Bichromatic separability with two boxes: A general approach
Journal of Algorithms
Near-linear approximation algorithms for geometric hitting sets
Proceedings of the twenty-fifth annual symposium on Computational geometry
Geometric pattern matching for point sets in the plane under similarity transformations
Information Processing Letters
Delaunay Triangulation of Imprecise Points Simplified and Extended
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Enclosing weighted points with an almost-unit ball
Information Processing Letters
Data Structures for Approximate Orthogonal Range Counting
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximating the Fréchet distance for realistic curves in near linear time
Proceedings of the twenty-sixth annual symposium on Computational geometry
Approximate Halfspace Range Counting
SIAM Journal on Computing
Efficient robust digital hyperplane fitting with bounded error
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
The Maximum Box Problem for moving points in the plane
Journal of Combinatorial Optimization
Semialgebraic Range Reporting and Emptiness Searching with Applications
SIAM Journal on Computing
The mono- and bichromatic empty rectangle and square problems in all dimensions
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
The complexity of geometric problems in high dimension
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Hardness of discrepancy computation and ε-net verification in high dimension
Journal of Complexity
Minimizing the error of linear separators on linearly inseparable data
Discrete Applied Mathematics
Covering a bichromatic point set with two disjoint monochromatic disks
Computational Geometry: Theory and Applications
Small-size relative (p,ε)-approximations for well-behaved range spaces
Proceedings of the twenty-ninth annual symposium on Computational geometry
Union of random minkowski sums and network vulnerability analysis
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We study the question of finding a deepest point in an arrangement of regions and provide a fast algorithm for this problem using random sampling, showing it sufficient to solve this problem when the deepest point is shallow. This implies, among other results, a fast algorithm for approximately solving linear programming problems with violations. We also use this technique to approximate the disk covering the largest number of red points, while avoiding all the blue points, given two such sets in the plane. Using similar techniques implies that approximate range counting queries have roughly the same time and space complexity as emptiness range queries.