Disser, Y., Feldmann, A.E. orcid.org/0000-0001-6229-5332, Klimm, M. et al. (1 more author) (2021) Travelling on graphs with small highway dimension. Algorithmica, 83 (5). pp. 1352-1370. ISSN 0178-4617
Abstract
We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter roughly measures how many central nodes are visited by all shortest paths of a certain length. It has been shown that transportation networks, on which TSP and STP naturally occur for various applications in logistics, typically have a small highway dimension. While it was previously shown that these problems admit a quasi-polynomial time approximation scheme on graphs of constant highway dimension, we demonstrate that a significant improvement is possible in the special case when the highway dimension is 1. Specifically, we present a fully-polynomial time approximation scheme (FPTAS). We also prove that both TSP and STP are weakly NP-hard for these restricted graphs.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 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: | Travelling Salesperson; Steiner Tree; Highway dimension; Approximation scheme; NP-Hardness |
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 15:05 |
Last Modified: | 28 Jun 2023 09:25 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s00453-020-00785-5 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200946 |