Chou et al. (1990) presented two synchronizer algorithms for ABD networks. One of their synchronizers has a round time of three, and the other has a round time of only two but requires an additional bit in every message of the simulated algorithm. The authors show that ABD synchronization can be improved by using information that can be obtained, without exchanging more messages, during the initialization of the synchronizers. The authors first contribution is a synchronizer with a round time of two that does not require an additional bit in basic messages. The second result refutes the common belief that a round time of two is the best achievable for this type of synchronizer. They show that in some network topologies a smaller round time is achievable by making the local time of simulation of the pulses dependent on the arrival time of messages received during initialization. The correctness of the synchronizers is shown by modeling this class of synchronizers as functions, and using these functions lower bounds on the round time can also be easily obtained. The authors show that their synchronizers are optimal, i.e., further reduction of the round time by the same means is not possible.>

It is shown that the termination detection problem for distributed computations can be modeled as an instance of the garbage collection problem. Consequently, algorithms for the termination detection problem are obtained by applying transformations to garbage collection algorithms. The transformation can be applied to collectors of the “mark-and-sweep” type as well as to reference-counting protocol of Lermen and Maurer, the weighted-reference-counting protocol, the local-reference-counting protocol, and Ben-Ari's mark-and-sweep collector into termination detection algorithms. Known termination detection algorithms as well as new variants are obtained.