The reverse greedy algorithm for the metric k-median problem

Abstract

The Reverse Greedy algorithm (RGREEDY) for the k-median problem works as follows. It starts by placing facilities on all nodes. At each step, it removes a facility to minimize the resulting total distance from the customers to the remaining facilities. It stops when k facilities remain. We prove that, if the distance function is metric, then the approximation ratio of RGREEDY is between Ω (log n/log log n) and O(logn). © Springer-Verlag Berlin Heidelberg 2005.