We analyze the impact of transient and Byzantine faults on the construction of a maximal independent set in a general network. We adapt the self-stabilizing algorithm presented by Turau `for computing such a vertex set. Our algorithm is self-stabilizing and also works under the more difficult context of arbitrary Byzantine faults. Byzantine nodes can prevent nodes close to them from taking part in the independent set for an arbitrarily long time. We give boundaries to their impact by focusing on the set of all nodes excluding nodes at distance 1 or less of Byzantine nodes, and excluding some of the nodes at distance 2. As far as we know, we present the first algorithm tolerating both transient and Byzantine faults under the fair distributed daemon. We prove that this algorithm converges in $ \mathcal O(\Delta n)$ rounds w.h.p., where $n$ and $\Delta$ are the size and the maximum degree of the network, resp. Additionally, we present a modified version of this algorithm for anonymous systems under the adversarial distributed daemon that converges in $ \mathcal O(n^{2})$ expected number of steps.

翻译：我们分析了瞬态故障和拜占庭故障对一般网络中最大独立集构建的影响。我们改进了Turau提出的用于计算此类顶点集的自稳定算法。我们的算法不仅具有自稳定性，还能在更困难的任意拜占庭故障环境中运行。拜占庭节点可导致其邻近节点长时间无法参与独立集的构成。通过聚焦于排除拜占庭节点距离1及以内所有节点、并排除部分距离2节点的节点集合，我们给出了拜占庭节点影响的边界。据我们所知，这是首个在公平分布式守护进程下同时容忍瞬态故障和拜占庭故障的算法。我们证明该算法在$ \mathcal O(\Delta n)$轮内以高概率收敛，其中$n$和$\Delta$分别表示网络规模与最大度。此外，我们还提出了该算法在敌意分布式守护进程下匿名系统的改进版本，其期望步数收敛至$ \mathcal O(n^{2})$。