This Article 
 Bibliographic References 
 Add to: 
On the Asymptotical Optimality of Multilayered Decentralized Consensus Protocol
August 2002 (vol. 13 no. 8)
pp. 769-786

Abstract—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.

[1] W.C. Athas and C.L. Seitz, “Multicomputers: Message-Passing Concurrent Computers,” Computer, vol. 21, pp. 9-24, Aug. 1988.
[2] L. Bhuyan and D.P. Agrawal, “Generalized Hypercube and Hyperbus Structures for a Computer Network,” IEEE Trans. Computers, vol. 33, no. 4, pp. 323-333, Apr. 1984.
[3] T.D. Chandra and S. Toueg, “Unreliable Failure Detectors for Reliable Distributed Systems,” J. ACM, vol. 43, no. 2, pp. 225–267, 1996.
[4] M.-S. Chen, J.-C. Chen, and P.S. Yu, “On General Results for All-to-All Broadcast,” IEEE Trans. Parallel and Distributed System, vol. 7, no. 4, pp. 363-370, Apr. 1996.
[5] M.-S. Chen, K.-L. Wu, and P.S. Yu, “Efficient Decentralized Consensus Protocols in a Distributed Computing System,” Proc. 12th Int'l Conf. Distributed Computing Systems, pp. 426-433, June 1992.
[6] M.-S. Chen, P.S. Yu, K.-L. Wu, “Decentralized Consensus Protocols with Multi-Port Communication,” Proc. 13th Int'l Conf. Distributed Computing Systems, pp. 356-365, May 1993.
[7] S.B. Davidson, H. Garcia-Molina, and D. Skeen, "Consistency in Partitioned Networks," ACM Computing Surveys, vol. 17, no. 3, pp. 341-370, Sept. 1985.
[8] A.W. Fu, “Delay-Optimal Quorum Consensus for Distributed Systems,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 1, pp. 59-69, Jan. 1997.
[9] V. Hadzilacos and J. Halpern, “Message-Optimal Protocols for Byzantine Agreement,” Technical Report RJ 7879, IBM Almaden Research Laboratory, San Jose, Calif., Dec. 1990.
[10] S.M. Hedetniemi, S.T. Hedetniemi, and A. Liestman, “A Survey of Broadcasting and Gossiping in Communication Networks,” NETWORKS, vol. 18, pp. 319-351, 1988.
[11] M. Hurfin, A. Mostefaoui, and M. Raynal, “Consensus in Asynchronous Systems Where Processes can Crash and Recover,” Proc. 17th IEEE Symp. Reliable Distributed Systems, pp. 280-286, 1998.
[12] S.L. Johnsson and C.T. Ho,“Spanning graphs for optimum broadcasting and personalizedcommunication in hypercubes,” IEEE Trans. Computers, vol. 38, no. 9, pp. 1,249-1,268, Sept. 1989.
[13] T.V. Lakshman and A.K. Agrawala, “Efficient Decentralized Consensus Protocols,” IEEE Trans. Software Eng., vol. 12, no. 5, pp. 600-607, May 1986.
[14] S. Lee and K.G. Shin, “Interleaved All-to-All Reliable Broadcast on Meshes and Hypercube,” IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 5, pp. 449-458, 1994.
[15] Z.-R. Lin and M.-S. Chen, “An Asymptotically Optimal Multi-Layered Decentralized Consensus Protocol with an Initiator,” Proc. 20th IEEE Int'l Conf. Distributed Computing Systems, 280-287, Apr. 2000.
[16] E.A. Monakhova, “Algorithms and Lower Bounds for P-Gossiping in Circulant Networks,” Proc. Third Int'l Symp. Parallel Architectures, Algorithms, and Networks (I-SPAN '97), pp. 132-137, 1997.
[17] K.N. Venkataraman, G. Cybenko, and D.W. Krumme, “Simultaneous Broadcasting in Multiprocessor Networks,” Proc. Int'l Conf. Parallel Processing, pp. 555-558, 1986.
[18] S.-M. Yuan and A.K. Agrawala, “A Class of Optimal Decentralized Commit Protocols,” Proc. Eighth Int'l Conf. Distributed Computing Systems, pp. 234-241, 1988.

Index Terms:
Consensus protocol, distributed systems, multiport communication, performance analysis.
Cheng-Ru Lin, Ming-Syan Chen, "On the Asymptotical Optimality of Multilayered Decentralized Consensus Protocol," IEEE Transactions on Parallel and Distributed Systems, vol. 13, no. 8, pp. 769-786, Aug. 2002, doi:10.1109/TPDS.2002.1028435
Usage of this product signifies your acceptance of the Terms of Use.