Given a planar point set, we wish to label the points with uniform circular labels such that each input point lies on the boundary of two labels, none of the interiors of the labels intersect, and the size of the labels is maximized. This problem is known as map-labeling with uniform circular pairs (MLUCP) and has been shown to be NP-hard. In this paper, we give an O(nlogn) time, O(n) space algorithm that computes a labeling, such that the diameter of the circular labels in an optimum solution is no more than (1 +
Michael J. Spriggs, J. Mark Keil