Open guard edges and edge guards in simple polygons

Csaba D. Tóth, Godfried Toussaint, Andrew Winslow

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

    Abstract

    An open edge of a simple polygon is the set of points in the relative interior of an edge. We revisit several art gallery problems, previously considered for closed edge guards, using open edge guards. A guard edge of a polygon is an edge that sees every point inside the polygon. We show that every simple non-starshaped polygon admits at most one open guard edge, and give a simple new proof that it admits at most three closed guard edges. We also characterize open guard edges using a special type of kernel. Finally, we present lower bound constructions for simple polygons with n vertices that require ⌊n/3⌋ open edge guards, and conjecture that this bound is tight.

    Original languageEnglish (US)
    Title of host publicationComputational Geometry - XIV Spanish Meeting, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Revised Selected Papers
    Pages54-64
    Number of pages11
    DOIs
    StatePublished - Nov 30 2012
    Event14th Spanish Meeting on Computational Geometry - Alcala de Henares, Spain
    Duration: Jun 27 2011Jun 30 2011

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume7579 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other14th Spanish Meeting on Computational Geometry
    CountrySpain
    CityAlcala de Henares
    Period6/27/116/30/11

    Fingerprint

    Simple Polygon
    Polygon
    Art Gallery Problem
    Closed
    Set of points
    Interior
    Lower bound
    kernel

    Keywords

    • art gallery
    • illumination
    • mobile guards
    • visibility

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Tóth, C. D., Toussaint, G., & Winslow, A. (2012). Open guard edges and edge guards in simple polygons. In Computational Geometry - XIV Spanish Meeting, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Revised Selected Papers (pp. 54-64). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7579 LNCS). https://doi.org/10.1007/978-3-642-34191-5_5

    Open guard edges and edge guards in simple polygons. / Tóth, Csaba D.; Toussaint, Godfried; Winslow, Andrew.

    Computational Geometry - XIV Spanish Meeting, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Revised Selected Papers. 2012. p. 54-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7579 LNCS).

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

    Tóth, CD, Toussaint, G & Winslow, A 2012, Open guard edges and edge guards in simple polygons. in Computational Geometry - XIV Spanish Meeting, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7579 LNCS, pp. 54-64, 14th Spanish Meeting on Computational Geometry, Alcala de Henares, Spain, 6/27/11. https://doi.org/10.1007/978-3-642-34191-5_5
    Tóth CD, Toussaint G, Winslow A. Open guard edges and edge guards in simple polygons. In Computational Geometry - XIV Spanish Meeting, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Revised Selected Papers. 2012. p. 54-64. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-34191-5_5
    Tóth, Csaba D. ; Toussaint, Godfried ; Winslow, Andrew. / Open guard edges and edge guards in simple polygons. Computational Geometry - XIV Spanish Meeting, EGC 2011, Dedicated to Ferran Hurtado on the Occasion of His 60th Birthday, Revised Selected Papers. 2012. pp. 54-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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