Content-Oblivious Leader Election in 2-Edge-Connected Networks

TL;DR

This paper introduces a leader election algorithm for 2-edge-connected networks that works without a predesignated leader in fully-defective, content-oblivious communication models, challenging prior conjectures and improving on existing methods.

Contribution

It presents a leader election algorithm for 2-edge-connected networks that operates without a leader preselection, and extends to unoriented rings, showing equivalence between fully-defective and noiseless communication.

Findings

Leader election in 2-edge-connected networks without predesignated leader.

Algorithm works in unoriented rings with optimal message complexity.

Refutes previous conjecture about the necessity of a leader in content-oblivious models.

Abstract

Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022 & Distributed Computing 2023) studied fully-defective asynchronous networks, where communication channels may suffer an extreme form of alteration errors, rendering messages completely corrupted. The model is equivalent to content-oblivious computation, where nodes communicate solely via pulses. They showed that if the network is 2-edge-connected, then any algorithm for a noiseless setting can be simulated in the fully-defective setting; otherwise, no non-trivial computation is possible in the fully-defective setting. However, their simulation requires a predesignated leader, which they conjectured to be necessary for any non-trivial content-oblivious task. In this work, we present two results: General 2-edge-connected topologies: First, we show an asynchronous content-oblivious leader election algorithm that quiescently terminates in any 2-edge-connected network with message complexity $O(m \cdot N \cdot \mathsf{ID}_{\min})$, where $m$ is the number of edges, $N$ is a known upper bound on the number of nodes, and $\mathsf{ID}_{\min}$ is the smallest $\mathsf{ID}$. Combined with the above simulation, this result shows that whenever a size bound $N$ is known, any noiseless algorithm can be simulated in the fully-defective model without a preselected leader, fully refuting the conjecture. Unoriented rings: We then show that the knowledge of $N$ can be dropped in unoriented ring topologies by presenting a quiescently terminating election algorithm with message complexity $O(n \cdot \mathsf{ID}_{\max})$ that matches the previous bound. Consequently, this result constitutes a strict improvement over the previous leader election in oriented rings by Frei, Gelles, Ghazy, and Nolin (DISC 2024) and shows that, on rings, fully-defective and noiseless communication are computationally equivalent, with no additional assumptions.