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Abstract
The quadratic shortest path problem (QSPP) in a directed graph asks for a directed path from a given source vertex to a given sink vertex, so that the sum of the interaction costs over all pairs of arcs on the path is minimized. We consider special cases of the QSPP that are linearizable as a shortest path problem in the sense of Bookhold. If the QSPP on a directed graph is linearizable under all possible choices of the arc interaction costs, the graph is called universally linearizable.
We provide various combinatorial characterizations of universally linearizable graphs that are centered around the structure of source-to-sink paths and around certain forbidden subgraphs. Our characterizations lead to fast and simple recognition algorithms for universally linearizable graphs. Furthermore, we establish the intractability of deciding whether a concrete instance of the QSPP (with a given graph and given arc interaction costs) is linearizable.
We provide various combinatorial characterizations of universally linearizable graphs that are centered around the structure of source-to-sink paths and around certain forbidden subgraphs. Our characterizations lead to fast and simple recognition algorithms for universally linearizable graphs. Furthermore, we establish the intractability of deciding whether a concrete instance of the QSPP (with a given graph and given arc interaction costs) is linearizable.
Originalsprache | englisch |
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Titel | Graph-Theoretic Concepts in Computer Science |
Untertitel | WG 2021 |
Redakteure/-innen | Łukasz Kowalik, Michał Pilipczuk, Pawel Rzążewski |
Herausgeber (Verlag) | Springer |
Seiten | 245-256 |
Seitenumfang | 12 |
ISBN (Print) | 9783030868376 |
DOIs | |
Publikationsstatus | Veröffentlicht - 20 Sept. 2021 |
Veranstaltung | 47th International Workshop on Graph-Theoretic Concepts in Computer Science: WG 2021 - Warsaw, Polen Dauer: 23 Juni 2021 → 25 Juni 2021 |
Publikationsreihe
Name | Springer Lecture Notes in Computer Science |
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Herausgeber (Verlag) | Springer |
Band | 12911 |
Konferenz
Konferenz | 47th International Workshop on Graph-Theoretic Concepts in Computer Science |
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Kurztitel | WG 2021 |
Land/Gebiet | Polen |
Ort | Warsaw |
Zeitraum | 23/06/21 → 25/06/21 |
ASJC Scopus subject areas
- Mathematik (insg.)
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)
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DK Diskrete Mathematik
Ebner, O., Lehner, F., Greinecker, F., Burkard, R., Wallner, J., Elsholtz, C., Woess, W., Raseta, M., Bazarova, A., Krenn, D., Lehner, F., Kang, M., Tichy, R., Sava-Huss, E., Klinz, B., Heuberger, C., Grabner, P., Barroero, F., Cuno, J., Kreso, D., Berkes, I. & Kerber, M.
1/05/10 → 30/06/24
Projekt: Forschungsprojekt