Combinatorics and complexity of guarding polygons with edge and point 2-transmitters
arXiv:1503.05681 · doi:10.1016/j.comgeo.2017.06.004
Abstract
We consider a generalization of the classical Art Gallery Problem, where instead of a light source, the guards, called -transmitters, model a wireless device with a signal that can pass through at most walls. We show it is NP-hard to compute a minimum cover of point 2-transmitters, point -transmitters, and edge 2-transmitters in a simple polygon. The point 2-transmitter result extends to orthogonal polygons. In addition, we give necessity and sufficiency results for the number of edge 2-transmitters in general, monotone, orthogonal monotone, and orthogonal polygons.
15 pages, 11 figures