Article ID Journal Published Year Pages File Type
415845 Computational Geometry 2008 12 Pages PDF
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 CR and CB with disjoint interiors such that the number of red points covered by CR plus the number of blue points covered by CB is maximized. We give an algorithm to solve this problem in O(n8/3log2n) time, where n denotes the total number of points. We also show that the analogous problem of finding two axis-aligned unit squares SR and SB 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(n3logn) time.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics