Adaptive Plausible Clocks

Report, 2003

Having small-sized logical clocks with high causal-ordering accuracy is useful, especially where (i) the precision of the knowledge of the causal dependencies among events implies savings in time overhead and (ii) the cost of transmitting Full Vector clock timestamps |that precisely characterise the causal relation| is high. Plausible clocks can be used as timestamps to order events in a distributed system in a way that is consistent with the causal order as long as the events are causally dependent. The inaccuracy of a plausible clock algorithm is measured by the number of ordering errors it makes in an execution, i.e. the number of causally independent event pairs that it relates. In this work we study the accuracy of plausible clocks, which is measured by the number of causally independent event pairs that they relate. We introduce the Non-Uniformly Mapped R-Entries Vector (NUREV) clocks, a general class of plausible clocks, which allow the use of clock vectors with a small number of entries and which also allow each process in the system to use a di erent mapping between process-ids and clock-entry indices, the idea being that dynamic mappings allow self-tuning and adaptation to improve the accuracy of the clocks. Furthermore, we analyse the ways that these clocks may relate causally independent event pairs. Our analysis resulted in a set of conclusions and the formulation of new, adaptive plausible clocks algorithms, with improved accuracy, even when the number of clock entries is very small, which is important in peer-to-peer communication systems.