Linearizable Special Cases of the Quadratic Shortest Path Problem

Eranda Dragoti-Cela, Bettina Klinz, Stefan Lendl, James B. Orlin, Gerhard Woeginger, Lasse Wulf

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in einem KonferenzbandBegutachtung

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.
Originalspracheenglisch
TitelGraph-Theoretic Concepts in Computer Science
UntertitelWG 2021
Redakteure/-innenŁukasz Kowalik, Michał Pilipczuk, Pawel Rzążewski
Herausgeber (Verlag)Springer
Seiten245-256
Seitenumfang12
ISBN (Print)9783030868376
DOIs
PublikationsstatusVeröffentlicht - 20 Sep 2021
Veranstaltung47th International Workshop on Graph-Theoretic Concepts in Computer Science: WG 2021 - Warsaw, Polen
Dauer: 23 Jun 202125 Jun 2021

Publikationsreihe

NameSpringer Lecture Notes in Computer Science
Herausgeber (Verlag)Springer
Band12911

Konferenz

Konferenz47th International Workshop on Graph-Theoretic Concepts in Computer Science
KurztitelWG 2021
LandPolen
OrtWarsaw
Zeitraum23/06/2125/06/21

ASJC Scopus subject areas

  • Mathematik (insg.)

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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