On the asymptotical optimality of multilayered decentralized consensus protocol

A decentralized consensus protocol refers to a process for all nodes in a distributed system to collect the information/status from every other node and reach a consensus among them. Two classes of decentralized consensus protocols have been studied before: the one without an initiator and the one with an initiator. While the one without an initiator has been well studied in the literature, it is noted that the prior protocols with an initiator mainly relied upon the one without an initiator and thus did not fully exploit the intrinsic properties of having an initiator. By exploiting the concept of multilayered execution, we develop in this paper an efficient multilayered decentralized consensus protocol for a distributed system with an initiator. By adapting itself to the number of nodes in the system, the proposed protocol can determine a proper layer for execution and reach the consensus in the minimal numbers of message steps while incurring a much smaller number of messages than required by prior works. Several illustrative examples are given and performance analysis of the proposed algorithm is conducted to provide many insights into the problem studied. It is shown that the decentralized consensus protocols developed in this paper for the case of having an initiator significantly outperform prior schemes. Specifically, it is proven that (1) the ratio of the average number of messages incurred by the proposed algorithm to that by the prior method approaches zero as the number of nodes increases and (2) the proposed algorithm is asymptotically optimal in the sense that the message number required by the proposed algorithm and that of the optimal one are asymptotically of the same complexity with respect to the number of nodes in the system, showing the very important advantage of the proposed algorithm.