Parallelizability of Some P-Complete Geometric Problems in the EREW-PRAM
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Point set stratification and Delaunay depth
Computational Statistics & Data Analysis
Algorithms for bivariate zonoid depth
Computational Geometry: Theory and Applications
Algorithms for optimal outlier removal
Journal of Discrete Algorithms
Computational Geometry: Theory and Applications
Convex onion peeling genetic algorithm: an efficient solution to map labeling of point-feature
Proceedings of the 2010 ACM Symposium on Applied Computing
On the red/blue spanning tree problem
Theoretical Computer Science
Unions of onions: preprocessing imprecise points for fast onion layer decomposition
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
| Hi-index | 754.84 |
LetSbe a set ofnpoints in the Euclidean plane. The convex layers ofSare the convex polygons obtained by iterating on the following procedure: compute the convex hull ofSand remove its vertices fromS. 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 morphology of a set of sites and has proven to be an efficient preconditioning for range search problems. An optimal algorithm is described for computing the convex layers of S. The algorithm runs in0 (n log n)time and requiresO(n)space. Also addressed is the problem of determining the depth of a query point within the convex layers ofS, 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.