Journal of Computer and System Sciences
Covering a set of points by two axis-parallel boxes
Information Processing Letters
Programming pearls: algorithm design techniques
Communications of the ACM
Principles of data mining
The Maximum Box Problem and its Application to Data Analysis
Computational Optimization and Applications
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
On Approximating the Depth and Related Problems
SIAM Journal on Computing
On the range maximum-sum segment query problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
The Maximum Box Problem for moving points in the plane
Journal of Combinatorial Optimization
Minimizing the error of linear separators on linearly inseparable data
Discrete Applied Mathematics
On the coarseness of bicolored point sets
Computational Geometry: Theory and Applications
Covering a bichromatic point set with two disjoint monochromatic disks
Computational Geometry: Theory and Applications
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Let S be a set of n points on the plane in general position such that its elements are colored red or blue. We study the following problem: Find a largest subset of S which can be enclosed by the union of two, not necessarily disjoint, axis-aligned rectanglesRandBsuch thatR (resp.B) contains only red (resp. blue) points. We prove that this problem can be solved in O(n^2logn) time and O(n) space. Our approach is based on solving some instances of Bentley's maximum-sum consecutive subsequence problem. We introduce the first known data structure to dynamically maintain the optimal solution of this problem. We show that our techniques can be used to efficiently solve a more general class of problems in data analysis.