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

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 $O(U \cdot \log\mathsf{ID}{\min})$ messages in one direction and $O(\log\mathsf{ID}{\min})$ 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 $1 - U^{-c}$.