License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.17
URN: urn:nbn:de:0030-drops-128837
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Bertschinger, Daniel ; Lengler, Johannes ; Martinsson, Anders ; Meier, Robert ; Steger, Angelika ; Trujić, Miloš ; Welzl, Emo

An Optimal Decentralized (Δ + 1)-Coloring Algorithm

LIPIcs-ESA-2020-17.pdf (0.5 MB)


Consider the following simple coloring algorithm for a graph on n vertices. Each vertex chooses a color from {1, ..., Δ(G) + 1} uniformly at random. While there exists a conflicted vertex choose one such vertex uniformly at random and recolor it with a randomly chosen color. This algorithm was introduced by Bhartia et al. [MOBIHOC'16] for channel selection in WIFI-networks. We show that this algorithm always converges to a proper coloring in expected O(n log Δ) steps, which is optimal and proves a conjecture of Chakrabarty and de Supinski [SOSA'20].

BibTeX - Entry

  author =	{Daniel Bertschinger and Johannes Lengler and Anders Martinsson and Robert Meier and Angelika Steger and Milo{\v{s}} Trujić and Emo Welzl},
  title =	{{An Optimal Decentralized (Δ + 1)-Coloring Algorithm}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{17:1--17:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-128837},
  doi =		{10.4230/LIPIcs.ESA.2020.17},
  annote =	{Keywords: Decentralized Algorithm, Distributed Computing, Graph Coloring, Randomized Algorithms}

Keywords: Decentralized Algorithm, Distributed Computing, Graph Coloring, Randomized Algorithms
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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