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Art gallery theorems for guarded guards
Resource type
Authors/contributors
- Michael, T.S. (Author)
- Pinciu, V. (Author)
Title
Art gallery theorems for guarded guards
Abstract
We prove two art gallery theorems in which the guards must guard one another in addition to the gallery. A set G of points (the guards) in a simple closed polygon (the art gallery) is a guarded guard set provided (i) every point in the polygon is visible to some point in G; and (ii) every point in G is visible to some other point in G. We prove that a polygon with n sides always has a guarded guard set of cardinality ⌊(3n-1)/7⌋ and that this bound is sharp (n5); our result corrects an erroneous formula in the literature. We also use a coloring argument to give an entirely new proof that the corresponding sharp function for orthogonal polygons is ⌊n/3⌋ for n≤6; this result was originally established by induction by Hernández-Peñalver. © 2003 Elsevier B.V.
Publication
Computational Geometry: Theory and Applications
Date
2003
Volume
26
Issue
3
Pages
247-258
Journal Abbr
Comput Geom Theory Appl
Citation Key
michaelArtGalleryTheorems2003
ISSN
09257721 (ISSN)
Archive
Scopus
Language
English
Extra
16 citations (Crossref) [2023-10-31]
Citation
Michael, T. S., & Pinciu, V. (2003). Art gallery theorems for guarded guards. Computational Geometry: Theory and Applications, 26(3), 247–258. Scopus. https://doi.org/10.1016/S0925-7721(03)00039-7
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