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arXiv · 1611.08315

Universal Guard Problems

Sándor P. Fekete·Qian Li·Joseph S. B. Mitchell·Christian Scheffer
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Abstract

We provide a spectrum of results for the Universal Guard Problem, in which one is to obtain a small set of points ("guards") that are "universal" in their ability to guard any of a set of possible polygonal domains in the plane. We give upper and lower bounds on the number of universal guards that are always sufficient to guard all polygons having a given set of n vertices, or to guard all polygons in a given set of k polygons on an n-point vertex set. Our upper bound proofs include algorithms to construct universal guard sets of the respective cardinalities.

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Sándor P. Fekete, Qian Li, Joseph S. B. Mitchell, Christian Scheffer. 2016-11-24. Universal Guard Problems. https://arxiv.org/abs/1611.08315

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