Computing the Rectilinear Center of Uncertain Points in the Plane

In this paper, we consider the rectilinear one-center problem on uncertain points in the plane. In this problem, we are given a set P of n (weighted) uncertain points in the plane and each uncertain point has m possible locations each associated with a probability for the point appearing at that location. The goal is to find a point q∗ in the plane which minimizes the maximum expected rectilinear distance from q∗ to all uncertain points of P , and q∗ is called a rectilinear center. We present an algorithm that solves the problem in O(mn) time. Since the input size of the problem is Θ(mn), our algorithm is optimal.