Projects per year
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.
Original language | English |
---|---|
Title of host publication | Graph-Theoretic Concepts in Computer Science |
Subtitle of host publication | WG 2021 |
Editors | Łukasz Kowalik, Michał Pilipczuk, Pawel Rzążewski |
Publisher | Springer |
Pages | 245-256 |
Number of pages | 12 |
ISBN (Print) | 9783030868376 |
DOIs | |
Publication status | Published - 20 Sept 2021 |
Event | 47th International Workshop on Graph-Theoretic Concepts in Computer Science: WG 2021 - Warsaw, Poland Duration: 23 Jun 2021 → 25 Jun 2021 |
Publication series
Name | Springer Lecture Notes in Computer Science |
---|---|
Publisher | Springer |
Volume | 12911 |
Conference
Conference | 47th International Workshop on Graph-Theoretic Concepts in Computer Science |
---|---|
Abbreviated title | WG 2021 |
Country/Territory | Poland |
City | Warsaw |
Period | 23/06/21 → 25/06/21 |
Keywords
- quadratic shortest path problem
- linearizable instances
- Computational complexity
- special cases
ASJC Scopus subject areas
- Mathematics(all)
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)
Fingerprint
Dive into the research topics of 'Linearizable Special Cases of the Quadratic Shortest Path Problem'. Together they form a unique fingerprint.Projects
- 1 Active
-
Doctoral Program: Discrete Mathematics
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
Project: Research project