Self-stabilizing algorithms for minimal global powerful alliance sets in graphs

•We propose a self-stabilizing distributed algorithm for the minimal global powerful alliance set problem.•We give self-stabilizing algorithms for two generalizations of the problem.•Using an unfair distributed scheduler, the proposed algorithms converge in O(mn) moves.

We propose a self-stabilizing distributed algorithm for the minimal global powerful alliance set problem in an arbitrary graph. Then, we give self-stabilizing algorithms for some generalizations of the problem. Using an unfair distributed scheduler, the proposed algorithms converge in O(mn) moves starting from an arbitrary state.