A near-quadratic algorithm for the alpha-connected two-center problem

[[abstract]]Given a set S of n points in the plane and a constant alpha, 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 - alpha)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.[[fileno]]2030209010004[[department]]資訊工程學