Delay Optimization in Quorum Consensus

The management of replicated data in distributed database systems is a classic problem with great practical importance. Quorum consensus is one of the popular methods, combined with eager replication, for managing replicated data. In this paper we investigate the problems of delay-optimal quorum consensus. Firstly, we show that the problem of minimizing the total delay (or mean delay) restricted to a ring can be solved in a constant time in contrast to the existing approximation results. Secondly, we show that the problem of minimizing the total delay (or mean delay) is NP-hard. Thirdly, we present an approximate algorithm with an approximate ratio 2; and the approximate algorithm can guarantee the exact solutions for some specific network topology, such as trees and meshes. Finally, we present an improvement on the existing algorithm to solve the problem of minimizing the maximal delay; this reduces the time complexity from O(n 3 log n) to O(n 3) where n is the number of nodes.