An Upper Bound on the k-Modem Illumination Problem
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Published:2015-12
Issue:04
Volume:25
Page:299-308
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ISSN:0218-1959
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Container-title:International Journal of Computational Geometry & Applications
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language:en
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Short-container-title:Int. J. Comput. Geom. Appl.
Author:
Duque Frank1,
Hidalgo-Toscano Carlos1
Affiliation:
1. Departamento de Matemáticas, Cinvestav-IPN, Av. IPN 2508, Col. San Pedro Zacatenco 07360, México, D.F., Mexico
Abstract
A variation on the classical polygon illumination problem was introduced in [Aichholzer et al. EuroCG’09]. In this variant light sources are replaced by wireless devices called [Formula: see text]-modems, which can penetrate a fixed number [Formula: see text], of “walls”. A point in the interior of a polygon is “illuminated” by a [Formula: see text]-modem if the line segment joining them intersects at most [Formula: see text] edges of the polygon. It is easy to construct polygons of [Formula: see text] vertices where the number of [Formula: see text]-modems required to illuminate all interior points is [Formula: see text]. However, no non-trivial upper bound is known. In this paper we prove that the number of kmodems required to illuminate any polygon of [Formula: see text] vertices is [Formula: see text]. For the cases of illuminating an orthogonal polygon or a set of disjoint orthogonal segments, we give a tighter bound of [Formula: see text]. Moreover, we present an [Formula: see text] time algorithm to achieve this bound.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science
Cited by
1 articles.
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