Abstract
We study the impact of faulty processors on the communication cost of distributed algorithms in a message-passing model. The system is synchronous but prone to various kinds of processor failures: crashes, message omissions, (authenticated) Byzantine faults. One of the basic communication tasks, called fault-tolerant gossip, or gossip for short, is to exchange the initial values among all non-faulty processors. In this paper we address the question if there is a gossip algorithm which is both fault-tolerant, fast and communication-efficient? We answer this question in affirmative in the model allowing only crash failures, and in some sense negatively when the other kinds of failures may occur. More precisely, in an execution by n processors when f of them are faulty, each non-faulty processor contributes a constant to the message complexity, each crashed processor contributes Θ(f ε) (ε> 0 could be an arbitrarily small constant independent from n,f but dependent on the algorithm), each omission (or authenticated Byzantine) processor contributes Θ(t), and each—even potential—Byzantine failure results in additional Θ(n) messages sent.
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References
Attiya, H., Welch, J.: Distributed Computing. John Willey & Sons, West Sussex, England (2004)
Capalbo, M.R., Reingold, O., Vadhan, S.P., Wigderson, A.: Randomness conductors and constant-degree lossless expanders. In: Proc. of 34th ACM Symposium on Theory of Computing (STOC), pp. 659–668 (2002)
Chlebus, B.S., Kowalski, D.R.: Robust gossiping with an application to consensus. Journal of Computer and System Sciences 72, 1262–1281 (2006)
Chlebus, B.S., Kowalski, D.R.: Time and communication efficient consensus for crash failures. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 314–328. Springer, Heidelberg (2006)
Chlebus, B.S., Kowalski, D.R., Rokicki, M.A.: Adversarial queuing on the multiple-access channel. In: Proc. of 25th ACM Symposium on Principles of Distributed Computing (PODC), pp. 92–101 (2006)
Chlebus, B.S., Kowalski, D.R., Shvartsman, A.A.: Collective asynchronous reading with polylogarithmic worst-case overhead. In: Proc. of 36th ACM Symposium on Theory of Computing (STOC), pp. 321–330 (2004)
Diks, K., Pelc, A.: Optimal adaptive broadcasting with a bounded fraction of faulty nodes. Algorithmica 28(1), 37–50 (2000)
Dolev, D., Reischuk, R.: Bounds on information exchange for Byzantine Agreement. Journal of ACM 32(1), 191–204 (1985)
Fischer, M., Lynch, N.: A lower bound for the time to assure interactive consistency. Information Processing Letters 14(4), 183–186 (1982)
Fujita, S., Yamashita, M.: Optimal group gossiping in hypercubes under circuit switching model. SIAM J. on Computing 25(5), 1045–1060 (1996)
Galil, Z., Mayer, A., Yung, M.: Resolving message complexity of Byzantine agreement and beyond. In: Proc. of 36th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 724–733 (1995)
Georgiou, C., Kowalski, D.R., Shvartsman, A.A.: Efficient gossip and robust distributed computation. In: Fich, F.E. (ed.) DISC 2003. LNCS, vol. 2848, pp. 224–238. Springer, Heidelberg (2003)
Hromkovic, J., Klasing, R., Pelc, A., Ruzicka, P., Unger, W.: Dissemination of information in communication networks: broadcasting, gossiping, leader election, and fault-tolerance. In: Theoretical Computer Science. EATCS Series, Springer, Heidelberg (2005)
Lynch, N.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)
Neiger, G., Toueg, S.: Automatically increasing the fault-tolerance of distributed systems. Journal of Algorithms 11, 374–419 (1990)
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Kowalski, D.R., Strojnowski, M. (2007). On the Communication Surplus Incurred by Faulty Processors. In: Pelc, A. (eds) Distributed Computing. DISC 2007. Lecture Notes in Computer Science, vol 4731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75142-7_26
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DOI: https://doi.org/10.1007/978-3-540-75142-7_26
Publisher Name: Springer, Berlin, Heidelberg
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