We consider self-stabilizing algorithms to compute a Maximal Independent Set (MIS) in the extremely weak beeping communication model. The model consists of an anonymous network with synchronous rounds. In each round, each vertex can optionally transmit a signal to all its neighbors (beep). After the transmission of a signal, each vertex can only differentiate between no signal received, or at least one signal received. We assume that vertices have some knowledge about the topology of the network. We revisit the not self-stabilizing algorithm proposed by Jeavons, Scott, and Xu (2013), which computes an MIS in the beeping model. We enhance this algorithm to be self-stabilizing, and explore two different variants, which differ in the knowledge about the topology available to the vertices. In the first variant, every vertex knows an upper bound on the maximum degree $\Delta$ of the graph. For this case, we prove that the proposed self-stabilizing version maintains the same run-time as the original algorithm, i.e. it stabilizes after $O(\log n)$ rounds w.h.p. on any $n$-vertex graph. In the second variant, each vertex only knows an upper bound on its own degree. For this case, we prove that the algorithm stabilizes after $O(\log n\cdot \log \log n)$ rounds on any $n$-vertex graph, w.h.p.

翻译：本文考虑在极弱信标（beeping）通信模型下计算最大独立集（MIS）的自稳定算法。该模型由匿名网络和同步轮次构成。每轮中，每个顶点可选择向所有邻居发送信号（beep）。信号传输后，每个顶点仅能区分是否接收至少一个信号。假设顶点对网络拓扑有一定了解。我们重新审视Jeavons、Scott和Xu（2013）提出的非自稳定算法（该算法在beeping模型中计算MIS），将其增强为自稳定算法，并探索两种不同变体——区别在于顶点对拓扑知识的掌握程度。第一种变体中，每个顶点已知图最大度Δ的上界。我们证明，该自稳定版本保持原算法相同的运行时间：对任意n顶点图，以高概率在O(log n)轮后稳定。第二种变体中，每个顶点仅已知自身度的上界。我们证明，对任意n顶点图，该算法以高概率在O(log n·log log n)轮后稳定。