An optimal convex hull algorithm in any fixed dimension

Abstract

We present a deterministic algorithm for computing the convex hull of n points in Ed in optimal O(n log n+n{down left corner}d/2{down right corner} ) time. Optimal solutions were previously known only in even dimension and in dimension 3. A by-product of our result is an algorithm for computing the Voronoi diagram of n points in d-space in optimal O(n log n+n{top left corner}d/2{top right corner} ) time. © 1993 Springer-Verlag New York Inc.