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

Boris Aronov, Muriel Dulieu

    Research output: Contribution to journalArticle

    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( n2logn) 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)logn+(n/ ε3 /2) log2(1/ε)). A much simpler constant-factor approximation algorithm is also described.

    Original languageEnglish (US)
    Pages (from-to)298-309
    Number of pages12
    JournalComputational Geometry: Theory and Applications
    Volume46
    Issue number3
    DOIs
    StatePublished - Apr 2013

    Fingerprint

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

    Keywords

    • Approximation algorithm
    • Computational metrology
    • Curve reconstruction
    • Fitting
    • Geometric optimization

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Computer Science Applications
    • Computational Mathematics
    • Control and Optimization
    • Geometry and Topology

    Cite this

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

    In: Computational Geometry: Theory and Applications, Vol. 46, No. 3, 04.2013, p. 298-309.

    Research output: Contribution to journalArticle

    Aronov, Boris ; Dulieu, Muriel. / How to cover a point set with a V-shape of minimum width. In: Computational Geometry: Theory and Applications. 2013 ; Vol. 46, No. 3. pp. 298-309.
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