On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
On levels in arrangements and Voronoi diagrams
Discrete & Computational Geometry
Fat triangles determine linearly many holes
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Reporting points in halfspaces
Computational Geometry: Theory and Applications
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The complexity of the union of (&agr;, &bgr;)-covered objects
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
When crossings count — approximating the minimum spanning tree
Proceedings of the sixteenth annual symposium on Computational geometry
Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
SIAM Journal on Computing
Computational Geometry: Theory and Applications
Learning in Neural Networks: Theoretical Foundations
Learning in Neural Networks: Theoretical Foundations
Determining the Separation of Preprocessed Polyhedra - A Unified Approach
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Low-Dimensional Linear Programming with Violations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
High-dimensional computational geometry
High-dimensional computational geometry
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
SIAM Journal on Computing
The Clarkson–Shor Technique Revisited and Extended
Combinatorics, Probability and Computing
Robust shape fitting via peeling and grating coresets
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Computing longest duration flocks in trajectory data
GIS '06 Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems
On approximate halfspace range counting and relative epsilon-approximations
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
On approximate range counting and depth
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Covering point sets with two disjoint disks or squares
Computational Geometry: Theory and Applications
Stabbing Convex Polygons with a Segment or a Polygon
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Shape Matching by Random Sampling
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
A general approach for cache-oblivious range reporting and approximate range counting
Proceedings of the twenty-fifth annual symposium on Computational geometry
Efficient Sensor Placement for Surveillance Problems
DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
Probabilistic matching of planar regions
Computational Geometry: Theory and Applications
A general approach for cache-oblivious range reporting and approximate range counting
Computational Geometry: Theory and Applications
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Covering many or few points with unit disks
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Shape matching by random sampling
Theoretical Computer Science
A scalable algorithm for maximizing range sum in spatial databases
Proceedings of the VLDB Endowment
The resilience of WDM networks to probabilistic geographical failures
IEEE/ACM Transactions on Networking (TON)
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In this paper, we study the problem of finding a disk covering the largest number of red points, while avoiding all the blue points. We reduce it to the question of finding a deepest point in an arrangement of pseudodisks and provide a near-linear expected-time randomized approximation algorithm for this problem. As an application of our techniques, we show how to solve linear programming with violations approximately. We also prove that approximate range counting has roughly the same time and space complexity as answering emptiness range queries.