2021 Volume 29 Pages 247-255
We consider the 1-maximal independent set (1-MIS) problem: given a graph G = (V, E), our goal is to find a 1-maximal independent set (1-MIS) of a given network G, that is, a maximal independent set (MIS) S ⊂ V of G such that S ∪ {v, w} ∖ {u} is not an independent set for any nodes u ∈ S, and v, w ∉ S (v ≠ w). We give a silent, self-stabilizing, and asynchronous distributed algorithm to construct a 1-MIS on a network of any topology. We assume the processes have unique identifiers and the scheduler is weakly-fair and distributed. The time complexity, i.e., the number of rounds to reach a legitimate configuration in the worst case of the proposed algorithm is O(nD), where n is the number of processes in the network and D is the diameter of the network. We use a composition technique called loop composition [Datta et al., 2017] to iterate the same procedure consistently, which results in a small space complexity, O(log n) bits per process.
