Modem illumination of monotone polygons

We study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of walls. We call these objects k-modems and study the minimum number of k-modems necessary to illuminate monotone and monotone orthogonal polygons. We show that every monotone polygon on n vertices can be illuminated with ⌈ n 2k ⌉ k-modems and exhibit examples of monotone polygons requiring ⌈