Feldmann, A.E. orcid.org/0000-0001-6229-5332 (2019) Fixed-parameter approximations for k-Center problems in low highway dimension graphs. Algorithmica, 81 (3). pp. 1031-1052. ISSN 0178-4617
Abstract
We consider the k-Center problem and some generalizations. For k-Center a set of kcenter vertices needs to be found in a graph G with edge lengths, such that the distance from any vertex of G to its nearest center is minimized. This problem naturally occurs in transportation networks, and therefore we model the inputs as graphs with bounded highway dimension, as proposed by Abraham et al. (SODA, pp 782–793, 2010). We show both approximation and fixed-parameter hardness results, and how to overcome them using fixed-parameter approximations, where the two paradigms are combined. In particular, we prove that for any ε> 0 computing a (2 - ε) -approximation is W[2]-hard for parameter k, and NP-hard for graphs with highway dimension O(log 2 n). The latter does not rule out fixed-parameter (2 - ε) -approximations for the highway dimension parameter h, but implies that such an algorithm must have at least doubly exponential running time in h if it exists, unless ETH fails. On the positive side, we show how to get below the approximation factor of 2 by combining the parameters k and h: we develop a fixed-parameter 3 / 2-approximation with running time 2 O(khlogh) · n O(1) . Additionally we prove that, unless P=NP, our techniques cannot be used to compute fixed-parameter (2 - ε) -approximations for only the parameter h. We also provide similar fixed-parameter approximations for the weightedk-Center and (k, F) -Partition problems, which generalize k-Center.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Springer Science+Business Media, LLC, part of Springer Nature. This is an author-produced version of a paper subsequently published in Algorithmica. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Parameterized approximation; k-Center; 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: | 27 Jun 2023 15:50 |
Last Modified: | 28 Jun 2023 09:42 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s00453-018-0455-0 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200961 |