Amnesiac Flooding: Easy to break, hard to escape

2025-02-09

AI Summary

This work investigates the uniqueness and robustness of Amnesiac Flooding (AF), a stateless protocol for distributed broadcast. Whether AF is uniquely characterized by natural protocol properties and how resilient it is to faults. Method: We employ configuration-space modeling, graph-theoretic analysis, and synchronous Byzantine fault modeling. Contribution/Results: We formally prove that AF is the *only* linear-time terminating broadcast protocol satisfying four natural properties—statelessness, determinism, termination, and broadcast correctness—and that weakening any one property admits alternative protocols. We establish a “Configuration Bipartition Theorem” and introduce the “Byzantine Proxy Structure” to precisely characterize AF’s fault-tolerance threshold: dropping a single message by one node in a single round suffices to cause non-termination or broadcast failure. These results establish AF’s dual theoretical extremities—maximal syntactic simplicity and minimal fault tolerance.

Technology Category

• Multiagent Systems: Other Foundations of Multi Agent Systems
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

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 emph{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 emph{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 relaxations of extit{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 extit{configurations} of transmissions between nodes in the network, and obtain a extit{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.

Problem

• Uniqueness of Amnesiac Flooding in stateless broadcast.
• Robustness of Amnesiac Flooding against message faults.
• Impact of Byzantine agents on protocol termination.

Innovation

• Stateless broadcasting protocol
• Asymptotically optimal time
• Dichotomy in configurations