Computing the longest diagonal of a simple polygon

An O(n log3n) algorithm is presented for computing the longest diagonal of a simple n-gon. The longest diagonal problem requires the determination of two vertices of the polygon that are visible to each other and that are farthest from each other among all such pairs. This problem is a variation of the "biggest stick" problem for which the most efficient algorithm that is known, is O(n1.98) time. © 1990.