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.
CITATION STYLE
Çela, E., Klinz, B., Lendl, S., Orlin, J. B., Woeginger, G. J., & Wulf, L. (2021). Linearizable Special Cases of the Quadratic Shortest Path Problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12911 LNCS, pp. 245–256). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-86838-3_19
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