A parallel algorithm for enclosed and enclosing triangles

We consider the problems of computing the largest area triangle enclosed within a given n-sided convex polygon and the smallest area triangle which encloses a given convex polygon. We show that these problems are closely related by presenting a single sequential linear time algorithm which essentially solves both problems simultaneously. We also present a cost-optimal parallel algorithm that solves both of these problems in O(log log n) time using n/log log n processors on a CRCW PRAM. In order to achieve these bounds we develop new techniques for the design of parallel algorithms for computational problems involving the rotating calipers method.