The content-oblivious model, introduced by Censor-Hillel, Cohen, Gelles, and Sel (PODC 2022; Distributed Computing 2023), captures an extremely weak form of communication where nodes can only send asynchronous, content-less pulses. Censor-Hillel, Cohen, Gelles, and Sel showed that no non-constant function $f(x,y)$ can be computed correctly by two parties using content-oblivious communication over a single edge, where one party holds $x$ and the other holds $y$. This seemingly ruled out many natural graph problems on non-2-edge-connected graphs. In this work, we show that, with the knowledge of network topology $G$, leader election is possible in a wide range of graphs. Impossibility: Graphs symmetric about an edge admit no randomized terminating leader election algorithm, even when nodes have unique identifiers and full knowledge of $G$. Leader election algorithms: Trees that are not symmetric about any edge admit a quiescently terminating leader election algorithm with topology knowledge, even in anonymous networks, using $O(n^2)$ messages, where $n$ is the number of nodes. Moreover, even-diameter trees admit a terminating leader election given only the knowledge of the network diameter $D = 2r$, with message complexity $O(nr)$. Necessity of topology knowledge: In the family of graphs $\mathcal{G} = \{P_3, P_5\}$, both the 3-path $P_3$ and the 5-path $P_5$ admit a quiescently terminating leader election if nodes know the topology exactly. However, if nodes only know that the underlying topology belongs to $\mathcal{G}$, then terminating leader election is impossible.

翻译：由Censor-Hillel、Cohen、Gelles和Sel（PODC 2022；Distributed Computing 2023）提出的内容无关模型，刻画了一种极弱的通信形式：节点仅能发送异步、无内容的脉冲信号。Censor-Hillel等人证明，在单条边上通过内容无关通信，两方无法正确计算任何非常值函数$f(x,y)$（其中一方持有$x$，另一方持有$y$）。这表面上排除了在非2-边连通图上求解许多自然图问题的可能性。本文研究表明，在已知网络拓扑$G$的前提下，领导者选举可在广泛图类中实现。不可能性结果：关于某条边对称的图不存在随机化终止型领导者选举算法，即使节点具有唯一标识符且完全知晓$G$。领导者选举算法：对于不关于任何边对称的树，在匿名网络中仅需拓扑知识即可实现静默终止的领导者选举算法，消息复杂度为$O(n^2)$（其中$n$为节点数）。此外，对于偶数直径的树，仅需网络直径$D = 2r$的知识即可实现终止型领导者选举，消息复杂度为$O(nr)$。拓扑知识的必要性：在图族$\mathcal{G} = \{P_3, P_5\}$中，若节点精确知晓拓扑结构，则3-路径$P_3$和5-路径$P_5$均支持静默终止的领导者选举；但若节点仅知拓扑属于$\mathcal{G}$，则终止型领导者选举不可实现。