Optimal parallel algorithms for computing convex hulls and for sorting

Abstract

A parallel algorithm is presented for computing the convex hull of a set ofn points in the plane. The algorithm usesn1−e processors, 0<e<1, and runs inO(ne logh) time, whereh is the number of edges on the convex hull, for a total cost ofO (n logh). This performance matches that of the best currently known sequential convex hull algorithm. In addition, sinceh≤n, the algorithm is worst-case optimal in view of the Ω (n logn) worst-case lower bound on sequential convex hull computation. It is also shown that the convex hull algorithm leads to a parallel sorting algorithm whose total cost isO(n logn), which is optimal.