Computer Science > Computational Geometry
[Submitted on 24 Nov 2016 (v1), last revised 27 Mar 2017 (this version, v2)]
Title:Universal Guard Problems
View PDFAbstract: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.
Submission history
From: Sandor P. Fekete [view email][v1] Thu, 24 Nov 2016 21:38:59 UTC (440 KB)
[v2] Mon, 27 Mar 2017 07:19:12 UTC (4,139 KB)
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