An “Art Gallery Theorem” for pyramids

An “Art Gallery Theorem” for pyramids

Every orthogonal polygon can be illuminated by ⌊ n / 4 ⌋ lights situated in the vertices of the polygon. In this paper we improve this bound for pyramids, showing that ⌈ n / 6 ⌉ guards situated in vertices are always sufficient and sometimes necessary for watching any pyramid of n vertices. Our proo...

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Veröffentlicht in:Information processing letters 2009-06, Vol.109 (13), p.719-721
Hauptverfasser: Abellanas, M., Canales, S., Hernández-Peñalver, G.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Art galleries & museums
Art Gallery
Computational geometry
Computer science
control theory
systems
Exact sciences and technology
Geometry
Mathematics
Miscellaneous
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Orthogonal polygon
Polygons
Pyramid
Sciences and techniques of general use
Studies
Theoretical computing
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Beschreibung
Zusammenfassung:Every orthogonal polygon can be illuminated by ⌊ n / 4 ⌋ lights situated in the vertices of the polygon. In this paper we improve this bound for pyramids, showing that ⌈ n / 6 ⌉ guards situated in vertices are always sufficient and sometimes necessary for watching any pyramid of n vertices. Our proof leads to a linear time algorithm for placing those guards.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2009.03.014