Conflict-free coloring for rectangle ranges using O(n .382) colors

Deepak Ajwani, Khaled Elbassioni, Sathish Govindarajan, Saurabh Ray

    Research output: Contribution to journalArticle

    Abstract

    Given a set of points P ⊆ ℝ 2, a conflict-free coloring of P w. r. t. rectangle ranges is an assignment of colors to points of P, such that each nonempty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to base stations (points) such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in ℝ 2 can be conflict-free colored with O(n β*+o(1)) colors in expected polynomial time, where.

    Original languageEnglish (US)
    Pages (from-to)39-52
    Number of pages14
    JournalDiscrete and Computational Geometry
    Volume48
    Issue number1
    DOIs
    StatePublished - Jul 1 2012

    Fingerprint

    Coloring
    Rectangle
    Colouring
    Color
    Range of data
    Frequency Assignment
    Base stations
    Cellular Networks
    Set of points
    Polynomials
    Wireless Networks
    Polynomial time
    Assignment
    Interference
    Conflict
    Distinct
    Minimise

    Keywords

    • Axis-parallel rectangles
    • Boundary sets
    • Conflict-free coloring
    • Frequency assignment in wireless networks
    • Monotone sequences

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics
    • Computational Theory and Mathematics

    Cite this

    Conflict-free coloring for rectangle ranges using O(n .382) colors. / Ajwani, Deepak; Elbassioni, Khaled; Govindarajan, Sathish; Ray, Saurabh.

    In: Discrete and Computational Geometry, Vol. 48, No. 1, 01.07.2012, p. 39-52.

    Research output: Contribution to journalArticle

    Ajwani, Deepak ; Elbassioni, Khaled ; Govindarajan, Sathish ; Ray, Saurabh. / Conflict-free coloring for rectangle ranges using O(n .382) colors. In: Discrete and Computational Geometry. 2012 ; Vol. 48, No. 1. pp. 39-52.
    @article{17cb55434edf48ca9b2beeb6193fd9be,
    title = "Conflict-free coloring for rectangle ranges using O(n .382) colors",
    abstract = "Given a set of points P ⊆ ℝ 2, a conflict-free coloring of P w. r. t. rectangle ranges is an assignment of colors to points of P, such that each nonempty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to base stations (points) such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in ℝ 2 can be conflict-free colored with O(n β*+o(1)) colors in expected polynomial time, where.",
    keywords = "Axis-parallel rectangles, Boundary sets, Conflict-free coloring, Frequency assignment in wireless networks, Monotone sequences",
    author = "Deepak Ajwani and Khaled Elbassioni and Sathish Govindarajan and Saurabh Ray",
    year = "2012",
    month = "7",
    day = "1",
    doi = "10.1007/s00454-012-9425-5",
    language = "English (US)",
    volume = "48",
    pages = "39--52",
    journal = "Discrete and Computational Geometry",
    issn = "0179-5376",
    publisher = "Springer New York",
    number = "1",

    }

    TY - JOUR

    T1 - Conflict-free coloring for rectangle ranges using O(n .382) colors

    AU - Ajwani, Deepak

    AU - Elbassioni, Khaled

    AU - Govindarajan, Sathish

    AU - Ray, Saurabh

    PY - 2012/7/1

    Y1 - 2012/7/1

    N2 - Given a set of points P ⊆ ℝ 2, a conflict-free coloring of P w. r. t. rectangle ranges is an assignment of colors to points of P, such that each nonempty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to base stations (points) such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in ℝ 2 can be conflict-free colored with O(n β*+o(1)) colors in expected polynomial time, where.

    AB - Given a set of points P ⊆ ℝ 2, a conflict-free coloring of P w. r. t. rectangle ranges is an assignment of colors to points of P, such that each nonempty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to base stations (points) such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in ℝ 2 can be conflict-free colored with O(n β*+o(1)) colors in expected polynomial time, where.

    KW - Axis-parallel rectangles

    KW - Boundary sets

    KW - Conflict-free coloring

    KW - Frequency assignment in wireless networks

    KW - Monotone sequences

    UR - http://www.scopus.com/inward/record.url?scp=84860881461&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84860881461&partnerID=8YFLogxK

    U2 - 10.1007/s00454-012-9425-5

    DO - 10.1007/s00454-012-9425-5

    M3 - Article

    VL - 48

    SP - 39

    EP - 52

    JO - Discrete and Computational Geometry

    JF - Discrete and Computational Geometry

    SN - 0179-5376

    IS - 1

    ER -