Square meshes are not optimal for convex hull computation

Recently it has been noticed that for semigroup computations and for selection, rectangular meshes with multiple broadcasting yield faster algorithms than their square counterparts. The contribution of the paper is to provide yet another example of a fundamental problem for which this phenomenon occurs. Specifically, we show that the problem of computing the convex hull of a set of n sorted points in the plane can be solved in O(n ¹8/ log ³4/) time on a rectangular mesh with multiple broadcasting of size n ³8/ log ¹4/ n×n ⁵8//log ¹4/n. The fastest previously known algorithms on a square mesh of size √n×√n run in O(n ¹6/) time in case the n points are pixels in a binary image, and in O(n ¹6/log ³2/ n) time for sorted points in the plane.