Agreement Tasks in Fault-Prone Synchronous Networks of Arbitrary Structure

Authors Pierre Fraigniaud , Minh Hang Nguyen , Ami Paz



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Author Details

Pierre Fraigniaud
  • Institut de Recherche en Informatique Fondamentale (IRIF), CNRS, Université Paris Cité, France
Minh Hang Nguyen
  • Institut de Recherche en Informatique Fondamentale (IRIF), CNRS, Université Paris Cité, France
Ami Paz
  • Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), CNRS, Université Paris-Saclay, France

Acknowledgements

The authors thank Stephan Felber, Mikaël Rabie, Hugo Rincon Galeana, and Ulrich Schmid for fruitful discussions on this paper.

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Pierre Fraigniaud, Minh Hang Nguyen, and Ami Paz. Agreement Tasks in Fault-Prone Synchronous Networks of Arbitrary Structure. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 34:1-34:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.34

Abstract

Consensus is arguably the most studied problem in distributed computing as a whole, and particularly in the distributed message-passing setting. In this latter framework, research on consensus has considered various hypotheses regarding the failure types, the memory constraints, the algorithmic performances (e.g., early stopping and obliviousness), etc. Surprisingly, almost all of this work assumes that messages are passed in a complete network, i.e., each process has a direct link to every other process. A noticeable exception is the recent work of Castañeda et al. (Inf. Comput. 2023) who designed a generic oblivious algorithm for consensus running in radius(G,t) rounds in every graph G, when up to t nodes can crash by irrevocably stopping, where t is smaller than the node-connectivity κ of G. Here, radius(G,t) denotes a graph parameter called the radius of G whenever up to t nodes can crash. For t = 0, this parameter coincides with radius(G), the standard radius of a graph, and, for G = K_n, the running time radius(K_n,t) = t+1 of the algorithm exactly matches the known round-complexity of consensus in the clique K_n.
Our main result is a proof that radius(G,t) rounds are necessary for oblivious algorithms solving consensus in G when up to t nodes can crash, thus validating a conjecture of Castañeda et al., and demonstrating that their consensus algorithm is optimal for any graph G. We also extend the result of Castañeda et al. to two different settings: First, to the case where the number t of failures is not necessarily smaller than the connectivity κ of the considered graph; Second, to the k-set agreement problem for which agreement is not restricted to be on a single value as in consensus, but on up to k different values.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Consensus
  • set-agreement
  • fault tolerance
  • crash failures

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