Fault-tolerant clock synchronization of large multicomputers via multistep interactive convergence

We present a fault-tolerant algorithm that internally synchronizes clocks in multicomputer systems employing not completely connected networks (NCCNs). The algorithm is referred to as multistep interactive convergence, and is locally implemented in each node by a time sewer process (TSP). The algorithm proceeds in rounds, and bases its operation on a logical mapping of the system's TSPs into an m-dimensional array. A TSP executes m steps per round, each step including a call to an interactive convergence procedure. Clock readings in step i are gathered only from TSPs sharing a row along dimension i of the array, which reduces the number of messages by orders of magnitude over a conventional interactive convergence algorithm. The algorithm can be used in systems of arbitrary topology, and provides the added benefit of increased locality of communication in regular NCCNs. These advantages can be combined with a variety of message staggering mechanisms to maintain network contention at a minimum. We characterize the maximum clock skew maximum clock drift, maximum clock discontinuity, and number of messages produced by the algorithm, and show that it tolerates arbitrary faults. A comparison with other algorithms is provided.