In this paper, we present a randomized constant factor approximation
algorithm for the metric minimum facility location problem with uniform
costs and demands in a distributed setting, in which every point can
open a facility. In particular, our distributed algorithm uses three
communication rounds with message sizes bounded to O(log n) bits where
n is the number of points. We also extend our algorithm to constant
powers of metric spaces, where we also obtain a randomized constant
factor approximation algorithm.