Approximation schemes for clustering problems

W. Fernandez de la Vega, Marek Karpinski, Claire Kenyon, Yuval Rabani

Research output: Contribution to journalConference articlepeer-review

119 Scopus citations


Let k be a fixed integer. We consider the problem of partitioning an input set of points endowed with a distance function into k clusters. We give polynomial time approximation schemes for the following three clustering problems: Metric k-Clustering, ℓ22 k-Clustering, and ℓ22 k-Median. In the k-Clustering problem, the objective is to minimize the sum of all intra-cluster distances. In the k-Median problem, the goal is to minimize the sum of distances from points in a cluster to the (best choice of) cluster center. In metric instances, the input distance function is a metric. In ℓ22 instances, the points are in ℝd and the distance between two points x, y is measured by ||x - y||22 (notice that (ℝd, || · ||22) is not a metric space). For the first two problems, our results are the first polynomial time approximation schemes. For the third problem, the running time of our algorithms is a vast improvement over previous work.

Original languageAmerican English
Pages (from-to)50-58
Number of pages9
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
StatePublished - 2003
Externally publishedYes
Event35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States
Duration: 9 Jun 200311 Jun 2003


  • Algorithms
  • Theory


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