Planar point location using persistent search trees
Communications of the ACM
On k-hulls and related problems
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Globally-Equiangular triangulations of co-circular points in 0(n log n) time
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Symbolic treatment of geometric degeneracies
Journal of Symbolic Computation
A general approach to removing degeneracies
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Integrating robust clustering techniques in S-PLUS
Computational Statistics & Data Analysis
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Lower bounds for computing statistical depth
Computational Statistics & Data Analysis
C2P: Clustering based on Closest Pairs
Proceedings of the 27th International Conference on Very Large Data Bases
Efficient computation of location depth contours by methods of computational geometry
Statistics and Computing
A lower bound for computing Oja depth
Information Processing Letters
On the convex layers of a planar set
IEEE Transactions on Information Theory
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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In the study of depth functions it is important to decide whether a depth function is required to be sensitive to multimodality. An analysis of the Delaunay depth function shows that it is sensitive to multimodality. This notion of depth can be compared to other depth functions such as the convex and location depths. The stratification that Delaunay depth induces in the point set (layers) and in the whole plane (levels) is investigated. An algorithm for computing the Delaunay depth contours associated with a point set in the plane is developed. The worst case and expected complexities of the algorithm are O(nlog^2n) and O(nlogn), respectively. The depth of a query point p with respect to a data set S in the plane is the depth of p in S@?{p}. The Delaunay depth can be computed in O(nlogn) time, which is proved to be optimal, when S and p are given in the input.