The art gallery theorem for simple polygons in terms of the number of reflex and convex vertices

Authors:
Justin Iwerks;Joseph S. B. Mitchell
Affiliations:
Dept. of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, United States;Dept. of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, United States
Venue:
Information Processing Letters
Year:
2012

Citing 3
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Art gallery theorems and algorithms

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Computational geometry and convexity
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SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory

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Abstract

We present an art gallery theorem for simple polygons having n vertices in terms of the number, r, of reflex vertices and the number, c, of convex vertices (n=r+c). Tight combinatorial bounds have previously been shown when 0==5c-12. We give a lower bound construction that matches the @?n3@? sufficiency condition from the traditional art gallery theorem when @?c2@?=3.