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We present a deterministic algorithm for computing the convex hull ofn points inE  d  in optimalO(n logn+n  ⌞d/2⌟ ) 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 ofn points ind-space in optimalO(n logn+n  ⌜d/2⌝ ) time.

An optimal convex hull algorithm in any fixed dimension