Computational Geometry pp 54-64

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579) | Cite as

Open Guard Edges and Edge Guards in Simple Polygons

  • Csaba D. Tóth
  • Godfried T. Toussaint
  • Andrew Winslow

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 \(\lfloor n/3 \rfloor\) open edge guards, and conjecture that this bound is tight.

Keywords

art gallery illumination visibility mobile guards 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Csaba D. Tóth
    • 1
    • 2
  • Godfried T. Toussaint
    • 3
    • 4
  • Andrew Winslow
    • 2
  1. 1.University of CalgaryCalgaryCanada
  2. 2.Tufts UniversityMedfordUSA
  3. 3.New York University Abu DhabiAbu DhabiUnited Arab Emirates
  4. 4.McGill UniversityMontrealCanada

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