Iterative algorithms for the planar convex hull problem on mesh-connected arrays

Abstract

Algorithms are presented which solve the planar convex hull problem on a variety of mesh-connected arrays of processors without using recursion or divide-and-conquer techniques. The algorithms for one-way iterative arrays, one-way linear cellular arrays, and two-way linear cellular arrays all operate in time O( n). The algorithm for a two-way d-dimensional cellular array operates in time O(n 1 d ) . These algorithms are optimal for their arrays. The last algorithm can be used on an O( n) processor hypercube with a time complexity of O(log 2 n). We also show how these algorithms can be adapted to fully dynamic implementations with optimal throughput and turn-around. We believe that these algorithms may have performance advantages over existing parallel divide-and-conquer algorithms for planar convex hull.