Quick Algorithms for the k(<10)-Center Problem

Quick algorithms for solving 3 center problem, 4 center problem, 5 center problem and k(<10) center problems are proposed. This algorithm is designed in terms of which the convex hulls covering a set of points must cover the set of points. The algorithm decides first the character of the convex hulls of the point set. It then determines the mode of arrangement of k circles and finally computes the positions of the circular centers by the mode determined. The paper also proves their correctness and analyzes their time complexity.