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

Deepak Ajwani, Khaled Elbassioni, Sathish Govindarajan, Saurabh Ray

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

    Abstract

    Given a set of points P R2, a conflict-free coloring of P w.r.t. rectangle ranges is an assignment of colors to points of P, such that each non-empty 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 bases stations (points), such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R2 can be conflict-free colored with (nΒ+) colors in expected polynomial time, for any arbitrarily small > 0 and Β = 3?5<over>2 < 0.382. This improves upon the previously known bound of O(nlog log n/ log n).

    Original languageEnglish (US)
    Title of host publicationSPAA'07
    Subtitle of host publicationProceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures
    Pages181-187
    Number of pages7
    DOIs
    StatePublished - Oct 18 2007
    EventSPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures - San Diego, CA, United States
    Duration: Jun 9 2007Jun 11 2007

    Other

    OtherSPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures
    CountryUnited States
    CitySan Diego, CA
    Period6/9/076/11/07

    Fingerprint

    Coloring
    Color
    Base stations
    Polynomials

    Keywords

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

    ASJC Scopus subject areas

    • Engineering(all)

    Cite this

    Ajwani, D., Elbassioni, K., Govindarajan, S., & Ray, S. (2007). Conflict-free coloring for rectangle ranges using O(n.382) colors. In SPAA'07: Proceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures (pp. 181-187) https://doi.org/10.1145/1248377.1248406

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

    SPAA'07: Proceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures. 2007. p. 181-187.

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

    Ajwani, D, Elbassioni, K, Govindarajan, S & Ray, S 2007, Conflict-free coloring for rectangle ranges using O(n.382) colors. in SPAA'07: Proceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures. pp. 181-187, SPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures, San Diego, CA, United States, 6/9/07. https://doi.org/10.1145/1248377.1248406
    Ajwani D, Elbassioni K, Govindarajan S, Ray S. Conflict-free coloring for rectangle ranges using O(n.382) colors. In SPAA'07: Proceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures. 2007. p. 181-187 https://doi.org/10.1145/1248377.1248406
    Ajwani, Deepak ; Elbassioni, Khaled ; Govindarajan, Sathish ; Ray, Saurabh. / Conflict-free coloring for rectangle ranges using O(n.382) colors. SPAA'07: Proceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures. 2007. pp. 181-187
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