On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Linear-time triangulation of a simple polygon made easier via randomization
Proceedings of the sixteenth annual symposium on Computational geometry
Approximation algorithms for layered manufacturing
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
An Efficient k Nearest Neighbor Searching Algorithm for a Query Line
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Higher Order Delaunay Triangulations
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Incremental constructions con BRIO
Proceedings of the nineteenth annual symposium on Computational geometry
An efficient k nearest neighbors searching algorithm for a query line
Theoretical Computer Science
Dynamic Planar Convex Hull Operations in Near-Logarithmic Amortized Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Taking a Walk in a Planar Arrangement
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
PERCOM '03 Proceedings of the First IEEE International Conference on Pervasive Computing and Communications
Spatial queries in wireless broadcast systems
Wireless Networks - Special issue: Pervasive computing and communications
Computational Geometry: Theory and Applications
The interface between computational and combinatorial geometry
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Detecting cuts in sensor networks
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Euclidean push-pull partial covering problems
Computers and Operations Research
Region-restricted clustering for geographic data mining
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Note: Computing closest and farthest points for a query segment
Theoretical Computer Science
Region-restricted clustering for geographic data mining
Computational Geometry: Theory and Applications
Near-linear approximation algorithms for geometric hitting sets
Proceedings of the twenty-fifth annual symposium on Computational geometry
Obstacle discovery in distributed actuator and sensor networks
ACM Transactions on Sensor Networks (TOSN)
Algorithms and theory of computation handbook
Multi cover of a polygon minimizing the sum of areas
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
An output-sensitive approach for the L1/L∞k-nearest-neighbor Voronoi diagram
ESA'11 Proceedings of the 19th European conference on Algorithms
Higher order city voronoi diagrams
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Visualization of generalized voronoi diagrams
EGVISSYM'01 Proceedings of the 3rd Joint Eurographics - IEEE TCVG conference on Visualization
Covering a bichromatic point set with two disjoint monochromatic disks
Computational Geometry: Theory and Applications
Nearest neighbor searching under uncertainty II
Proceedings of the 32nd symposium on Principles of database systems
Information Processing Letters
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We give simple randomized incremental algorithms for computing the Amk-level in an arrangement of n lines in the plane or in an arrangement of n planes in $\Reals^3$. The expected running time of our algorithms is $O(nk+n\alpha(n)\log n)$ for the planar case and O(nk2 + n log3 n) for the three-dimensional case. Both bounds are optimal unless k is very small. The algorithm generalizes to computing the Amk-level in an arrangement of discs or x-monotone Jordan curves in the plane. Our approach can also compute the k-level; this yields a randomized algorithm for computing the order-k Voronoi diagram of n points in the plane in expected time O(k(n-k)log n + n log3 n).