Motivated by a technique in privacy protection, in which n points are randomly perturbed by at most a distance r, we study the following problem: Given n points and m circles in the plane, what is the maximum r such that the number of points included in each circle does not change? We also consider a more general question, where we allow the number of points included in each circle to change by a certain factor. We discuss several algorithms for the problems, analyze what parameters of the input influence their running times, and consider a special case where the circles are aligned on a grid, which has important applications.

Peer Reviewed