Stabilizing Phase-Clocks

This note considers the problem of synchronizing a network of digital clocks: the clocks all run at the same rate, however, an initial state of the network may place the clocks in arbitrary phases. The problem is to devise a protocol to advance or retard clocks so that eventually all clocks are in phase. The solutions presented in this note are protocols in which all processes are identical and use a constant amount of space per process. One solution is a deterministic protocol for a tree network; another solution is a probabilistic protocol for a network of arbitrary topology.