License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2017.7
URN: urn:nbn:de:0030-drops-70278
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7027/
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Arvind, Vikraman ; Köbler, Johannes ; Kuhnert, Sebastian ; Torán, Jacobo

Parameterized Complexity of Small Weight Automorphisms

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Abstract

We show that checking if a given hypergraph has an automorphism that moves exactly k vertices is fixed parameter tractable, using k and additionally either the maximum hyperedge size or the maximum color class size as parameters. In particular, it suffices to use k as parameter if the hyperedge size is at most polylogarithmic in the size of the given hypergraph.

As a building block for our algorithms, we generalize Schweitzer's FPT algorithm [ESA 2011] that, given two graphs on the same vertex set and a parameter k, decides whether there is an isomorphism between the two graphs that moves at most k vertices. We extend this result to hypergraphs, using the maximum hyperedge size as a second parameter.

Another key component of our algorithm is an orbit-shrinking technique that preserves permutations that move few points and that may be of independent interest. Applying it to a suitable subgroup of the automorphism group allows us to switch from bounded hyperedge size to bounded color classes in the exactly-k case.

BibTeX - Entry

@InProceedings{arvind_et_al:LIPIcs:2017:7027,
  author =	{Vikraman Arvind and Johannes K{\"o}bler and Sebastian Kuhnert and Jacobo Tor{\'a}n},
  title =	{{Parameterized Complexity of Small Weight Automorphisms}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Heribert Vollmer and Brigitte Vallée},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7027},
  URN =		{urn:nbn:de:0030-drops-70278},
  doi =		{10.4230/LIPIcs.STACS.2017.7},
  annote =	{Keywords: Parameterized algorithms, hypergraph isomorphism.}
}

Keywords: Parameterized algorithms, hypergraph isomorphism.
Collection: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Issue Date: 2017
Date of publication: 06.03.2017

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