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 p 2).

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings
    Pages49-60
    Number of pages12
    Volume8037 LNCS
    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)03029743
    ISSN (Electronic)16113349

    Other

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

    Fingerprint

    Point Location
    Query
    Data structures
    Farthest Point
    Simple Polygon
    Subdivision
    Data Structures

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    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 (Vol. 8037 LNCS, 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

    Distance-sensitive planar point location. / Aronov, Boris; De Berg, Mark; Roeloffzen, Marcel; Speckmann, Bettina.

    Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings. Vol. 8037 LNCS 2013. p. 49-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8037 LNCS).

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

    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. vol. 8037 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8037 LNCS, pp. 49-60, 13th International Symposium on Algorithms and Data Structures, WADS 2013, London, ON, Canada, 8/12/13. https://doi.org/10.1007/978-3-642-40104-6_5
    Aronov B, De Berg M, Roeloffzen M, Speckmann B. Distance-sensitive planar point location. In Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings. Vol. 8037 LNCS. 2013. p. 49-60. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-40104-6_5
    Aronov, Boris ; De Berg, Mark ; Roeloffzen, Marcel ; Speckmann, Bettina. / Distance-sensitive planar point location. Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings. Vol. 8037 LNCS 2013. pp. 49-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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