A simple and efficient preprocessing step for convex hull problem

Abstract

The present paper is concerned with a recursive algorithm as a preprocessing step to find the convex hull of $n$ random points uniformly distributed in the plane. For such a set of points, it is shown that eliminating all but $O(\log n)$ of points can derive the same convex hull as the input set. Finally it will be shown that the running time of the algorithm is $O(n)