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.MFCS.2021.23
URN: urn:nbn:de:0030-drops-144633
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14463/
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Briański, Marcin ; Felsner, Stefan ; Hodor, Jędrzej ; Micek, Piotr

Reconfiguring Independent Sets on Interval Graphs

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LIPIcs-MFCS-2021-23.pdf (0.9 MB)


Abstract

We study reconfiguration of independent sets in interval graphs under the token sliding rule. We show that if two independent sets of size k are reconfigurable in an n-vertex interval graph, then there is a reconfiguration sequence of length 𝒪(k⋅ n²). We also provide a construction in which the shortest reconfiguration sequence is of length Ω(k²⋅ n).
As a counterpart to these results, we also establish that Independent Set Reconfiguration is PSPACE-hard on incomparability graphs, of which interval graphs are a special case.

BibTeX - Entry

@InProceedings{brianski_et_al:LIPIcs.MFCS.2021.23,
  author =	{Bria\'{n}ski, Marcin and Felsner, Stefan and Hodor, J\k{e}drzej and Micek, Piotr},
  title =	{{Reconfiguring Independent Sets on Interval Graphs}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{23:1--23:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14463},
  URN =		{urn:nbn:de:0030-drops-144633},
  doi =		{10.4230/LIPIcs.MFCS.2021.23},
  annote =	{Keywords: reconfiguration, independent sets, interval graphs}
}

Keywords: reconfiguration, independent sets, interval graphs
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021


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