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A Self-stabilizing Algorithm for the Maximal 2-packing in a Cactus Graph

In this paper we present a time optimal self-stabilizing algorithm for the maximal 2-packing in a cactus graph. The cactus is a network topology such that any edge belongs to at most one cycle. The cactus has important applications in telecommunication networks, location problems, biotechnology, among others. The execution time of this algorithm is proportional to the diameter of the cactus. To the best of our knowledge, this algorithm outperforms current algorithms presented in the literature for this problem and in this topology. Keywords-self-stabilization; cactus graph; 2-packing set