# An optimal convex hull algorithm in any fixed dimension

@article{Chazelle1993AnOC, title={An optimal convex hull algorithm in any fixed dimension}, author={Bernard Chazelle}, journal={Discrete \& Computational Geometry}, year={1993}, volume={10}, pages={377-409} }

We present a deterministic algorithm for computing the convex hull ofn points inEd 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.

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## 362 Citations

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