A Constant-Factor Approximation Algorithm for the k-Median Problem

• Published in: Journal of computer and system sciences Vol. 65; no. 1; pp. 129 - 149
• Main Authors: Charikar, Moses, Guha, Sudipto, Tardos, Éva, Shmoys, David B.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.08.2002
• ISSN: 0022-0000; 1090-2724
• DOI: 10.1006/jcss.2002.1882

We present the first constant-factor approximation algorithm for the metric k-median problem. The k-median problem is one of the most well-studied clustering problems, i.e., those problems in which the aim is to partition a given set of points into clusters so that the points within a cluster are relatively close with respect to some measure. For the metric k-median problem, we are given n points in a metric space. We select k of these to be cluster centers and then assign each point to its closest selected center. If point j is assigned to a center i, the cost incurred is proportional to the distance between i and j. The goal is to select the k centers that minimize the sum of the assignment costs. We give a 6 2 3 -approximation algorithm for this problem. This improves upon the best previously known result of O(log k log log k), which was obtained by refining and derandomizing a randomized O(log n log log n)-approximation algorithm of Bartal.