Minimum Separating Circle for Bichromatic Points in the Plane

Consider two point sets in the plane, a red set of size n, and a blue set of size m. In this paper we show how to find the minimum separating circle, which is the smallest circle that contains all points of the red set and as few points as possible of the blue set in its interior. If multiple minimum separating circles exist our algorithm finds all of them. We also give an exact solution for finding the largest separating circle that contains all points of the red set and as few points as possible of the blue set in its interior. Our solutions make use of the farthest neighbor Voronoi Diagram of point sites.