How to cover a point set with a V-shape of minimum width

Boris Aronov, Muriel Dulieu

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

    Abstract

    A balanced V-shape is a polygonal region in the plane contained in the union of two crossing equal-width strips. It is delimited by two pairs of parallel rays that emanate from two points x, y, are contained in the strip boundaries, and are mirror-symmetric with respect to the line xy. The width of a balanced V-shape is the width of the strips. We first present an O(n 2 log n) time algorithm to compute, given a set of n points P, a minimum-width balanced V-shape covering P. We then describe a PTAS for computing a (1 + ε)-approximation of this V-shape in time O((n/ε)log n + (n/ε 3/2)log 2(1/ε)).

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings
    Pages61-72
    Number of pages12
    Volume6844 LNCS
    DOIs
    StatePublished - 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)03029743
    ISSN (Electronic)16113349

    Other

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

    Fingerprint

    Point Sets
    Mirrors
    Cover
    Strip
    P-point
    Half line
    Mirror
    Union
    Covering
    Computing
    Line
    Approximation

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Aronov, B., & Dulieu, M. (2011). How to cover a point set with a V-shape of minimum width. In Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings (Vol. 6844 LNCS, pp. 61-72). (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_6

    How to cover a point set with a V-shape of minimum width. / Aronov, Boris; Dulieu, Muriel.

    Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings. Vol. 6844 LNCS 2011. p. 61-72 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6844 LNCS).

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

    Aronov, B & Dulieu, M 2011, How to cover a point set with a V-shape of minimum width. in Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings. vol. 6844 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6844 LNCS, pp. 61-72, 12th International Symposium on Algorithms and Data Structures, WADS 2011, New York, NY, United States, 8/15/11. https://doi.org/10.1007/978-3-642-22300-6_6
    Aronov B, Dulieu M. How to cover a point set with a V-shape of minimum width. In Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings. Vol. 6844 LNCS. 2011. p. 61-72. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-22300-6_6
    Aronov, Boris ; Dulieu, Muriel. / How to cover a point set with a V-shape of minimum width. Algorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings. Vol. 6844 LNCS 2011. pp. 61-72 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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