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Amnesiac Flooding: Easy to Break, Hard to Escape

Authors Henry Austin , Maximilien Gadouleau , George B. Mertzios , Amitabh Trehan

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ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Distributed algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Amnesiac flooding
  • Terminating protocol
  • Algorithm state
  • Stateless protocol
  • Flooding algorithm
  • Network algorithms
  • Graph theory
  • Termination
  • Communication
  • Broadcast

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Abstract

Broadcast is a central problem in distributed computing. Recently, Hussak and Trehan [PODC'19/ STACS'20/DC'23] proposed a stateless broadcasting protocol (Amnesiac Flooding), which was surprisingly proven to terminate in asymptotically optimal time (linear in the diameter of the network). However, it remains unclear: (i) Are there other stateless terminating broadcast algorithms with the desirable properties of Amnesiac Flooding, (ii) How robust is Amnesiac Flooding with respect to faults?
In this paper we make progress on both of these fronts. Under a reasonable restriction (obliviousness to message content) additional to the fault-free synchronous model, we prove that Amnesiac Flooding is the only strictly stateless deterministic protocol that can achieve terminating broadcast. We achieve this by identifying four natural properties of a terminating broadcast protocol that Amnesiac Flooding uniquely satisfies. In contrast, we prove that even minor relaxations of any of these four criteria allow the construction of other terminating broadcast protocols.
On the other hand, we prove that Amnesiac Flooding can become non-terminating or non-broadcasting, even if we allow just one node to drop a single message on a single edge in a single round. As a tool for proving this, we focus on the set of all configurations of transmissions between nodes in the network, and obtain a dichotomy characterizing the configurations, starting from which, Amnesiac Flooding terminates. Additionally, we characterise the structure of sets of Byzantine agents capable of forcing non-termination or non-broadcast of the protocol on arbitrary networks.

Cite As Get BibTex

Henry Austin, Maximilien Gadouleau, George B. Mertzios, and Amitabh Trehan. Amnesiac Flooding: Easy to Break, Hard to Escape. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.10

Author Details

Henry Austin
  • Durham University, UK
Maximilien Gadouleau
  • Durham University, UK
George B. Mertzios
  • Durham University, UK
Amitabh Trehan
  • Durham University, UK

Funding

  • Mertzios, George B.: Supported by the EPSRC grant EP/P020372/1.
  • Trehan, Amitabh: Supported by the EPSRC grant EP/P021247/1.

Acknowledgements

We would like to thank Danial Maqbool (Durham University) for his insightful work with a precursor to the uniqueness result.

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