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Optimal Distributed t-Resilient Election in Complete Networks
April 1990 (vol. 16 no. 4)
pp. 415-420

The problem of distributed leader election in an asynchronous complete network, in the presence of faults that occurred prior to the execution of the election algorithm, is discussed. Failures of this type are encountered, for example, during a recovery from a crash in the network. For a network with n processors, k of which start the algorithm that uses at most O(n log k+n+kt) messages is presented and shown to be optimal. An optimal algorithm for the case where the identities of the neighbors are known is also presented. It is noted that the order of the message complexity of a t-resilient algorithm is not always higher than that of a nonresilient one. The t-resilient algorithm is a systematic modification of an existing algorithm for a fault-free network.

[1] H. H. Abu-Amara, "Fault tolerance distributed algorithm for election in complete networks,"IEEE Trans. Comput., vol. 37, no. 4, pp. 449-453, 1988.
[2] Y. Afek and E. Gafni, "Simple and efficient distributed algorithms for election in complete networks," inProc. 22nd Annu. Allerton Conf. Communication, Control, and Computing, Allerton House, Monticello, IL, Oct. 1984, pp. 689-698.
[3] Y. Afek and E. Gafni, "Time and message bounds for election in synchronous and asynchronous complete networks," inProc. 4th ACM Symp. Principles Distributed Comput., Minacki, Ont., Canada, Aug. 1985, pp. 186-195.
[4] R. Bar-Yehuda, S. Kutten, Y. Wolfstahl, and S. Zaks, "Making distributed spanning tree algorithms fault-resilient," inProc. 4th Symp. Theoretical Aspects of Comput. Sci., Passau, Germany, Feb. 1987, pp. 432-444.
[5] M. J. Fischer, "The consensus problem in unreliable distributed systems (a brief survey)," Rep. YALE/DCS/RR-273, June 1983.
[6] M. J. Fischer, N. A. Lynch, and M. Merritt, "Easy impossibility proofs for distributed consensus problems," inProc. 4th ACM Symp. Principles of Distributed Computing, Minaki, Canada, Aug. 1985, pp. 59-70.
[7] 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, Apr. 1985.
[8] R. G. Gallager, "Finding a leader in a network withOE(
[9] H. Garcia-Molina, "Elections in a distributed computing system,"IEEE Trans. Comput., vol. C-31, no. 1, 1982.
[10] R. G. Gallager, P. A. Humblet, and P. M. Spira, "A distributed algorithm for minimum weight spanning trees,"ACM Trans. Programming Languages and Syst., vol. 5, no. 1, pp. 66-67, Jan. 1983.
[11] P. M. Humblet, "Selecting a leader in a clique inO(nlogn) messages," Lab. Inform. Decision Syst., M.I.T., Internal Memo, Feb. 1984.
[12] E. Korach, S. Moran, and S. Zaks, "Tight lower and upper bounds for some distributed algorithms for a complete network of processors," inProc. 3rd ACM Symp. Principles Distributed Comput., Vancouver, B.C., Canada, Aug. 1984, pp. 199-207.
[13] S. Kutten and Y. Wolfstahl, "Finding a leader in a distributed system where elements may fail," inProc. 17th IEEE Annu. Electronics and Aerospace Conf., Washington, DC, Sept. 1984, pp. 101-105.
[14] S. Kutten, Y. Wolfstahl, and S. Zaks, "Optimal distributedt-resilient election in complete networks," IBM, Res. Rep. RC 12177, Sept. 1986.
[15] G. Le-Lann, "Distributed systems--Towards a formal approach," inInformation Processing 77, B. Gilchrist, Ed. Amsterdam, The Netherlands: North-Holland, 1977, pp. 155-160.
[16] S. Moran and Y. Wolfstahl, "An extended impossibility result for asynchronous complete networks,"Inform. Processing Lett., vol. 26, pp. 145-151, 1987/1988.
[17] L. Shrira and O. Goldreich, "Electing a leader in the presence of faults: A ring as a special case,"Acta Informatica, vol. 24, pp. 79-91, 1987.
[18] A. Itai and M. Rodeh, "The multi-tree approach to reliability in distributed networks,"Inform. Computat., vol. 79, no. 1, pp. 43-59. Oct. 1988; also preliminary version inProc. 25th Symp. Foundations of Computer Science, Oct. 1984.

Index Terms:
optimal distributed t-resilient election; complete networks; distributed leader election; election algorithm; message complexity; fault-free network; computer networks; distributed processing; fault tolerant computing; software engineering.
A. Itai, S. Kutten, Y. Wolfstahl, S. Zaks, "Optimal Distributed t-Resilient Election in Complete Networks," IEEE Transactions on Software Engineering, vol. 16, no. 4, pp. 415-420, April 1990, doi:10.1109/32.54293
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