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.ESA.2021.72
URN: urn:nbn:de:0030-drops-146533
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14653/
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Neuen, Daniel

Isomorphism Testing Parameterized by Genus and Beyond

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LIPIcs-ESA-2021-72.pdf (0.8 MB)


Abstract

We present an isomorphism test for graphs of Euler genus g running in time 2^{{O}(g⁴ log g)}n^{{O}(1)}. Our algorithm provides the first explicit upper bound on the dependence on g for an fpt isomorphism test parameterized by the Euler genus of the input graphs. The only previous fpt algorithm runs in time f(g)n for some function f (Kawarabayashi 2015). Actually, our algorithm even works when the input graphs only exclude K_{3,h} as a minor. For such graphs, no fpt isomorphism test was known before.
The algorithm builds on an elegant combination of simple group-theoretic, combinatorial, and graph-theoretic approaches. In particular, we introduce (t,k)-WL-bounded graphs which provide a powerful tool to combine group-theoretic techniques with the standard Weisfeiler-Leman algorithm. This concept may be of independent interest.

BibTeX - Entry

@InProceedings{neuen:LIPIcs.ESA.2021.72,
  author =	{Neuen, Daniel},
  title =	{{Isomorphism Testing Parameterized by Genus and Beyond}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{72:1--72:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14653},
  URN =		{urn:nbn:de:0030-drops-146533},
  doi =		{10.4230/LIPIcs.ESA.2021.72},
  annote =	{Keywords: graph isomorphism, fixed-parameter tractability, Euler genus, Weisfeiler-Leman algorithm}
}

Keywords: graph isomorphism, fixed-parameter tractability, Euler genus, Weisfeiler-Leman algorithm
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021


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