We present a new approach for fault-tolerant internal clock synchronization in multicomputer systems employing not completely connected networks (NCCNs). The approach is referred to as multistep interactive convergence and is locally implemented in each multicomputer node by a time server process (TSP). We describe a specific algorithm that uses multistep interactive convergence 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 of synchronization, with each step including a call to an interactive convergence procedure. For any TSP, clock readings in step i are gathered only from TSPs with which it shares a row along dimension i of the array. Hence, a TSP reads clocks only from a small subset of the TSPs in the system, which reduces the number of messages by orders of magnitude over a conventional interactive convergence algorithm in which reliable all-to-all broadcast of clock values is done. The algorithm can be used in systems of arbitrary topology and provides the added benefit of increased locality of communication in regular NCCNs such as hypercubes and tori. These advantages can be combined with a variety of message staggering mechanisms to maintain network contention at a minimum. We present expressions for 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 that elucidates the advantages of multistep interactive convergence is also provided.
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