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Exact Bounds for Distributed Graph Colouring

  • Joel Rybicki
  • Jukka Suomela
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Time Complexity Directed Path Chromatic Number SIAM Journal Exact Bound 
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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Joel Rybicki
    • 1
    • 2
  • Jukka Suomela
    • 1
  1. 1.Helsinki Institute for Information Technology HIIT, Department of Computer ScienceAalto UniversitySaarbrückenGermany
  2. 2.Department of Algorithms and ComplexityMax Planck Institute for InformaticsSaarbrückenGermany

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