Computing a shortest weakly externally visible line segment for a simple polygon

A simple polygon P is said to be weakly externally visible from a line segm ent L if it lies outside P and for every point p on the boundary of P there is a point q on L such that no point in the interior of <(pq)over bar> lie s inside P. In this paper, a linear time algorithm is proposed for computin g a shortest line segment from which P is weakly externally visible. This i s done by a suitable generalization of a linear time algorithm which solves the same problem for a convex polygon.