Comparative Study of the Algorithms for the Weighted Rectilinear Min-Sum Facility Location Problem

Given a set of n points in R^d with nonnegative weights, we consider the weighted rectilinear min-sum facility problem to minimize the sum of weighted rectilinear distance between the given points and a new added point. We present four simple algorithms for the weighted rectilinear min-sum facility location problem. The computational experiments demonstrate that the achieved results are not only of theoretical interest, but also that the techniques developed may actually lead to considerably faster algorithms.