Reconfiguration of Spanning Trees with Degree Constraint or Diameter Constraint

Nicolas Bousquet, Yusuke Kobayashi, Paul Ouvrard, Kunihiro Wasa, Takehiro Ito, Haruka Mizuta, Akira Suzuki

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

2 Citations (Scopus)

Abstract

We investigate the complexity of finding a transformation from a given spanning tree in a graph to another given spanning tree in the same graph via a sequence of edge flips. The exchange property of the matroid bases immediately yields that such a transformation always exists if we have no constraints on spanning trees. In this paper, we wish to find a transformation which passes through only spanning trees satisfying some constraint. Our focus is bounding either the maximum degree or the diameter of spanning trees, and we give the following results. The problem with a lower bound on maximum degree is solvable in polynomial time, while the problem with an upper bound on maximum degree is PSPACE-complete. The problem with a lower bound on diameter is NP-hard, while the problem with an upper bound on diameter is solvable in polynomial time.

Original languageEnglish
Title of host publication39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022
EditorsPetra Berenbrink, Benjamin Monmege
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772228
DOIs
Publication statusPublished - 2022 Mar 1
Event39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022 - Virtual, Marseille, France
Duration: 2022 May 152022 May 18

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume219
ISSN (Print)1868-8969

Conference

Conference39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022
Country/TerritoryFrance
CityVirtual, Marseille
Period22/5/1522/5/18

Keywords

  • Algorithms
  • Combinatorial reconfiguration
  • Polynomial-time
  • PSPACE
  • Spanning trees

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