Abstract
Given a set S of n points in the plane and a constant α, the alpha-connected two-center problem is to find two congruent closed disks of the smallest radius covering S, such that the distance of the two centers is at most 2(1 - α)r. We present an O(n 2 log 2 n) expected-time algorithm for this problem, improving substantially the previous O(n 5 )-time solution. The algorithm translates the alpha-connected two-center problem into a distance problem between two circular hulls.