An efficient algorithm for the connected two-center problem

Abstract

This paper considers the connected two-center problem, which is to find two congruent closed discs of smallest radius whose union covers a set of n given points in the plane and whose centers are close as specified connectivity. The previously best known algorithm for this problem is straightforward and based on the exhaustive searching paradigm shich leads to O(n5)time complexity. In this paper, we design an O(n3)time algorithm for solving the problem by using a new data structure called center-hull, which has rather close relationships with the farthest-point voronoi diagram. The properties of center-hull are also discussed in this paper.