Efficient Reduction for Wait-Free Termination Detection in a Crash-Prone Distributed System

We investigate the problem of detecting termination of a distributed computation in systems where processes can fail by crashing. Specifically, when the communication topology is fully connected, we describe a way to transform any termination detection algorithm A that has been designed for a failure-free environment into a termination detection algorithm B that can tolerate process crashes. Our transformation assumes the existence of a perfect failure detector. We show that a perfect failure detector is in fact necessary to solve the termination detection problem in a crash-prone distributed system even if at most one process can crash. Let μ(n,M) and δ(n,M) denote the message complexity and detection latency, respectively, of A when the system has n processes and the underlying computation exchanges M application messages. The message complexity of B is at most O(n + μ(n, 0)) messages per failure more than the message complexity of A. Also, its detection latency is at most O(δ(n, 0)) per failure more than that of A. Furthermore, the overhead (that is, the amount of control data piggybacked) on an application message increases by only O(log n) bits per failure. The fault-tolerant termination detection algorithm resulting from the transformation satisfies two desirable properties. First, it can tolerate failure of up to n−1 processes, that is, it is wait-free. Second, it does not impose any overhead on the fault-sensitive termination detection algorithm until one or more processes crash, that is, it is fault-reactive. Our transformation can be extended to arbitrary communication topologies provided process crashes do not partition the system.