Preconditioning 2D integer data for fast convex hull computations

Abstract

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s < n, which also contains the same hull.We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p à q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) < n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q)