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Exact Bounds for Distributed Graph Colouring

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Structural Information and Communication Complexity (SIROCCO 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9439))

Abstract

We prove exact bounds on the time complexity of distributed graph colouring. If we are given a directed path that is properly coloured with n colours, by prior work it is known that we can find a proper 3-colouring in \(\frac{1}{2} \log^{*}(n) \pm O(1)\) communication rounds. We close the gap between upper and lower bounds: we show that for infinitely many n the time complexity is precisely \(\frac{1}{2} \log^{*} n\) communication rounds.

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Author information

Authors and Affiliations

  1. Helsinki Institute for Information Technology HIIT, Department of Computer Science, Aalto University, Saarbrücken, Germany

    Joel Rybicki & Jukka Suomela

  2. Department of Algorithms and Complexity, Max Planck Institute for Informatics, Saarbrücken, Germany

    Joel Rybicki

Authors
  1. Joel Rybicki
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  2. Jukka Suomela
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Editor information

Editors and Affiliations

  1. Dept of Mathematics and Comp Science, Paderborn University, Paderborn, Nordrhein-Westfalen, Germany

    Christian Scheideler

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Rybicki, J., Suomela, J. (2015). Exact Bounds for Distributed Graph Colouring. In: Scheideler, C. (eds) Structural Information and Communication Complexity. SIROCCO 2015. Lecture Notes in Computer Science(), vol 9439. Springer, Cham. https://doi.org/10.1007/978-3-319-25258-2_4

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  • DOI: https://doi.org/10.1007/978-3-319-25258-2_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25257-5

  • Online ISBN: 978-3-319-25258-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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