An optimal convex hull algorithm in any fixed dimension
- First Online:
- 462 Downloads
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.
Unable to display preview. Download preview PDF.
- 5.Chazelle, B., Matoušek, J. Derandomizing an output-sensitive convex hull algorithm in three dimensions (submitted for publication).Google Scholar
- 7.Clarkson, K. L. Randomized geometric algorithms, inEuclidean Geometry and Computers, D. Z. Du and F. K. Hwang, eds., World Scientific, to appear.Google Scholar
- 13.Matoušek, J. Approximations and optimal geometric divide-and-conquer,Proc. 23rd Annual ACM Symp. on Theory of Computing, 1991, pp. 505–511.Google Scholar
- 14.Matoušek, J. Efficient partition trees,Proc. 7th Annual ACM Symp. on Computational Geometry, 1991, pp. 1–9.Google Scholar
- 16.Matoušek, J. Linear optimization queries,J. Algorithms, to appear.Google Scholar
- 19.Seidel, R. A convex hull algorithm optimal for point sets in even dimensions, Technical Report 81-14, University of British Columbia, 1981.Google Scholar
- 20.Seidel, R. Constructing higher-dimensional convex hulls at logarithmic cost per face,Proc. 18th Annual ACM Symp. on Theory of Computing, 1986, pp. 404–413.Google Scholar