2026-07-23T21:56:21Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14709 2024-03-06T10:54:42Z ddc:004 open_access

Min-Sum Clustering (With Outliers) Banerjee, Sandip Ostrovsky, Rafail Rabani, Yuval Clustering approximation algorithms primal-dual 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 1/(ε). 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). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sandip Banerjee and Rafail Ostrovsky and Yuval Rabani 2021 Is Part Of LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2021.16 urn:nbn:de:0030-drops-147093 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.16 eng https://creativecommons.org/licenses/by/4.0/legalcode