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.
['Sergio Cabello', 'J. Miguel Díaz-Báòez', 'Carlos Seara', 'J. Antoni Sellarès', 'Jorge Urrutia', 'Inmaculada Ventura']
Covering point sets with two disjoint disks or squares