2026-07-21T20:02:55Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24827 2026-02-09T07:41:36Z ddc:004 open_access

Amnesiac Flooding: Easy to Break, Hard to Escape Austin, Henry Gadouleau, Maximilien Mertzios, George B. Trehan, Amitabh Amnesiac flooding Terminating protocol Algorithm state Stateless protocol Flooding algorithm Network algorithms Graph theory Termination Communication Broadcast 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Henry Austin and Maximilien Gadouleau and George B. Mertzios and Amitabh Trehan 2025 Is Part Of LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DISC.2025.10 urn:nbn:de:0030-drops-248273 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.10 eng https://creativecommons.org/licenses/by/4.0/legalcode