On 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, combining with eager replication, for managing replicated data. In this paper, we will investigate the problems of delay-optimal quorum consensus. Firstly, we will 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 will show that the problem of minimizing the total-delay (or mean-delay) is NP-hard. Thirdly, we will 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 will present an improvement on the existing algorithm to solve the problem of minimizing the maximal-delay; this will reduce the time complexity from O(n log n) to ) where n is the number of nodes