposium on Computational Geometry. Vol. Part F129851. Association for Computing Machinery. 1991. p. 351-356 https://doi.org/10.1145/109648.109687
    Aronov, Boris ; Erdos, Paul ; Goddard, Wayne ; Kleitman, Daniel J. ; Klugerman, Michael ; Pach, János ; Schulman, Leonard J. / Crossing families. Proceedings of the Annual Symposium on Computational Geometry. Vol. Part F129851 Association for Computing Machinery, 1991. pp. 351-356
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