Abstract
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 / 3 log 2 n ) 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 ( n log n ) 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 3 log n ) time.
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