Computational geometry: an introduction
Computational geometry: an introduction
Computing
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
An Expander-Based Approach to Geometric Optimization
SIAM Journal on Computing
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
On approximating the depth and related problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Euclidean push-pull partial covering problems
Computers and Operations Research
Covering many or few points with unit disks
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Covering many or few points with unit disks
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Covering a bichromatic point set with two disjoint monochromatic disks
Computational Geometry: Theory and Applications
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We study the following problem: Given a set of red points and a set of blue points on the plane, find two unit disks C"R and C"B with disjoint interiors such that the number of red points covered by C"R plus the number of blue points covered by C"B is maximized. We give an algorithm to solve this problem in O(n^8^/^3log^2n) time, where n denotes the total number of points. We also show that the analogous problem of finding two axis-aligned unit squares S"R and S"B instead of unit disks can be solved in O(nlogn) time, which is optimal. If we do not restrict ourselves to axis-aligned squares, but require that both squares have a common orientation, we give a solution using O(n^3logn) time.