A self-stabilizing distributed algorithm for minimal total domination in an arbitrary system graph

In a graph G = (V, E), a set S ⊆ V is said to be total dominating if every v ∈ V is adjacent to some member of S. When the graph represents a communication network, a total dominating set corresponds to a collection of servers having a certain desirable backup property, namely, that every server is adjacent to some other server. Self-stabilization, introduced by Dijkstra (1974, 1986), is the most inclusive approach to fault tolerance in distributed systems. We propose a new self-stabilizing distributed algorithm for finding a minimal total dominating set in an arbitrary graph. We also show how the basic ideas behind the proposed protocol can be generalized to solve other related problems.