Distance-sensitive planar point location

Boris Aronov, Mark De Berg, Marcel Roeloffzen, Bettina Speckmann

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

    Abstract

    Let S be a connected planar polygonal subdivision with n edges and of total area 1. We present a data structure for point location in S where queries with points far away from any region boundary are answered faster. More precisely, we show that point location queries can be answered in time O(1 + min(log 1/Δp, log n)), where Δp is the distance of the query point p to the boundary of the region containing p. Our structure is based on the following result: any simple polygon P can be decomposed into a linear number of convex quadrilaterals with the following property: for any point p ∈ P, the quadrilateral containing p has area Ω(δ p2).

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings
    Pages49-60
    Number of pages12
    DOIs
    StatePublished - 2013
    Event13th International Symposium on Algorithms and Data Structures, WADS 2013 - London, ON, Canada
    Duration: Aug 12 2013Aug 14 2013

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume8037 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other13th International Symposium on Algorithms and Data Structures, WADS 2013
    CountryCanada
    CityLondon, ON
    Period8/12/138/14/13

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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  • Cite this

    Aronov, B., De Berg, M., Roeloffzen, M., & Speckmann, B. (2013). Distance-sensitive planar point location. In Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings (pp. 49-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8037 LNCS). https://doi.org/10.1007/978-3-642-40104-6_5