An efficient fault-containing self-stabilizing algorithm for finding a maximal independent set

An independent set is a useful structure because, in some situations, it defines a set of mutually compatible operations, i.e., operations that can be executed simultaneously. We design a fault-containing self-stabilizing algorithm that finds a maximal independent set for an asynchronous distributed system. Our algorithm is an improvement on the self-stabilizing algorithm in Shukla et al. [1995]. In the single-fault situation, the worst-case stabilization time of Shukla´s algorithm is Ω(n), where n is the number of nodes in the system, whereas the worst-case stabilization time of our algorithm is O(Δ), where Δ is the maximum node degree in the system. Compared also with the fault-containing algorithm that is induced from applying the general transformer in Ghosh et al. [1996] to Shukla´s algorithm, our algorithm is also seen to be faster in stabilization time, in the single-fault situation. Therefore, our algorithm can be considered to be the most efficient fault-containing self-stabilizing algorithm for the maximal independent set finding up to this point.