A self-stabilizing algorithm for constructing weakly connected minimal dominating sets

This paper presents a new distributed self-stabilizing algorithm for the weakly connected minimal dominating set problem. It assumes a self-stabilizing algorithm to compute a breadth-first tree. Using an unfair distributed scheduler the algorithm stabilizes in at most O(nmA) moves, where A is the number of moves to construct a breadth-first tree. All previously known algorithms required an exponential number of moves.