The Bloom Clock to Characterize Causality in Distributed Systems

Abstract

Determining the causality between events in distributed executions is a fundamental problem. Vector clocks solve this problem but do not scale well. The probabilistic Bloom filter data structure can be used as a Bloom clock to determine causality between events with lower space overhead than vector clock; however, the Bloom filter and hence the Bloom clock naturally suffer from false positives. We give a formal protocol of the Bloom clock based on Counting Bloom filters and study its properties. We formulate the probabilities of a positive outcome, a positive being false, and a false positive for Bloom clocks as a function of the corresponding vector clocks, as well as their estimates as a function of the Bloom clocks. We also indicate how to estimate the accuracy, precision, and false positive rate of an execution slice that is identified by the Bloom timestamps of two events.