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Self-Stabilizing Algorithm for Minimal Dominating Set with Safe Convergence in an Arbitrary Graph

    In a graph or a network G=(V,E), a set 𝒮V is a dominating set if each node in V-𝒮 is adjacent to at least one node in 𝒮. A dominating set 𝒮 is called minimal when there does not exist a node i𝒮 such that the set 𝒮-{i} is a dominating set. In this paper, we propose a new self-stabilizing algorithm for minimal dominating set. It has safe convergence property under synchronous daemon in the sense that starting from an arbitrary state, it quickly converges to a dominating set (a safe state) in two rounds, and then stabilizes in a minimal dominating set (the legitimate state) in O(n) rounds without breaking safety during the convergence interval, where n is the number of nodes. Space requirement at each node is O(logn) bits.

    Communicated by K. Qiu