An Optimal Parallel Algorithm for Finding the Smallest Enclosing Rectangle on a Mesh-connected Computer

In this paper, we consider the problem of finding the smallest triangle circumscribing a convex polygon with n edges. We shall show that this can be done in O( p n) time by the efficient data partition schemes and the proper set mapping and comparison operations using what so called p n-decomposition technique. Since the nontrivial operation on MCC requires\Omega\Gamma p n), the time complexity is optimal within constant time factor. 1 Introduction Mesh-connected computer(MCC) is composed of n identical processing elements(PE's) arranged on a p n \Theta p n array, where each PE is connected to its four neighbors [1]. In this paper, we consider the problem of finding the smallest triangle circumscribing a convex polygon with n edges on MCC. The smallest triangle problem(STP) is a special case of the smallest k-gons problems with applications to collision avoidance in robotics, packing and optimal layout problems [4, 5, 6]. Klee and Laskowski[5] first presented an O(nlog 2..