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/ε3/2)log2(1/ε)).

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 12th International Symposium, WADS 2011, Proceedings
    Pages61-72
    Number of pages12
    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. (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 (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