Trade-off between Time, Space, and Workload: the case of the Self-stabilizing Unison

We present a self-stabilizing algorithm for the (asynchronous) unison problem which achieves an efficient trade-off between time, workload, and space in a weak model. Precisely, our algorithm is defined in the atomic-state model and works in anonymous 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 a $n$-node network of diameter $D$ and assuming a period $B \geq 2D+2$, our algorithm only requires $O(\log B)$ bits per node to achieve full polynomiality as it stabilizes in at most $2D-2$ rounds and $O(\min(n^2B, n^3))$ moves. In particular and to the best of our knowledge, it is the first self-stabilizing unison for arbitrary anonymous networks achieving an asymptotically optimal stabilization time in rounds using a bounded memory at each node. Finally, we show that our solution allows to efficiently simulate synchronous self-stabilizing algorithms in an asynchronous environment. This provides a new state-of-the-art algorithm solving both the leader election and the spanning tree construction problem in any identified connected network which, to the best of our knowledge, beat all existing solutions of the literature.Comment: arXiv admin note: substantial text overlap with arXiv:2307.0663

A Taxonomy of Daemons in Self-stabilization

We survey existing scheduling hypotheses made in the literature in self-stabilization, commonly referred to under the notion of daemon. We show that four main characteristics (distribution, fairness, boundedness, and enabledness) are enough to encapsulate the various differences presented in existing work. Our naming scheme makes it easy to compare daemons of particular classes, and to extend existing possibility or impossibility results to new daemons. We further examine existing daemon transformer schemes and provide the exact transformed characteristics of those transformers in our taxonomy.Comment: 26 page