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Coordination Through Stochastic Channels

Authors Pierre Fraigniaud , Boaz Patt-Shamir , Sergio Rajsbaum

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LIPIcs.DISC.2025.32.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Probabilistic computation
  • Theory of computation → Distributed computing models
  • Theory of computation → Random network models
  • Theory of computation → Distributed algorithms
Keywords
  • Approximate agreement
  • randomized consensus
  • stochastic models
  • topology

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Abstract

We consider a stochastic network model consisting of a set of n synchronous processes communicating by message passing. In each round, processes send messages directly to each other over a complete communication graph. The processes do not fail, but messages can be lost. Each message is delivered with probability p, for a given parameter p ∈ [0,1]. We study the following optimization version of approximate agreement in this model. We assume that processes start with binary input values, execute an algorithm for a fixed number of rounds, and decide values in [0,1] satisfying the usual validity requirement stating that if all processes start with the same input value, then they should all decide that value. We propose deterministic algorithms that minimize the expected discrepancy, namely, the expected maximum distance between the decided values. We also present lower bounds on the expected discrepancy, which demonstrate the optimality of our algorithms for two processes. Finally, we present applications of our algorithms to solve randomized consensus and randomized approximate agreement.

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Pierre Fraigniaud, Boaz Patt-Shamir, and Sergio Rajsbaum. Coordination Through Stochastic Channels. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.32

Author Details

Pierre Fraigniaud
  • Inst. de Recherche en Informatique Fondamentale (IRIF), CNRS and Université Paris Cité, France
Boaz Patt-Shamir
  • School of Electrical Engineering, Tel Aviv University, Israel
Sergio Rajsbaum
  • Instituto de Matemáticas, UNAM, Mexico City, Mexico

Funding

  • Fraigniaud, Pierre: Additional support from ANR projects DUCAT (ANR-20-CE48-0006), ENEDISC (ANR-24-CE48-7768-01), and PREDICTIONS (ANR-23-CE48-0010), and from the InIDEX Project METALG.
  • Patt-Shamir, Boaz: This research was supported by the Israel Science Foundation, grant No. 1948/21.
  • Rajsbaum, Sergio: Part of this work was done while visiting IRIF, France, supported by ENEDISC (ANR-24-CE48-7768-01) and Ecole Polytechnique Gaspard Monge.

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