Information centre allocation

A large number of potential sites are given and we have to choose k sites in order to set up information centres, where each centre is able to serve a limited number ofclients. The price a client pays for accessing a centre is proportional to the distance between the client and the centre. This problem belongs to a class of problems for which most theoretical computer scientists believe that there is no fast algorithm for finding an optimal solution. We therefore look for algorithms that produce an approximate solution. In this paper we present a fast algorithm that chooses k sites and assigns the clients to the centres in such a way that the maximum price a client pays is at most nine times the maximum price in an optimal solution. This algorithm works under the assumption that the number of chosen sites is small in comparison to the number of possible sites.