Results on k-sets and j-facets via continuous motion

Artur Andrzejak, Boris Aronov, Sariel Har-Peled, Raimund Seidel, Emo Welzl

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

    Abstract

    The set P of n points in Rd in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

    Original languageEnglish (US)
    Title of host publicationProceedings of the Annual Symposium on Computational Geometry
    PublisherACM
    Pages192-199
    Number of pages8
    StatePublished - 1998
    EventProceedings of the 1998 14th Annual Symposium on Computational Geometry - Minneapolis, MN, USA
    Duration: Jun 7 1998Jun 10 1998

    Other

    OtherProceedings of the 1998 14th Annual Symposium on Computational Geometry
    CityMinneapolis, MN, USA
    Period6/7/986/10/98

    Fingerprint

    Facet
    Motion
    Hyperplane

    ASJC Scopus subject areas

    • Chemical Health and Safety
    • Software
    • Safety, Risk, Reliability and Quality
    • Geometry and Topology

    Cite this

    Andrzejak, A., Aronov, B., Har-Peled, S., Seidel, R., & Welzl, E. (1998). Results on k-sets and j-facets via continuous motion. In Proceedings of the Annual Symposium on Computational Geometry (pp. 192-199). ACM.

    Results on k-sets and j-facets via continuous motion. / Andrzejak, Artur; Aronov, Boris; Har-Peled, Sariel; Seidel, Raimund; Welzl, Emo.

    Proceedings of the Annual Symposium on Computational Geometry. ACM, 1998. p. 192-199.

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

    Andrzejak, A, Aronov, B, Har-Peled, S, Seidel, R & Welzl, E 1998, Results on k-sets and j-facets via continuous motion. in Proceedings of the Annual Symposium on Computational Geometry. ACM, pp. 192-199, Proceedings of the 1998 14th Annual Symposium on Computational Geometry, Minneapolis, MN, USA, 6/7/98.
    Andrzejak A, Aronov B, Har-Peled S, Seidel R, Welzl E. Results on k-sets and j-facets via continuous motion. In Proceedings of the Annual Symposium on Computational Geometry. ACM. 1998. p. 192-199
    Andrzejak, Artur ; Aronov, Boris ; Har-Peled, Sariel ; Seidel, Raimund ; Welzl, Emo. / Results on k-sets and j-facets via continuous motion. Proceedings of the Annual Symposium on Computational Geometry. ACM, 1998. pp. 192-199
    @inproceedings{010d61001e4d4787923bbaba9782bdb6,
    title = "Results on k-sets and j-facets via continuous motion",
    abstract = "The set P of n points in Rd in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.",
    author = "Artur Andrzejak and Boris Aronov and Sariel Har-Peled and Raimund Seidel and Emo Welzl",
    year = "1998",
    language = "English (US)",
    pages = "192--199",
    booktitle = "Proceedings of the Annual Symposium on Computational Geometry",
    publisher = "ACM",

    }

    TY - GEN

    T1 - Results on k-sets and j-facets via continuous motion

    AU - Andrzejak, Artur

    AU - Aronov, Boris

    AU - Har-Peled, Sariel

    AU - Seidel, Raimund

    AU - Welzl, Emo

    PY - 1998

    Y1 - 1998

    N2 - The set P of n points in Rd in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

    AB - The set P of n points in Rd in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

    UR - http://www.scopus.com/inward/record.url?scp=0031639759&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0031639759&partnerID=8YFLogxK

    M3 - Conference contribution

    SP - 192

    EP - 199

    BT - Proceedings of the Annual Symposium on Computational Geometry

    PB - ACM

    ER -