Feldmann, A.E. orcid.org/0000-0001-6229-5332 and Saulpic, D. (2020) Polynomial time approximation schemes for clustering in low highway dimension graphs. In: Grandoni, F., Herman, G. and Sanders, P., (eds.) Leibniz International Proceedings in Informatics, LIPIcs. 28th Annual European Symposium on Algorithms (ESA 2020), 07-09 Sep 2020, Pisa, Italy. Leibniz International Proceedings in Informatics, 173 . Schloss Dagstuhl - Leibniz-Zentrum , Dagstuhl, Germany , 46:1-46:22. ISBN 978-3-95977-162-7
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. SICOMP 2018] or run in FPT time (parameterized by the number of clusters k, the highway dimension, and the approximation factor) [Becker et al. ESA 2018, Braverman et al. 2020]. 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: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2020 The Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (https://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Approximation Scheme; Clustering; Highway Dimension |
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 13:30 |
Last Modified: | 28 Jun 2023 13:50 |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum |
Series Name: | Leibniz International Proceedings in Informatics |
Refereed: | Yes |
Identification Number: | 10.4230/LIPIcs.ESA.2020.46 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200949 |