Being Efficient in Time, Space, and Workload: a Self-stabilizing Unison and its Consequences
Résumé
We present a self-stabilizing algorithm for the unison problem which is efficient in time, workload, and space in a weak model. Precisely, our algorithm is defined in the atomic-state model and works in anonymous asynchronous connected networks in which even local ports are unlabeled. It makes no assumption on the daemon and thus stabilizes under the weakest one: the distributed unfair daemon.
In an $n$-node network of diameter $D$ and assuming the knowledge $B \geq 2D+2$, our algorithm only requires $\Theta(\log(B))$ bits per node and is fully polynomial as it stabilizes in at most $2D+2$ rounds and $O(\min(n^2B, n^3))$ moves. In particular, it is the first self-stabilizing unison for arbitrary asynchronous anonymous networks achieving an asymptotically optimal stabilization time in rounds using a bounded memory at each node.
Furthermore, we show that our solution can be used to efficiently simulate synchronous self-stabilizing algorithms in asynchronous environments. For example, this simulation allows us to design a new state-of-the-art algorithm solving both the leader election and the BFS (Breadth-First Search) spanning tree construction in any identified connected network which, to the best of our knowledge, beats all existing solutions in the literature.
Origine | Fichiers éditeurs autorisés sur une archive ouverte |
---|---|
Licence |