Abbasi, F., Banerjee, S., Byrka, J. et al. (6 more authors) (2023) Parameterized approximation schemes for clustering with general norm objectives. In: 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS) Proceedings. 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 06-09 Nov 2023, Santa Cruz, CA, USA. Institute of Electrical and Electronics Engineers (IEEE) , pp. 1377-1399. ISBN 9798350318951
Abstract
This paper considers the well-studied algorithmic regime of designing a (1+ϵ)-approximation algorithm for a k-clustering problem that runs in time f(k,ϵ)poly(n) (sometimes called an efficient parameterized approximation scheme or EPAS for short). Notable results of this kind include EPASes in the high-dimensional Euclidean setting for k-center [Badŏiu, Har-Peled, Indyk; STOC'02] as well as k-median, and k-means [Kumar, Sabharwal, Sen; J. ACM 2010]. However, existing EPASes handle only basic objectives (such as k-center, k-median, and k-means) and are tailored to the specific objective and metric space. Our main contribution is a clean and simple EPAS that settles more than ten clustering problems (across multiple well-studied objectives as well as metric spaces) and unifies well-known EPASes. Our algorithm gives EPASes for a large variety of clustering objectives (for example, k-means, k-center, k-median, priority k-center, ℓ-centrum, ordered k-median, socially fair k-median aka robust k-median, or more generally monotone norm k-clustering) and metric spaces (for example, continuous high-dimensional Euclidean spaces, metrics of bounded doubling dimension, bounded treewidth metrics, and planar metrics). Key to our approach is a new concept that we call bounded ϵ-scatter dimension--an intrinsic complexity measure of a metric space that is a relaxation of the standard notion of bounded doubling dimension. Our main technical result shows that two conditions are essentially sufficient for our algorithm to yield an EPAS on the input metric M for any clustering objective: (i) The objective is described by a monotone (not necessarily symmetric!) norm, and (ii) the ϵ-scatter dimension of M is upper bounded by a function of ϵ.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 The Authors. Except as otherwise noted, this author-accepted version of a paper published in 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS) Proceedings is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ |
Keywords: | clustering; parameterized approximation algorithms; scattered dimension; norm clustering |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 11 Jul 2023 12:04 |
Last Modified: | 12 Jan 2024 14:19 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Refereed: | Yes |
Identification Number: | 10.1109/FOCS57990.2023.00085 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:201314 |
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