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. Recently, Frei, Gelles, Ghazy, and Nolin (DISC 2024) refuted this conjecture for the special case of oriented ring topology. They designed two asynchronous content-oblivious leader election algorithms with message complexity $O(n \cdot \mathsf{ID}_{\max})$, where $n$ is the number of nodes and $\mathsf{ID}_{\max}$ is the maximum $\mathsf{ID}$. The first algorithm stabilizes in unoriented rings without termination detection. The second algorithm quiescently terminates in oriented rings, thus enabling the execution of the simulation algorithm after leader election. In this work, we present 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 previous simulation result, our finding implies that any algorithm from the noiseless setting can be simulated in the fully-defective setting without assuming a preselected leader, entirely refuting the original conjecture.

翻译：Censor-Hillel、Cohen、Gelles和Sela（PODC 2022 & Distributed Computing 2023）研究了完全缺陷的异步网络，其中通信信道可能遭受极端形式的篡改错误，导致消息完全损坏。该模型等价于内容无关计算，节点仅通过脉冲进行通信。他们证明，如果网络是2-边连通的，则任何无噪声设置下的算法都可以在完全缺陷设置中进行模拟；否则，在完全缺陷设置中无法进行任何非平凡计算。然而，他们的模拟需要一个预先指定的领导者，他们推测这对于任何非平凡的内容无关任务是必要的。最近，Frei、Gelles、Ghazy和Nolin（DISC 2024）针对有向环拓扑的特殊情况反驳了这一推测。他们设计了两种异步内容无关的领导者选举算法，消息复杂度为$O(n \cdot \mathsf{ID}_{\max})$，其中$n$是节点数，$\mathsf{ID}_{\max}$是最大$\mathsf{ID}$。第一种算法在无向环中稳定但不具备终止检测。第二种算法在有向环中静默终止，从而能够在领导者选举后执行模拟算法。在本工作中，我们提出了一种异步内容无关的领导者选举算法，该算法在任何2-边连通网络中静默终止，消息复杂度为$O(m \cdot N \cdot \mathsf{ID}_{\min})$，其中$m$是边数，$N$是节点数的已知上界，$\mathsf{ID}_{\min}$是最小$\mathsf{ID}$。结合先前的模拟结果，我们的发现意味着无噪声设置下的任何算法都可以在完全缺陷设置中进行模拟，而无需假设预先选定的领导者，从而完全反驳了最初的推测。