A fast parallel algorithm for finding the convex hull of a sorted point set

We present a parallel algorithm for finding the convex hull of a sorted point set. The algorithm runs in O(loglog n) (doubly logarithmic) time using n/loglog n processors on a Common CRCW PRAM. To break the Omega(log n/loglog n) time barrier required to output the convex hull in a contiguous array, we introduce a novel data structure for representing the convex hull. The algorithm is optimal in two respects: (1) the time-processor product of the algorithm, which is linear, cannot be improved, and (2) the running time, which is doubly logarithmic, cannot be improved even by using a linear number of processors. The algorithm demonstrates the power of the ''the divide-and-conquer doubly logarithmic paradigm'' by presenting a non-trivial extension to situations that previously were known to have only slower algorithm.