2026-07-24T08:08:33Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16379 2024-03-06T10:57:19Z ddc:004 open_access

Polylogarithmic Sketches for Clustering Charikar, Moses Waingarten, Erik sketching clustering Given n points in 𝓁_p^d, we consider the problem of partitioning points into k clusters with associated centers. The cost of a clustering is the sum of p-th powers of distances of points to their cluster centers. For p ∈ [1,2], we design sketches of size poly(log(nd),k,1/ε) such that the cost of the optimal clustering can be estimated to within factor 1+ε, despite the fact that the compressed representation does not contain enough information to recover the cluster centers or the partition into clusters. This leads to a streaming algorithm for estimating the clustering cost with space poly(log(nd),k,1/ε). We also obtain a distributed memory algorithm, where the n points are arbitrarily partitioned amongst m machines, each of which sends information to a central party who then computes an approximation of the clustering cost. Prior to this work, no such streaming or distributed-memory algorithm was known with sublinear dependence on d for p ∈ [1,2). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Moses Charikar and Erik Waingarten 2022 Is Part Of LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2022.38 urn:nbn:de:0030-drops-163793 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.38 eng https://creativecommons.org/licenses/by/4.0/legalcode