The Illumination of Polygonal Regions with Modems

The Illumination of Polygonal Regions with Modems

Mahsa Soheil Shamaee, Ali Mohades Khorasani, Marzieh Eskandari

Abstract

In this paper, the problem of finding the minimum number of -modems to cover a monotone polygon is considered. A -modem is a point guard which can see a point, if the line segment joining them crosses at most edges of the polygon. The parameter is referred as the power of the -modem. It is shown that every monotone polygon on vertices can be illuminated with modems. This bound is tight. It is also shown that every orthogonal polygon (with or without holes) on 2 vertices can be covered with a ( 4)- modem for odd and with a ( 3)- modem for even . When the purpose is covering a simple orthogonal polygon with a single modem placed at a point in its interior or boundary, these bounds on the power of the modem are tight. It is also shown if there is a monotone orthogonal polygon in the plane, a 4-modem will be enough to illuminate the plane. This bound on the power of the modem is tight.

Keywords

Illumination, K-Modem, Visibility, Art gallery, Computational Geometry

References