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Condition Adaptation in Synchronous Consensus
July 2006 (vol. 55 no. 7)
pp. 843-853
The condition-based approach is one of the sophisticated methods used to overcome several impossibility results in the distributed consensus problem (e.g., impossibility of fault tolerance in asynchronous consensus or time complexity lower bounds in synchronous consensus). It introduces conditions on input vectors to specify subsets of all possible input vectors to consensus algorithms and condition-based algorithms can circumvent the impossibility if actual input vectors satisfy a particular condition. In this paper, we present a new condition-based paradigm for synchronous consensus. We introduce the new concept of adaptation on the time complexity of condition-based algorithms and present the adaptive condition-based approach to synchronous consensus. In our approach, all possible input vectors are classified into hierarchical conditions according to their difficulty called the legality level. The execution time of adaptive condition-based algorithms depends on the legality level of input vectors. We propose two adaptive condition-based algorithms for synchronous consensus. The first algorithm requires that the majority of processes be correct, and terminates within \min\{f + 2, t+ 1\} - l rounds if l < f, where f and t are the actual and the maximum numbers of faults, respectively, and l is the legality level of the input vector. Moreover, the algorithm terminates in one round if l \geq t and f=0 and terminates within two rounds if l \geq f holds. Compared with previous algorithms, this algorithm achieves the best time complexity. The second algorithm can tolerate any number of faults, and terminates within \max\{3, \min\{f + 3, t + 2\} - l\} rounds if l < f holds, terminates in one round if l \geq t and f=0, and terminates within three rounds if l \geq f holds.

[1] H. Attiya and Z. Avidor, “Wait-Free n-Set Consensus when Inputs Are Restricted,” Proc. 17th Int'l Conf. Distributed Computing (DISC), pp. 326-338, 2002.
[2] H. Attiya and J.L. Welch, “Sequential Consistency versus Linearizability,” ACM Trans. Computer Systems, vol. 12, no. 2, pp. 91-122, 1994.
[3] M. Ben-Or, “Another Advantage of Free Choice: Completely Asynchronous Agreement Protocols (Extended Abstract),” Proc. Second Ann. ACM Symp. Principles of Distributed Computing (PODC), pp. 27-30, 1983.
[4] F.V. Brasileiro, F. Greve, A. Mostéfaoui, and M. Raynal, “Consensus in One Communication Step,” Proc. Sixth Int'l Conf. Parallel Computing Techniquea (PACT), pp. 42-50, 2001.
[5] T.D. Chandra and S. Toueg, “Unreliable Failure Detectors for Reliable Distributed Systems,” J. ACM, vol. 43, no. 2, pp. 225-267, 1996.
[6] B. Charron-Bost and A. Schiper, “Uniform Consensus Is Harder than Consensus,” J. Algorithms, vol. 51, no. 1, pp. 15-37, Apr. 2004.
[7] D. Dolev, C. Dwork, and L. Stockmeyer, “On the Minimal Synchronism Needed for Distributed Consensus,” J. ACM, vol. 34, no. 1, pp. 77-97, 1987.
[8] D. Dolev, R. Reischuk, and R. Strong, “Early Stopping in Byzantine Agreement,” J. ACM, vol. 37, no. 4, pp. 720-741, 1990.
[9] M.J. Fischer, N.A. Lynch, and M.S. Paterson, “Impossibility of Distributed Consensus with One Faulty Process,” J. ACM, vol. 32, no. 2, pp. 374-382, 1985.
[10] R. Friedman, A. Mostéfaoui, S. Rajsbaum, and M. Raynal, “Distributed Agreement and Its Relation with Error-Correcting Codes,” Proc. 17th Int'l Conf. Distributed Computing (DISC), pp. 63-87, 2002.
[11] R. Guerraoui, “Revisiting the Relationship between Non-Blocking Atomic Commitment and Consensus,” Proc. Ninth Int'l Workshop Distributed Algorithms (WDAG), Sept. 1995.
[12] R. Guerraoui and M. Raynal, “The Information Structure of Indulgent Consensus,” IEEE Trans. Computers, vol. 53, no. 4, pp. 453-466, 2004.
[13] V. Hadzilacos and S. Toueg, “Fault-Tolerant Broadcasts and Related Problems,” Distributed Systems, S. Mullender, ed., chapter 5, pp. 97-145, Addison-Wesley, 1993.
[14] M. Herlihy, “Wait-Free Synchronization,” ACM Trans. Programming Languages and Systems, vol. 13, pp. 124-149, 1991.
[15] A. Mostéfaoui, E. Mourgaya, P.R. Parvédy, and M. Raynal, “Evaluating the Condition-Based Approach to Solve Consensus,” Proc. Int'l Conf. Dependable Systems and Networks (DSN), pp. 541-550, 2003.
[16] A. Mostéfaoui, S. Rajsbaum, and M. Raynal, “Conditions on Input Vectors for Consensus Solvability in Asynchronous Distributed Systems,” J. ACM, vol. 50, no. 6, pp. 922-954, 2003.
[17] A. Mostéfaoui, S. Rajsbaum, and M. Raynal, “Using Conditions to Exppedite Consensus in Synchronous Distributed Systems,” Proc. 17th Int'l Conf. Distributed Computing (DISC), pp. 249-263, Oct. 2003.
[18] A. Mostéfaoui, S. Rajsbaum, and M. Raynal, “The Synchronous Condition-Based Consensus Hierarchy,” Proc. 18th Int'l Conf. Distributed Computing (DISC), pp. 1-15, Oct. 2004.
[19] A. Mostéfaoui, S. Rajsbaum, and M. Raynal, “The Combined Power of Conditions and Failure Detectors to Solve Asynchronous Set Agreement,” Proc. 24th Ann. ACM Symp. Principles of Distributed Computing (PODC), pp. 179-188, 2005.
[20] A. Mostéfaoui, S. Rajsbaum, M. Raynal, and M. Roy, “Condition-Based Protocols for Set Agreement Problems,” Proc. 17th Int'l Conf. Distributed Computing (DISC), pp. 48-62, 2002.
[21] A. Mostéfaoui, S. Rajsbaum, M. Raynal, and M. Roy, “Condition-Based Consensus Solvability: A Hierarchy of Conditions and Efficient Protocols,” Distributed Computing, vol. 17, no. 1, pp. 1-20, 2004.
[22] K.J. Perry and S. Toueg, “Distributed Agreement in the Presence of Processor and Communication Faults,” IEEE Trans. Software Eng., vol. 12, no. 3, pp. 477-482, Mar. 1986.
[23] M. Raynal, “Consensus in Synchronous Systems: A Concise Guided Tour,” Proc. Pacific Rim Int'l Symp. Dependable Computing (PRDC), pp. 221-228, 2002.
[24] G. Taubenfeld and S. Moran, “Possibility and Impossibility Results in a Shared Memory Environment,” Acta Informatica, vol. 33, no. 1, pp. 1-20, 1996.
[25] Y. Zibin, “Condition-Based Consensus in Synchronous Systems,” Proc. 17th Int'l Conf. Distributed Computing (DISC), pp. 239-248, Oct. 2003.

Index Terms:
Distributed algorithm, synchronous system, consensus problem, fault tolerance, crash fault, condition-based approach, adaptiveness.
Citation:
Taisuke Izumi, Toshimitsu Masuzawa, "Condition Adaptation in Synchronous Consensus," IEEE Transactions on Computers, vol. 55, no. 7, pp. 843-853, July 2006, doi:10.1109/TC.2006.99
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