Academic Journal
Clustering in Varying Metrics
| Τίτλος: | Clustering in Varying Metrics |
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| Συγγραφείς: | Chakrabarty, Deeparnab, Conroy, Jonathan, Sarkar, Ankita |
| Συνεισφορές: | Deeparnab Chakrabarty and Jonathan Conroy and Ankita Sarkar |
| Στοιχεία εκδότη: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| Έτος έκδοσης: | 2025 |
| Συλλογή: | DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| Θεματικοί όροι: | Clustering, approximation algorithms, LP rounding, parameterized and exact algorithms, dynamic programming, fixed parameter tractability, hardness of approximation |
| Περιγραφή: | 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). |
| Τύπος εγγράφου: | article in journal/newspaper conference object |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Relation: | Is Part Of LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.19 |
| DOI: | 10.4230/LIPIcs.FSTTCS.2025.19 |
| Διαθεσιμότητα: | https://doi.org/10.4230/LIPIcs.FSTTCS.2025.19 https://nbn-resolving.org/urn:nbn:de:0030-drops-251007 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.19 |
| Rights: | https://creativecommons.org/licenses/by/4.0/legalcode |
| Αριθμός Καταχώρησης: | edsbas.2FBE2C79 |
| Βάση Δεδομένων: | BASE |
| DOI: | 10.4230/LIPIcs.FSTTCS.2025.19 |
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