An Efficient Algorithm of the Planar 3-Center Problem for a set of the convex position points

Abstract

The planar 3-center problem for a set S of points given in the plane asks for three congruent circular disks with the minimum radius, whose union can cover all points of S completely. In this paper, we present an O(n2 log3n) time algorithm for a restricted planar 3-center problem in which the given points are in the convex positions , i.e. The given points are the vertices of a convex polygon exactly.