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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.DISC.2022.23
URN: urn:nbn:de:0030-drops-172147
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17214/
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Fraigniaud, Pierre ; Lambein-Monette, Patrick ; Rabie, Mikaël

Fault Tolerant Coloring of the Asynchronous Cycle

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LIPIcs-DISC-2022-23.pdf (0.9 MB)

Abstract

We present a wait-free algorithm for proper coloring the n nodes of the asynchronous cycle C_n, where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of n ≥ 3, and runs in O(log^*n) rounds in C_n. This round-complexity is optimal thanks to a known matching lower bound, which applies even to synchronous (failure-free) executions. The range of colors used by our algorithm, namely {0,…,4}, is optimal too, thanks to a known lower bound on the minimum number of names for which renaming is solvable wait-free in shared-memory systems, whenever n is a power of a prime. Indeed, our model coincides with the shared-memory model whenever n = 3, and the minimum number of names for which renaming is possible in 3-process shared-memory systems is 5.

BibTeX - Entry

@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2022.23,
  author =	{Fraigniaud, Pierre and Lambein-Monette, Patrick and Rabie, Mika\"{e}l},
  title =	{{Fault Tolerant Coloring of the Asynchronous Cycle}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17214},
  URN =		{urn:nbn:de:0030-drops-172147},
  doi =		{10.4230/LIPIcs.DISC.2022.23},
  annote =	{Keywords: graph coloring, LOCAL model, shared-memory model, immediate snapshot, renaming, wait-free algorithms}
}

Keywords: graph coloring, LOCAL model, shared-memory model, immediate snapshot, renaming, wait-free algorithms
Collection: 36th International Symposium on Distributed Computing (DISC 2022)
Issue Date: 2022
Date of publication: 17.10.2022

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