The Illumination of Polygonal Regions with Modems

The Illumination of Polygonal Regions with Modems

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.

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