Linearizable Special Cases of the Quadratic Shortest Path Problem

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

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

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.
Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science
Subtitle of host publicationWG 2021
EditorsŁukasz Kowalik, Michał Pilipczuk, Pawel Rzążewski
PublisherSpringer
Pages245-256
Number of pages12
ISBN (Print)9783030868376
DOIs
Publication statusPublished - 20 Sep 2021
Event47th International Workshop on Graph-Theoretic Concepts in Computer Science: WG 2021 - Warsaw, Poland
Duration: 23 Jun 202125 Jun 2021

Publication series

NameSpringer Lecture Notes in Computer Science
PublisherSpringer
Volume12911

Conference

Conference47th International Workshop on Graph-Theoretic Concepts in Computer Science
Abbreviated titleWG 2021
Country/TerritoryPoland
CityWarsaw
Period23/06/2125/06/21

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)

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