Self-stabilizing space optimal synchronization algorithms on trees

We present a space and (asymptotically) time optimal self-stabilizing algorithm for simultaneously activating non-adjacent processes in a rooted tree (Algorithm SSDST). We then give two applications of the proposed algorithm: a time and space optimal solution to the local mutual exclusion problem (Algorithm LMET) and a space and (asymptotically) time optimal distributed algorithm to place the values in min-heap order (Algorithm HEAP). All algorithms are self-stabilizing and uniform, and they work under any unfair distributed daemon. In proving the time complexity of the heap construction, we use the notion of pseudo-time. Pseudo-time is similar to logical time introduced by Lamport [12].