Mixed Materials
Clustering in Varying Metrics
| Τίτλος: | Clustering in Varying Metrics |
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| Additional Titles: | We introduce the aggregated clustering problem, where one is given T instances of a center-based clustering task over the same n points, but under different metrics. The goal is to open k centers to minimize an aggregate of the clustering costs - e.g., the average or maximum - where the cost is measured via k-center/median/means objectives. More generally, we minimize a norm Ψ over the T cost values. We show that for T ≥ 3, the problem is inapproximable to any finite factor in polynomial time. For T = 2, we give constant-factor approximations. We also show W[2]-hardness when parameterized by k, but obtain f(k,T)poly(n)-time 3-approximations when parameterized by both k and T. When the metrics have structure, we obtain efficient parameterized approximation schemes (EPAS). If all T metrics have bounded ε-scatter dimension, we achieve a (1+ε)-approximation in f(k,T,ε)poly(n) time. If the metrics are induced by edge weights on a common graph G of bounded treewidth tw, and Ψ is the sum function, we get an EPAS in f(T,ε,tw)poly(n,k) time. Conversely, unless (randomized) ETH is false, any finite factor approximation is impossible if parametrized by only T, even when the treewidth is tw = Ω(polylog n). |
| Συγγραφείς: | Deeparnab Chakrabarty and Jonathan Conroy and Ankita Sarkar, Chakrabarty, Deeparnab, Conroy, Jonathan, Sarkar, Ankita |
| Στοιχεία εκδότη: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik 2025 |
| Τύπος εγγράφου: | Mixed materials |
| Όροι ευρετηρίου: | Clustering, approximation algorithms, LP rounding, parameterized and exact algorithms, dynamic programming, fixed parameter tractability, hardness of approximation, InProceedings, Text, doc-type:ResearchArticle, publishedVersion |
| DOI: | 10.4230.LIPIcs.FSTTCS.2025.19 |
| Σύνδεσμος: | Is Part Of LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025) |
| Διαθεσιμότητα: | Open access content. Open access content https://creativecommons.org/licenses/by/4.0/legalcode |
| Σημείωση: | application/pdf English |
| Other Numbers: | DEDAG oai:drops-oai.dagstuhl.de:25100 doi:10.4230/LIPIcs.FSTTCS.2025.19 urn:nbn:de:0030-drops-251007 1567998551 |
| Πηγή συνεισφοράς: | SCHLOSS DAGSTUHL LEIBNIZ ZENTRUM GMBH From OAIster®, provided by the OCLC Cooperative. |
| Αριθμός Καταχώρησης: | edsoai.on1567998551 |
| Βάση Δεδομένων: | OAIster |
| DOI: | 10.4230.LIPIcs.FSTTCS.2025.19 |
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