Optimal implementation of the weakest failure detector for solving consensus

The concept of unreliable failure detector was introduced by T.D. Chandra and S. Toueg (1996) as a mechanism that provides information about process failures. Depending on the properties which the failure detectors guarantee, they proposed a taxonomy of failure detectors. It has been shown that one of the classes of this taxonomy, namely Eventually Strong (∇S), is the weakest class allowing a solution of the Consensus problem. The authors present a new algorithm implementing ∇S. Our algorithm guarantees that eventually all the correct processes agree on a common correct process. This property trivially allows us to provide the accuracy and completeness properties required by ∇S. We show then that our algorithm is better than any other proposed implementation of ∇S in terms of the number of messages and the total amount of information periodically sent. In particular, previous algorithms require periodic exchange of at least a quadratic amount of information, while ours only requires O(n log n) (where n is the number of processes). However, we also propose a new measure to evaluate the efficiency of this kind of algorithm, the eventual monitoring degree, which does not rely on a periodic behavior and expresses the degree of processing required by the algorithms better. We show that the runs of our algorithm have optimal eventual monitoring degree