License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2022.15
URN: urn:nbn:de:0030-drops-158253
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15825/
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Bousquet, Nicolas ; Ito, Takehiro ; Kobayashi, Yusuke ; Mizuta, Haruka ; Ouvrard, Paul ; Suzuki, Akira ; Wasa, Kunihiro

Reconfiguration of Spanning Trees with Degree Constraint or Diameter Constraint

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LIPIcs-STACS-2022-15.pdf (0.9 MB)

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.

BibTeX - Entry

@InProceedings{bousquet_et_al:LIPIcs.STACS.2022.15,
  author =	{Bousquet, Nicolas and Ito, Takehiro and Kobayashi, Yusuke and Mizuta, Haruka and Ouvrard, Paul and Suzuki, Akira and Wasa, Kunihiro},
  title =	{{Reconfiguration of Spanning Trees with Degree Constraint or Diameter Constraint}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{15:1--15:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15825},
  URN =		{urn:nbn:de:0030-drops-158253},
  doi =		{10.4230/LIPIcs.STACS.2022.15},
  annote =	{Keywords: combinatorial reconfiguration, spanning trees, PSPACE, polynomial-time algorithms}
}

Keywords: combinatorial reconfiguration, spanning trees, PSPACE, polynomial-time algorithms
Collection: 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
Issue Date: 2022
Date of publication: 09.03.2022

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