(n,1,1,α)-Center Problem

Given a set  of  points in the plane and a constant ,-center problem is to find two closed disks which each covers the whole , the diameter of the bigger one is minimized, and the distance of the two centers is at least . Constrained -center problem is the -center problem in which the centers are forced to lie on a given line . In this paper, we first introduce -center problem and its constrained version. Then, we present an  algorithm for solving the -center problem. Finally, we propose a linear time algorithm for its constrained version.