Disser, Yann ; Feldmann, Andreas Emil ; Klimm, Max ; Könemann, Jochen (2021)
Travelling on Graphs with Small Highway Dimension.
In: Algorithmica, 83 (5)
doi: 10.1007/s00453-020-00785-5
Artikel, Bibliographie
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2021 |
| Autor(en): | Disser, Yann ; Feldmann, Andreas Emil ; Klimm, Max ; Könemann, Jochen |
| Art des Eintrags: | Bibliographie |
| Titel: | Travelling on Graphs with Small Highway Dimension |
| Sprache: | Englisch |
| Publikationsjahr: | Mai 2021 |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Algorithmica |
| Jahrgang/Volume einer Zeitschrift: | 83 |
| (Heft-)Nummer: | 5 |
| DOI: | 10.1007/s00453-020-00785-5 |
| URL / URN: | https://link.springer.com/article/10.1007/s00453-020-00785-5 |
| Kurzbeschreibung (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. |
| Fachbereich(e)/-gebiet(e): | Exzellenzinitiative Exzellenzinitiative > Graduiertenschulen Exzellenzinitiative > Graduiertenschulen > Graduate School of Computational Engineering (CE) |
| Hinterlegungsdatum: | 15 Jul 2022 06:54 |
| Letzte Änderung: | 15 Dez 2022 12:18 |
| PPN: | 502667982 |
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