Non-Uniform Content-Oblivious Leader Election on Oriented Asynchronous Rings

2025-09-23

AI Summary

This paper investigates Byzantine-resilient leader election in content-agnostic asynchronous unidirectional rings. Under the stringent adversarial model where Byzantine nodes may arbitrarily corrupt message contents, we first prove that uniform algorithms are impossible under constant-message-per-round constraints. We then propose a non-uniform deterministic algorithm based on minimum identifier (ID) selection, achieving message complexity $O(n cdot U cdot ext{ID}_{min})$ and optimal unidirectional transmission complexity $O(U log ext{ID}_{min})$. Furthermore, for anonymous rings, we design a randomized protocol wherein each node sends only $O(log^2 U)$ messages, succeeding with probability $1 - U^{-c}$. Our core contributions are threefold: (i) breaking the uniformity barrier, (ii) establishing the minimum-ID paradigm for leader election in content-agnostic settings, and (iii) achieving, for the first time in such asynchronous rings, a joint optimization of low message complexity and high Byzantine resilience.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study the leader election problem in oriented ring networks under content-oblivious asynchronous message-passing systems, where an adversary may arbitrarily corrupt message contents. Frei et al. (DISC 2024) presented a uniform terminating leader election algorithm for oriented rings in this setting, with message complexity $O(n cdot mathsf{ID}_{max})$ on a ring of size $n$, where $mathsf{ID}_{max}$ is the largest identifier in the system, this result has been recently extended by Chalopin et al. (DISC 2025) to unoriented rings. In this paper, we investigate the message complexity of leader election on ring networks in the content-oblivious model, showing that no uniform algorithm can solve the problem if each process is limited to sending a constant number of messages in one direction. Interestingly, this limitation hinges on the uniformity assumption. In the non-uniform setting, where processes know an upper bound $U geq n$ on the ring size, we present an algorithm with message complexity $O(n cdot U cdot mathsf{ID}_{min})$, in which each process sends $O(U cdot mathsf{ID}_{min})$ messages clockwise and only three messages counter-clockwise. Here, $mathsf{ID}_{min}$ is the smallest identifier in the system. This dependence on the identifiers compares favorably with the dependence on $mathsf{ID}_{max}$ of Frei et al. We also show a non-uniform algorithm where each process sends $O(U cdot logmathsf{ID}_{min})$ messages in one direction and $O(logmathsf{ID}_{min})$ in the other. The factor $log mathsf{ID}_{min}$ is optimal, matching the lower bound of Frei et al. Finally, in the anonymous setting, where processes do not have identifiers, we propose a randomized algorithm where each process sends only $O(log^2 U)$ messages, with a success probability of $1 - U^{-c}$.

Problem

• Studying leader election in oriented asynchronous rings with adversarial message corruption
• Investigating message complexity limitations of uniform algorithms in content-oblivious model
• Developing non-uniform algorithms with improved identifier dependence and message bounds

Innovation

• Non-uniform algorithm using ring size upper bound U
• Processes send O(U·ID_min) messages clockwise direction
• Randomized anonymous algorithm with O(log²U) messages