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The Weakest Failure Detector for Genuine Atomic Multicast

Author Pierre Sutra

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  • Theory of computation → Distributed computing models
  • Software and its engineering → Distributed systems organizing principles
  • General and reference → Reliability
Keywords
  • Failure Detector
  • State Machine Replication
  • Consensus

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Abstract

Atomic broadcast is a group communication primitive to order messages across a set of distributed processes. Atomic multicast is its natural generalization where each message m is addressed to dst(m), a subset of the processes called its destination group. A solution to atomic multicast is genuine when a process takes steps only if a message is addressed to it. Genuine solutions are the ones used in practice because they have better performance.
Let 𝒢 be all the destination groups and ℱ be the cyclic families in it, that is the subsets of 𝒢 whose intersection graph is hamiltonian. This paper establishes that the weakest failure detector to solve genuine atomic multicast is 𝜇 = (∧_{g,h ∈ 𝒢} Σ_{g ∩ h}) ∧ (∧_{g ∈ 𝒢} Ω_g) ∧ γ, where Σ_P and Ω_P are the quorum and leader failure detectors restricted to the processes in P, and γ is a new failure detector that informs the processes in a cyclic family f ∈ ℱ when f is faulty.
We also study two classical variations of atomic multicast. The first variation requires that message delivery follows the real-time order. In this case, 𝜇 must be strengthened with 1^{g ∩ h}, the indicator failure detector that informs each process in g ∪ h when g ∩ h is faulty. The second variation requires a message to be delivered when the destination group runs in isolation. We prove that its weakest failure detector is at least 𝜇 ∧ (∧_{g, h ∈ 𝒢} Ω_{g ∩ h}). This value is attained when ℱ = ∅.

Cite As Get BibTex

Pierre Sutra. The Weakest Failure Detector for Genuine Atomic Multicast. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.DISC.2022.35

Author Details

Pierre Sutra
  • Telecom SudParis, Palaiseau, France

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