Brief Announcement: Amnesiac Flooding: Easy to Break, Hard to Escape

Austin, Henry; Gadouleau, Maximilien; Mertzios, George B; Trehan, Amitabh

Abstract

Broadcast is a central problem in distributed computing. Recently, Hussak and Trehan [PODC'19/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 identify four natural properties of a terminating broadcast protocol that Amnesiac Flooding uniquely satisfies. In contrast, we prove that even minor relax-ations 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 charac-terise the structure of sets of Byzantine agents capable of forcing non-termination or non-broadcast of the protocol on arbitrary networks .

Citation

Austin, H., Gadouleau, M., Mertzios, G. B., & Trehan, A. (2025, June). Brief Announcement: Amnesiac Flooding: Easy to Break, Hard to Escape. Presented at ACM Principles of Distributed Computing (PODC) 2025, Huatulco, Mexico

• Presentation Conference Type: Conference Paper (published)
• Conference Name: ACM Principles of Distributed Computing (PODC) 2025
• Start Date: Jun 16, 2025
• End Date: Jun 20, 2025
• Acceptance Date: Apr 17, 2025
• Deposit Date: May 19, 2025
• Peer Reviewed: Peer Reviewed
• Keywords: CCS Concepts • Mathematics of computing → Discrete mathematics; Graph al- gorithms; • Theory of computation → Distributed algorithms; Graph algorithms analysis Keywords Amnesiac flooding, Terminating protocol, Algorithm state, Stateless protocol, Flooding algorithm, Network algorithms, Graph theory, Termination, Communication, Broadcast
• Public URL: https://durham-repository.worktribe.com/output/3954797
• Publisher URL: https://dl.acm.org/conference/podc/proceedings