Separating Point Sets by Circles, and the Recognition of Digital Disks

Abstract

Given two sets A and B of points in the plane, we give a polynomial time algorithm to find the set S of points which are centers of circles that contain all the members of A and none of B. A consequence of the algorithm is that S is polygonal. Another application is an O(N2) time and O(N2) space algorithm for the recognition of digital disks.