A self-stabilizing distributed algorithm is guaranteed eventually to reach and stay at a legitimate configuration regardless of the initial configuration of a distributed system. In this paper, we propose the generalized dominating set problem, which is a generalization of the dominating set and k-redundant dominating set problems. In the generalized dominating set we propose in this paper, each node P-i is given its set of domination wish sets, and a generalized dominating set is a set of nodes such that each node is contained in the set or has a wish set in which all its members are in the set. We propose a self-stabilizing distributed algorithm for finding a minimal generalized dominating set in an arbitrary network under the unfair distributed daemon. The proposed algorithm converges in O(n(3)m) steps and O(n) rounds, where n (resp., m) is the number of nodes (resp., edges). Furthermore, it has the safe convergence property with safe convergence time in O(1) rounds. The space complexity of the proposed algorithm is O(Delta log n) bits per node, where Delta is the maximum degree of nodes.
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