Open guard edges and edge guards in simple polygons

Csaba D. Tóth, Godfried Toussaint, Andrew Winslow

    Research output: Contribution to conferencePaper

    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 poly- gon is an edge that sees every point inside the polygon. We show that every simple non-starshaped polygon ad- mits at most one open guard edge, and give a simple new proof that it admits at most three closed guard edges. We characterize open guard edges, and derive an algorithm that finds all open guard edges of a simple n-gon in O(n) time in the RAM model of computation. 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)
    StatePublished - Dec 1 2011
    Event23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 - Toronto, ON, Canada
    Duration: Aug 10 2011Aug 12 2011

    Other

    Other23rd Annual Canadian Conference on Computational Geometry, CCCG 2011
    CountryCanada
    CityToronto, ON
    Period8/10/118/12/11

    Fingerprint

    Simple Polygon
    Random access storage
    Polygon
    Art Gallery Problem
    n-gon
    Closed
    Models of Computation
    Set of points
    Interior
    Lower bound

    ASJC Scopus subject areas

    • Computational Mathematics
    • Geometry and Topology

    Cite this

    Tóth, C. D., Toussaint, G., & Winslow, A. (2011). Open guard edges and edge guards in simple polygons. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada.

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

    2011. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada.

    Research output: Contribution to conferencePaper

    Tóth, CD, Toussaint, G & Winslow, A 2011, 'Open guard edges and edge guards in simple polygons' Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada, 8/10/11 - 8/12/11, .
    Tóth CD, Toussaint G, Winslow A. Open guard edges and edge guards in simple polygons. 2011. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada.
    Tóth, Csaba D. ; Toussaint, Godfried ; Winslow, Andrew. / Open guard edges and edge guards in simple polygons. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada.
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