Being Efficient in Time, Space, and Workload: a Self-stabilizing Unison and its Consequences - Université de Picardie Jules Verne
Communication Dans Un Congrès Année : 2025

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.
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hal-04866194 , version 1 (06-01-2025)

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  • HAL Id : hal-04866194 , version 1

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Stéphane Devismes, David Ilcinkas, Colette Johnen, Frédéric Mazoit. Being Efficient in Time, Space, and Workload: a Self-stabilizing Unison and its Consequences. STACS 2025: 42nd International Symposium on Theoretical Aspects of Computer Science, Mar 2025, Jena, Germany. ⟨hal-04866194⟩
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