Self-stabilizing synchronization algorithms on oriented chains

We present a space and (asymptotically) time optimal, uniform, self-stabilizing scheme for a given synchronization problem on asynchronous oriented chains (algorithm SSDS), that works under an unfair distributed daemon. We use this scheme to solve local mutual exclusion and distributed sorting (where each process holds a single value and the values to be sorted are distinct). Algorithm SSDS can be used to obtain optimal space solutions for other problems such as broadcasting, leader election, mutual exclusion.