Improved Bounds for Beacon-Based Coverage and Routing in Simple Rectilinear Polygons

We establish tight bounds for beacon-based coverage problems, and improve the bounds for beacon-based routing problems in simple rectilinear polygons. Specifically, we show that bn6 c beacons are always sufficient and sometimes necessary to cover a simple rectilinear polygon P with n vertices. We also prove tight bounds for the case where P is monotone, and we present an optimal linear-time algorithm that computes the beacon-based kernel of P . For the routing problem, we show that b 3n−4 8 c − 1 beacons are always sufficient, and d n 4 e − 1 beacons are sometimes necessary to route between all pairs of points in P .