# An optimal convex hull algorithm in any fixed dimension

## Authors

Article

- First Online:

- Received:
- Revised:

DOI: 10.1007/BF02573985

- Cite this article as:
- Chazelle, B. Discrete Comput Geom (1993) 10: 377. doi:10.1007/BF02573985

- 81 Citations
- 421 Views

## Abstract

We present a deterministic algorithm for computing the convex hull of*n* points in*E*^{d} in optimal*O*(*n* log*n*+*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 of*n* points in*d*-space in optimal*O*(*n* log*n*+*n*^{⌜d/2⌝}) time.

## Copyright information

© Springer-Verlag New York Inc. 1993