Resumen de On Modem Illumination Problems
Ruy Fabila Monroy, Andres Ruiz Vargas, Jaime Urrutia Fucugauchi
In this paper we review recent results on a new variation of the Art Gallery problem. A common problem we face nowadays, is that of placing a set of wireless modems in a building in such a way that a computer placed anywhere within the building receives a signal strong enough to connect to the Web. In most buildings, the main limitation for this problem is not the distance of a computer to a wireless modem, but rather the number of walls that separate them. We study variations of the following problem: Let P be a simple polygon with n vertices. How many points p1, . . . , pk (representing wireless modems) are always sufficient such that for any other point p in P, there is a pi such that the line segment joining p to pi crosses at most k edges of P? The parameter k represents the strenght of the signal emited by the modems. We study variations of this problem for families of line segments, families of lines, orthogonal polygons, and sets of horizontal or vertical disjoint segments, or sets of lines.
