Discrete & Computational Geometry

, Volume 10, Issue 4, pp 377-409

First online:

An optimal convex hull algorithm in any fixed dimension

  • Bernard ChazelleAffiliated withDepartment of Computer Science, Princeton University

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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.