The priority k-median problem

Abstract

In this paper, we consider a generalized version of the k-median problem in metric spaces, called the priority k-median problem in which demands and facilities have priorities associated with them and a demand can only be assigned to a facility that has the same priority or better. We show that there exists a polynomial time constant factor approximation algorithm for this problem when there are two priorities. We also show that the natural integer program for the problem has an arbitrarily large integrality gap when there are four or more priorities. © Springer-Verlag Berlin Heidelberg 2007.