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.IPEC.2021.9
URN: urn:nbn:de:0030-drops-153920
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15392/
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Bodlaender, Hans L. ; Groenland, Carla ; Swennenhuis, Céline M. F.

Parameterized Complexities of Dominating and Independent Set Reconfiguration

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LIPIcs-IPEC-2021-9.pdf (0.8 MB)

Abstract

We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on the number of moves and XNL-complete when a maximum length ? for the sequence is given in binary in the input. The problems are known to be XNLP-complete when ? is given in unary instead, and W[1]- and W[2]-hard respectively when ? is also a parameter. We complete the picture by showing membership in those classes.
Moreover, we show that for all the variants that we consider, token sliding and token jumping are equivalent under pl-reductions. We introduce partitioned variants of token jumping and token sliding, and give pl-reductions between the four variants that have precise control over the number of tokens and the length of the reconfiguration sequence.

BibTeX - Entry

@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2021.9,
  author =	{Bodlaender, Hans L. and Groenland, Carla and Swennenhuis, C\'{e}line M. F.},
  title =	{{Parameterized Complexities of Dominating and Independent Set Reconfiguration}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15392},
  URN =		{urn:nbn:de:0030-drops-153920},
  doi =		{10.4230/LIPIcs.IPEC.2021.9},
  annote =	{Keywords: Parameterized complexity, independent set reconfiguration, dominating set reconfiguration, W-hierarchy, XL, XNL, XNLP}
}

Keywords: Parameterized complexity, independent set reconfiguration, dominating set reconfiguration, W-hierarchy, XL, XNL, XNLP
Collection: 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)
Issue Date: 2021
Date of publication: 22.11.2021

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