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We present a self-stabilizing algorithm for the (asynchronous) unison problemwhich achieves an efficient trade-off between time, workload, and space in aweak model. Precisely, our algorithm is defined in the atomic-state model andworks in anonymous networks in which even local ports are unlabeled. It makesno assumption on the daemon and thus stabilizes under the weakest one: thedistributed 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 fullpolynomiality 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 firstself-stabilizing unison for arbitrary anonymous networks achieving anasymptotically optimal stabilization time in rounds using a bounded memory ateach node.  Finally, we show that our solution allows to efficiently simulate synchronousself-stabilizing algorithms in an asynchronous environment. This provides a newstate-of-the-art algorithm solving both the leader election and the spanningtree construction problem in any identified connected network which, to thebest of our knowledge, beat all existing solutions of the literature.

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