Treffer: An improved algorithm for adaptive condition-based consensus

Condition-Based Approach studies restrictions on the inputs of a distributed problem, called conditions, to circumvent several impossibility results. Especially, for the synchronous consensus problem, the relation between conditions and time complexity bounds has been studied. In our previous work [12], we introduced the adaptiveness on time complexity of the condition-based approach, and established the adaptive condition-based approach: It classifies all possible input vectors into the hierarchical sequence of conditions according to their difficulty called legality level. For such hierarchy, adaptive algorithms achieve time complexity depending on the legality level of input vectors. In this paper, we propose an improved version of the adaptive condition-based algorithms for synchronous consensus that achieves better time complexity than the previous one. On the assumption that majority of processes are correct, the proposed algorithm terminates within min{f + 2, t + 1} - l rounds if I < f, where f and t is the actual and the maximum numbers of faults respectively, and l is the legality level of input vectors. Moreover, the algorithm terminates in 1 round if l > t and f = 0, and terminates within 2 rounds if l > f holds. Compared with our previous algorithm, the proposed algorithm improves time complexity by one round in the case of f = t and I > f.