Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Introduction to Algorithms
Towards Sensor Database Systems
MDM '01 Proceedings of the Second International Conference on Mobile Data Management
Pattern Classification (2nd Edition)
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Techniques for Efficient Road-Network-Based Tracking of Moving Objects
IEEE Transactions on Knowledge and Data Engineering
On Approximating the Depth and Related Problems
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Bichromatic separability with two boxes: A general approach
Journal of Algorithms
Review: Supervised classification and mathematical optimization
Computers and Operations Research
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Given a set R of r red points and a set B of b blue points in the plane, the static version of the Maximum Box Problem is to find an isothetic box H such that H驴R=驴 and the cardinality of H驴B is maximized. In this paper, we consider a kinetic version of the problem where the points in R驴B move along bounded degree algebraic trajectories. We design a compact and local quadratic-space kinetic data structure (KDS) for maintaining the optimal solution in O(rlog驴r+rlog驴b+b) time per each event. We also give an algorithm for solving the more general static problem where the maximum box can be arbitrarily oriented. This is an open problem in Aronov and Har-Peled (SIAM J. Comput. 38:899---921, 2008). We show that our approach can be used to solve this problem in O((r+b)2(rlog驴r+rlog驴b+b)) time. Finally we propose an efficient data structure to maintain an approximated solution of the kinetic Maximum Box Problem.