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Face guards for art galleries

By Diane L. Souvaine, Raoul Veroy and Andrew Winslow

Abstract

A classic problem in computational geometry is the art gallery problem: given an enclosure, how should guards be placed to ensure every location in the enclosure is seen by some guard. In this paper we consider guarding the interior of a simple polyhedron using face guards: guards that roam over an entire interior face of the polyhedron. Bounds for the number of face guards g that are necessary and sufficient to guard any polyhedron with f faces are given. We show that for orthogonal polyhedra, ⌊f/7 ⌋ ≤ g ≤ ⌊f/6⌋, while for general polyhedra ⌊f/5 − 2/5 ⌋ ≤ g ≤ ⌊f/2⌋

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.363.2687
Provided by: CiteSeerX
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