The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Cutting disjoint disks by straight lines
Discrete & Computational Geometry
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Randomized algorithms
Output-sensitive peeling of convex and maximal layers
Information Processing Letters
Computing Common Tangents Without a Separating Line
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Convex Layers: A New Tool for Recognition of Projectively Deformed Point Sets
CAIP '99 Proceedings of the 8th International Conference on Computer Analysis of Images and Patterns
Efficient Update Strategies for Geometric Computing with Uncertainty
Theory of Computing Systems
Triangulating input-constrained planar point sets
Information Processing Letters
Delaunay triangulation of imprecise points in linear time after preprocessing
Computational Geometry: Theory and Applications
A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
Journal of the ACM (JACM)
Preprocessing Imprecise Points and Splitting Triangulations
SIAM Journal on Computing
SIAM Journal on Computing
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
On the convex layers of a planar set
IEEE Transactions on Information Theory
Convex hull of points lying on lines in o(nlogn) time after preprocessing
Computational Geometry: Theory and Applications
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Let $\mathcal{D}$ be a set of n pairwise disjoint unit disks in the plane. We describe how to build a data structure for $\mathcal{D}$ so that for any point set P containing exactly one point from each disk, we can quickly find the onion decomposition (convex layers) of P. Our data structure can be built in O(n logn) time and has linear size. Given P, we can find its onion decomposition in O(n logk) time, where k is the number of layers. We also provide a matching lower bound. Our solution is based on a recursive space decomposition, combined with a fast algorithm to compute the union of two disjoint onion decompositions.