Message-Optimal and Latency-Optimal Termination Detection Algorithms for Arbitrary Topologies

Detecting termination of a distributed computation is a fundamental problem in distributed systems. We present two optimal algorithms for detecting termination of a non-diffusing distributed computation for an arbitrary topology. Both algorithms are optimal in terms of message complexity and detection latency. The first termination detection algorithm has to be initiated along with the underlying computation. The message complexity of this algorithm is Θ(N + M) and its detection latency is Θ(D), where N is the number of processes in the system, M is the number of application messages exchanged by the underlying computation, and D is the diameter of the communication topology. The second termination detection algorithm can be initiated at any time after the underlying computation has started. The message complexity of this algorithm is Θ(E + M) and its detection latency is Θ(D), where E is the number of channels.