Feldmann, A.E. orcid.org/0000-0001-6229-5332 and Saulpic, D. orcid.org/0000-0003-4208-8541 (2021) Polynomial time approximation schemes for clustering in low highway dimension graphs. Journal of Computer and System Sciences, 122. pp. 72-93. ISSN 0022-0000
Abstract
We study clustering problems such as k-Median, k-Means, and Facility Location in graphs of low highway dimension, which is a graph parameter modeling transportation networks. It was previously shown that approximation schemes for these problems exist, which either run in quasi-polynomial time (assuming constant highway dimension) (Feldmann et al., 2018) [8] or run in FPT time (parameterized by the number of clusters k, the highway dimension, and the approximation factor) (Becker et al., 2018; Braverman et al., 2021) [9], [10]. In this paper we show that a polynomial-time approximation scheme (PTAS) exists (assuming constant highway dimension). We also show that the considered problems are NP-hard on graphs of highway dimension 1.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Elsevier Inc. This is an author produced version of a paper subsequently published in Journal of Computer and System Sciences. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Approximation algorithm; Highway dimension; 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: | 28 Jun 2023 08:37 |
Last Modified: | 28 Jun 2023 08:39 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.jcss.2021.06.002 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200940 |