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Self-Stabilizing Computation of Perfect Neighborhood Set in Large Network Graphs

Given a graph G = (V, E), a node is called perfect (with respect to a set S ⊆ V) if its closed neighborhood contains exactly one node in set S, a node is called nearly perfect if it is not perfect but is adjacent to a perfect node. S is called a perfect neighborhood set if each node is either perfect or nearly perfect. We present the first self-stabilizing algorithm for computing a perfect neighborhood set in an arbitrary graph. This anonymous, constant space algorithm terminates in O(n2) steps using an unfair central daemon, where n is the number of nodes in the graph.