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European Symposium on Algorithms

ESA 2013: Algorithms – ESA 2013 pp 145–156Cite as

Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8125)

Abstract

An assignment of colours to the vertices of a graph is stable if any two vertices of the same colour have identically coloured neighbourhoods. The goal of colour refinement is to find a stable colouring that uses a minimum number of colours. This is a widely used subroutine for graph isomorphism testing algorithms, since any automorphism needs to be colour preserving. We give an O((m+n)log n) algorithm for finding a canonical version of such a stable colouring, on graphs with n vertices and m edges. We show that no faster algorithm is possible, under some modest assumptions about the type of algorithm, which captures all known colour refinement algorithms.

Keywords

  • Stable Colouring
  • Colour Class
  • Graph Isomorphism
  • Canonical Sequence
  • Stable Partition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-40450-4_13
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Author information

Authors and Affiliations

  1. RWTH Aachen University, Germany

    Christoph Berkholz & Martin Grohe

  2. University of Twente, The Netherlands

    Paul Bonsma

Authors
  1. Christoph Berkholz
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  2. Paul Bonsma
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  3. Martin Grohe
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Rome, Italy

    Giuseppe F. Italiano

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Berkholz, C., Bonsma, P., Grohe, M. (2013). Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_13

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  • DOI: https://doi.org/10.1007/978-3-642-40450-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40449-8

  • Online ISBN: 978-3-642-40450-4

  • eBook Packages: Computer ScienceComputer Science (R0)