A 4n-move self-stabilizing algorithm for the minimal dominating set problem using an unfair distributed daemon

• We propose a self-stabilizing algorithm for finding a minimal dominating set on a graph.
• This algorithm takes 4n moves and is under an unfair distributed daemon.
• This algorithm improves the previous best result, which takes 5n moves.

A distributed system is self-stabilizing if, regardless of its initial state, the system is guaranteed to reach a legitimate (i.e., correct) state in finite time. In 2007, Turau proposed the first linear-time self-stabilizing algorithm for the minimal dominating set (MDS) problem under an unfair distributed daemon [9]; this algorithm stabilizes in at most 9n moves, where n is the number of nodes in the system. In 2008, Goddard et al. [4] proposed a 5n-move algorithm. In this paper, we present a 4n-move algorithm.