  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.

Distributed, Parallel, and Cluster Computing