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DOI: 10.4230/LIPIcs.MFCS.2021.23

Reconfiguring Independent Sets on Interval Graphs

Authors: Marcin Briański, Stefan Felsner, Jędrzej Hodor, and Piotr Micek

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

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.

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Marcin Briański, Stefan Felsner, Jędrzej Hodor, and Piotr Micek. Reconfiguring Independent Sets on Interval Graphs. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@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/entities/document/10.4230/LIPIcs.MFCS.2021.23},
  URN =		{urn:nbn:de:0030-drops-144633},
  doi =		{10.4230/LIPIcs.MFCS.2021.23},
  annote =	{Keywords: reconfiguration, independent sets, interval graphs}
}

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Reconfiguring Independent Sets on Interval Graphs

Abstract

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