Witness rectangle graphs

Boris Aronov, Muriel Dulieu, Ferran Hurtado

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

    Abstract

    In a witness rectangle graph (WRG) on vertex point set P with respect to witness point set W in the plane, two points x,y in P are adjacent whenever the open rectangle with x and y as opposite corners contains at least one point in W. WRGs are representative of a larger family of witness proximity graphs introduced in two previous papers. We study graph-theoretic properties of WRGs. We prove that any WRG has at most two non-trivial connected components. We bound the diameter of the non-trivial connected components of a WRG in both the one-component and two-component cases. In the latter case, we prove that a graph is representable as a WRG if and only if each component is a co-interval graph, thereby providing a complete characterization of WRGs of this type. We also completely characterize trees drawable as WRGs. Finally, we conclude with some related results on the number of points required to stab all the rectangles defined by a set of n points.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings
    Pages73-85
    Number of pages13
    DOIs
    StatePublished - Sep 1 2011
    Event12th International Symposium on Algorithms and Data Structures, WADS 2011 - New York, NY, United States
    Duration: Aug 15 2011Aug 17 2011

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume6844 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other12th International Symposium on Algorithms and Data Structures, WADS 2011
    CountryUnited States
    CityNew York, NY
    Period8/15/118/17/11

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    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Aronov, B., Dulieu, M., & Hurtado, F. (2011). Witness rectangle graphs. In Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings (pp. 73-85). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6844 LNCS). https://doi.org/10.1007/978-3-642-22300-6_7