Content-oblivious leader election on rings

In content-oblivious computation, n nodes wish to compute a given task over an asynchronous network that suffers from an extremely harsh type of noise, which corrupts the content of all messages across all channels. In a recent work, Censor-Hillel, Cohen, Gelles, and Sela (Distributed Computing, 2023) showed how to perform arbitrary computations in a content-oblivious way in 2-edge connected networks but only if the network has a distinguished node (called root) to initiate the computation. Our goal is to remove this assumption, which was conjectured to be necessary. Achieving this goal essentially reduces to performing a content-oblivious leader election since an elected leader can then serve as the root required to perform arbitrary content-oblivious computations. We focus on ring networks, which are the simplest 2-edge connected graphs. On oriented rings, we obtain a leader election algorithm with message complexity $$O(n \cdot \textsf{ID}_{\max })$$ , where $$\textsf{ID}_{\max }$$ is the maximal assigned ID. As it turns out, this dependency on $$\textsf{ID}_{\max }$$ is inherent: we show a lower bound of $$\Omega (n \log {\textsf{ID}_{\max }})$$ messages for content-oblivious leader election algorithms. We also extend our results to non-oriented rings. Here, however, the algorithm does not terminate but only quiescently stabilizes: all nodes eventually settle on an internal decision and stop receiving messages. Preliminary versions of parts of this research have appeared at the conferences PODC 2024 as a brief announcement and at DISC 2024 as a full paper.