On the convex layers of a planar set (1985)
Cached
Download Links
- [www.cs.princeton.edu]
- [www.cs.fudan.edu.cn]
- DBLP
Other Repositories/Bibliography
| Venue: | IEEE Transactions on Information Theory |
| Citations: | 53 - 1 self |
BibTeX
@ARTICLE{Chazelle85onthe,
author = {Bernard Chazelle},
title = {On the convex layers of a planar set},
journal = {IEEE Transactions on Information Theory},
year = {1985},
volume = {31},
pages = {509--517}
}
Years of Citing Articles
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
Abstract-Let S be a set of n points in the Euclidean plane. The convex layers of S are the convex polygons obtained by iterating on the following procedure: compute the convex hull of S and remove its vertices from S. This process of peeling a planar point set is central in the study of robust estimators in statistics. It also provides valuable information on the mor-phology of a set of sites and has proven to be an efficient preconditioning for range search problems. An optimal algorithm is described for comput-ing the convex layers of S. The algorithm runs in O ( n log n) time and requires O(n) space. Also addressed is the problem of determining the depth of a query point within the convex layers of S, i.e., the number of layers that enclose the query point. This is essentially a planar point location problem, for which optimal solutions are therefore known. Taking advantage of structural properties of the problem, however, a much simpler optimal solution is derived. L I.
