In a paper by Biro et al., a novel twist on guarding in art galleries, motivated by geographical greedy routing in sensor networks, is introduced. A beacon is a point that when activated induces a force of attraction, or repulsion that can move points within the environment. The effect of a beacon is similar to standard visibility with some additional properties. The effects of a beacon are asymmetric leading to separate algorithms to compute the "beacon kernel" and "inverse beacon kernel". Previously O(*n*^{2}) algorithms are given to compute the beacon kernel and inverse beacon kernels in simple polygons. In this paper we revisit the problem of computing the shortest watchtower to guard a terrain, using the properties of beacons, and we present an O(*n* log *n*) time algorithm that computes the shortest beacon watchtower. In doing this we introduce O(*n* log *n*) algorithms to compute the beacon kernel in a simple polygon and an inverse beacon kernel in a terrain polygon. Similar ideas are then used for an algorithm to compute the inverse beacon kernel in a monotone polygon in O(*n* log *n*) time.