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.ISAAC.2021.24
URN: urn:nbn:de:0030-drops-154578
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15457/
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Anders, Markus ; Brachter, Jendrik ; Schweitzer, Pascal

A Characterization of Individualization-Refinement Trees

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LIPIcs-ISAAC-2021-24.pdf (0.6 MB)

Abstract

Individualization-Refinement (IR) algorithms form the standard method and currently the only practical method for symmetry computations of graphs and combinatorial objects in general. Through backtracking, on each graph an IR-algorithm implicitly creates an IR-tree whose order is the determining factor of the running time of the algorithm.
We give a precise and constructive characterization which trees are IR-trees. This characterization is applicable both when the tree is regarded as an uncolored object but also when regarded as a colored object where vertex colors stem from a node invariant. We also provide a construction that given a tree produces a corresponding graph whenever possible. This provides a constructive proof that our necessary conditions are also sufficient for the characterization.

BibTeX - Entry

@InProceedings{anders_et_al:LIPIcs.ISAAC.2021.24,
  author =	{Anders, Markus and Brachter, Jendrik and Schweitzer, Pascal},
  title =	{{A Characterization of Individualization-Refinement Trees}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15457},
  URN =		{urn:nbn:de:0030-drops-154578},
  doi =		{10.4230/LIPIcs.ISAAC.2021.24},
  annote =	{Keywords: individualization refinement algorithms, backtracking trees, graph isomorphism}
}

Keywords: individualization refinement algorithms, backtracking trees, graph isomorphism
Collection: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue Date: 2021
Date of publication: 30.11.2021

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