Min-sum clustering (with outliers)

Sandip Banerjee, Rafail Ostrovsky, Yuval Rabani

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to compute a solution that clusters 98% of the input data points and pays no more than a constant factor times the optimal solution that clusters 99% of the input data points. More generally, we give the following bicriteria approximation: For any ϵ > 0, for any instance with n input points and for any positive integer n ≤ n, we compute in polynomial time a clustering of at least (1 − ϵ)n points of cost at most a constant factor greater than the optimal cost of clustering n points. The approximation guarantee grows with 1ϵ. Our results apply to instances of points in real space endowed with squared Euclidean distance, as well as to points in a metric space, where the number of clusters, and also the dimension if relevant, is arbitrary (part of the input, not an absolute constant).

Original languageAmerican English
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021
EditorsMary Wootters, Laura Sanita
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772075
DOIs
StatePublished - 1 Sep 2021
Event24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2021 and 25th International Conference on Randomization and Computation, RANDOM 2021 - Virtual, Seattle, United States
Duration: 16 Aug 202118 Aug 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume207
ISSN (Print)1868-8969

Conference

Conference24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2021 and 25th International Conference on Randomization and Computation, RANDOM 2021
Country/TerritoryUnited States
CityVirtual, Seattle
Period16/08/2118/08/21

Bibliographical note

Publisher Copyright:
© Sandip Banerjee, Rafail Ostrovsky, and Yuval Rabani; licensed under Creative Commons License CC-BY 4.0

Keywords

  • Approximation algorithms
  • Clustering
  • Primal-dual

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