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An optimal convex hull algorithm in any fixed dimension
 Bernard Chazelle
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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 byproduct of our result is an algorithm for computing the Voronoi diagram ofn points indspace in optimalO(n logn+n ^{ ⌜d/2⌝ }) time.
This research was supported in part by the National Science Foundation under Grant CCR9002352 and The Geometry Center, University of Minnesota, an STC funded by NSF, DOE, and Minnesota Technology, Inc. A preliminary version of this paper has appeared in “An optimal convex hull algorithm and new results on cuttings”,Proceedings of the 32nd Annual IEEE Symposium on the Foundations of Computer Science, October 1991, pp. 29–38. The convex hull algorithm given in the present paper, although similar in spirit, is considerably simpler than the one given in the proceedings.
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 Title
 An optimal convex hull algorithm in any fixed dimension
 Journal

Discrete & Computational Geometry
Volume 10, Issue 1 , pp 377409
 Cover Date
 19931201
 DOI
 10.1007/BF02573985
 Print ISSN
 01795376
 Online ISSN
 14320444
 Publisher
 SpringerVerlag
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 Authors

 Bernard Chazelle ^{(1)}
 Author Affiliations

 1. Department of Computer Science, Princeton University, 08544, Princeton, NJ, USA