EGC 2011: Computational Geometry pp 54-64

# Open Guard Edges and Edge Guards in Simple Polygons

• Csaba D. Tóth
• Godfried T. Toussaint
• Andrew Winslow
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

## 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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## Authors and Affiliations

• Csaba D. Tóth
• 1
• 2
• Godfried T. Toussaint
• 3
• 4
• Andrew Winslow
• 2