K-Centerpoints Conjectures for Pointsets in Rd

Nabil H. Mustafa, Saurabh Ray, Mudassir Shabbir

    Research output: Contribution to journalArticle

    Abstract

    In this paper, we introduce the notion of k-centerpoints for any set P of n points in Rd. These unify and generalize previous results such as the classical centerpoint theorem,1 and the recently-proven ray-shooting theorem.2 We define two variants: affine k-centerpoints, and topological k-centerpoints. We prove their equivalence in R2, and conjecture that these are in fact equivalent in any dimension. We present the first non-trivial bounds for these problems in Rd, as well as present several conjectures related to them.

    Original languageEnglish (US)
    Pages (from-to)163-185
    Number of pages23
    JournalInternational Journal of Computational Geometry and Applications
    Volume25
    Issue number3
    DOIs
    StatePublished - Jan 1 2015

    Fingerprint

    Point Sets
    Ray Shooting
    Equivalence
    Generalise
    Theorem

    Keywords

    • Centerpoint
    • data depth
    • ray shooting depth

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Computational Theory and Mathematics
    • Computational Mathematics
    • Applied Mathematics

    Cite this

    K-Centerpoints Conjectures for Pointsets in Rd. / Mustafa, Nabil H.; Ray, Saurabh; Shabbir, Mudassir.

    In: International Journal of Computational Geometry and Applications, Vol. 25, No. 3, 01.01.2015, p. 163-185.

    Research output: Contribution to journalArticle

    Mustafa, Nabil H. ; Ray, Saurabh ; Shabbir, Mudassir. / K-Centerpoints Conjectures for Pointsets in Rd. In: International Journal of Computational Geometry and Applications. 2015 ; Vol. 25, No. 3. pp. 163-185.
    @article{95572846e6ea4dc4808f5d664da340fe,
    title = "K-Centerpoints Conjectures for Pointsets in Rd",
    abstract = "In this paper, we introduce the notion of k-centerpoints for any set P of n points in Rd. These unify and generalize previous results such as the classical centerpoint theorem,1 and the recently-proven ray-shooting theorem.2 We define two variants: affine k-centerpoints, and topological k-centerpoints. We prove their equivalence in R2, and conjecture that these are in fact equivalent in any dimension. We present the first non-trivial bounds for these problems in Rd, as well as present several conjectures related to them.",
    keywords = "Centerpoint, data depth, ray shooting depth",
    author = "Mustafa, {Nabil H.} and Saurabh Ray and Mudassir Shabbir",
    year = "2015",
    month = "1",
    day = "1",
    doi = "10.1142/S0218195915500107",
    language = "English (US)",
    volume = "25",
    pages = "163--185",
    journal = "International Journal of Computational Geometry and Applications",
    issn = "0218-1959",
    publisher = "World Scientific Publishing Co. Pte Ltd",
    number = "3",

    }

    TY - JOUR

    T1 - K-Centerpoints Conjectures for Pointsets in Rd

    AU - Mustafa, Nabil H.

    AU - Ray, Saurabh

    AU - Shabbir, Mudassir

    PY - 2015/1/1

    Y1 - 2015/1/1

    N2 - In this paper, we introduce the notion of k-centerpoints for any set P of n points in Rd. These unify and generalize previous results such as the classical centerpoint theorem,1 and the recently-proven ray-shooting theorem.2 We define two variants: affine k-centerpoints, and topological k-centerpoints. We prove their equivalence in R2, and conjecture that these are in fact equivalent in any dimension. We present the first non-trivial bounds for these problems in Rd, as well as present several conjectures related to them.

    AB - In this paper, we introduce the notion of k-centerpoints for any set P of n points in Rd. These unify and generalize previous results such as the classical centerpoint theorem,1 and the recently-proven ray-shooting theorem.2 We define two variants: affine k-centerpoints, and topological k-centerpoints. We prove their equivalence in R2, and conjecture that these are in fact equivalent in any dimension. We present the first non-trivial bounds for these problems in Rd, as well as present several conjectures related to them.

    KW - Centerpoint

    KW - data depth

    KW - ray shooting depth

    UR - http://www.scopus.com/inward/record.url?scp=84944329043&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84944329043&partnerID=8YFLogxK

    U2 - 10.1142/S0218195915500107

    DO - 10.1142/S0218195915500107

    M3 - Article

    VL - 25

    SP - 163

    EP - 185

    JO - International Journal of Computational Geometry and Applications

    JF - International Journal of Computational Geometry and Applications

    SN - 0218-1959

    IS - 3

    ER -