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Fault Tolerant Coloring of the Asynchronous Cycle

Authors Pierre Fraigniaud , Patrick Lambein-Monette , Mikaël Rabie

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ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Mathematics of computing → Graph coloring
  • Computer systems organization → Dependable and fault-tolerant systems and networks
  • Theory of computation → Models of computation
Keywords
  • graph coloring
  • LOCAL model
  • shared-memory model
  • immediate snapshot
  • renaming
  • wait-free algorithms

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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.

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Pierre Fraigniaud, Patrick Lambein-Monette, and Mikaël Rabie. Fault Tolerant Coloring of the Asynchronous Cycle. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.DISC.2022.23

Author Details

Pierre Fraigniaud
  • Université Paris Cité, CNRS, IRIF, F-75013, Paris, France
Patrick Lambein-Monette
  • Université Paris Cité, CNRS, IRIF, F-75013, Paris, France
Mikaël Rabie
  • Université Paris Cité, CNRS, IRIF, F-75013, Paris, France

Funding

  • Fraigniaud, Pierre: additional support from the project ANR-20-CE48-0006 (DUCAT).

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