The reverse greedy algorithm for the metric k-median problem

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 total distance 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 Omega(log n/log log n) and O(log n). (c) 2005 Elsevier B.V. All rights reserved.