The reverse greedy algorithm for the metric k-median problem

Authors:
Marek Chrobak;Claire Kenyon;Neal Young
Affiliations:
Department of Computer Science, University of California, Riverside, CA;Computer Science Department, Brown University, Providence, RI;Department of Computer Science, University of California, Riverside, CA
Venue:
Information Processing Letters
Year:
2006

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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 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 Ω(log n/log log n) and O(log n).