Guarding Art Galleries by Guarding Witnesses

Abstract

Let P be a simple polygon We define a witness setW to be a set of points such that if any (prospective) guard set G guards W, then it is guaranteed that G guards P Not all polygons admit a finite witness set If a finite minimal witness set exists, then it cannot contain any witness in the interior of P; all witnesses must lie on the boundary of P, and there can be at most one witness in the interior of every edge We give an algorithm to compute a minimum witness set for P in O(n2log n) time, if such a set exists, or to report the non-existence within the same time bounds.