Autostabilizing Minimal Clique Decomposition with Byzantine Faults tolerance
Résumé
We focus on computing a Minimal Clique Decomposition of the communication graph of a distributed system subject to transient and Byzantine faults. A minimal clique decomposition partitions the network into cliques such that each node belongs to exactly one clique, and no two cliques can be merged into a larger clique. We present a self-stabilizing distributed algorithm that achieves such a decomposition while tolerating Byzantine behavior. The algorithm excludes faulty nodes as well as those directly influenced by them, and guarantees convergence within $O(\Delta n)$ rounds with high probability, where $n$ and $\Delta$ denote the size and maximum degree of the network, respectively. We bound the impact of Byzantine nodes by restricting attention to the set of all nodes excluding those at distance at most one from a Byzantine node, and excluding some nodes at distance two. To the best of our knowledge, this is the first algorithm that tolerates both transient and Byzantine faults under the fair distributed daemon.
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