An “Art Gallery Theorem” for pyramids

Authors:
M. Abellanas;S. Canales;G. Hernández-Peòalver
Affiliations:
Universidad Politécnica de Madrid, Facultad de Informática, Departamento de Matemática Aplicada, Spain;Universidad Pontificia Comillas de Madrid, Escuela Técnica Superior de Ingeniería (ICAI), Departamento de Matemática Aplicada y Computación, Spain;Universidad Politécnica de Madrid, Facultad de Informática, Departamento de Matemática Aplicada, Spain
Venue:
Information Processing Letters
Year:
2009

Citing 2
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Abstract

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.