On the Inverse Beacon Attraction Region of a Point

Motivated by routing in sensor networks, Biro et al. [2] introduced the notion of beacon attraction and inverse attraction as a new variant of visibility in a simple polygon. A beacon b is a point inside a polygon P that can induce an attraction that moves a target point p greedily towards it in a trajectory that always reduces distance from p to b. The trajectory of p may require sliding p along the boundary of an obstacle. The attraction region of b is the set of all points that eventually reach b. The inverse attraction region of p is the set of points that can attract p. We present algorithms to efficiently compute the inverse attraction region of a point for simple, monotone, and terrain polygons with respective time complexities O(n), O(n log n) and O(n).