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 ≥ 2D+2, our algorithm only requires Θ(log(B)) bits per node and is fully polynomial as it stabilizes in at most 2D+2 rounds and O(min(n²B, n³)) 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.
@InProceedings{devismes_et_al:LIPIcs.STACS.2025.30, author = {Devismes, St\'{e}phane and Ilcinkas, David and Johnen, Colette and Mazoit, Fr\'{e}d\'{e}ric}, title = {{Being Efficient in Time, Space, and Workload: a Self-Stabilizing Unison and Its Consequences}}, booktitle = {42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)}, pages = {30:1--30:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-365-2}, ISSN = {1868-8969}, year = {2025}, volume = {327}, editor = {Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.30}, URN = {urn:nbn:de:0030-drops-228568}, doi = {10.4230/LIPIcs.STACS.2025.30}, annote = {Keywords: Self-stabilization, unison, time complexity, synchronizer} }
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