Points and triangles in the plane and halving planes in space

Boris Aronov, Leonidas J. Guibas, Bernard Chazelle, Micha Sharir, Herbert Edelsbrunner, Rephael Wenger

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

    Abstract

    We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.

    Original languageEnglish (US)
    Title of host publicationProc Sixth Annu Symp Comput Geom
    PublisherPubl by ACM
    Pages112-115
    Number of pages4
    ISBN (Print)0897913620
    StatePublished - 1990
    EventProceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA
    Duration: Jun 6 1990Jun 8 1990

    Other

    OtherProceedings of the Sixth Annual Symposium on Computational Geometry
    CityBerkeley, CA, USA
    Period6/6/906/8/90

    ASJC Scopus subject areas

    • Engineering(all)

    Cite this

    Aronov, B., Guibas, L. J., Chazelle, B., Sharir, M., Edelsbrunner, H., & Wenger, R. (1990). Points and triangles in the plane and halving planes in space. In Proc Sixth Annu Symp Comput Geom (pp. 112-115). Publ by ACM.

    Points and triangles in the plane and halving planes in space. / Aronov, Boris; Guibas, Leonidas J.; Chazelle, Bernard; Sharir, Micha; Edelsbrunner, Herbert; Wenger, Rephael.

    Proc Sixth Annu Symp Comput Geom. Publ by ACM, 1990. p. 112-115.

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

    Aronov, B, Guibas, LJ, Chazelle, B, Sharir, M, Edelsbrunner, H & Wenger, R 1990, Points and triangles in the plane and halving planes in space. in Proc Sixth Annu Symp Comput Geom. Publ by ACM, pp. 112-115, Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, CA, USA, 6/6/90.
    Aronov B, Guibas LJ, Chazelle B, Sharir M, Edelsbrunner H, Wenger R. Points and triangles in the plane and halving planes in space. In Proc Sixth Annu Symp Comput Geom. Publ by ACM. 1990. p. 112-115
    Aronov, Boris ; Guibas, Leonidas J. ; Chazelle, Bernard ; Sharir, Micha ; Edelsbrunner, Herbert ; Wenger, Rephael. / Points and triangles in the plane and halving planes in space. Proc Sixth Annu Symp Comput Geom. Publ by ACM, 1990. pp. 112-115
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