Abstract
This paper studies the problem of broadcasting in synchronous point-to-point networks, where one initiator owns a piece of information that has to be transmitted to all other vertices as fast as possible. The model of fractional dynamic faults with threshold is considered: in every step either a fixed number T, or a fraction α, of sent messages can be lost depending on which quantity is larger.
As the main result we show that in complete graphs and hypercubes it is possible to inform all but a constant number of vertices, exhibiting only a logarithmic slowdown, i.e. in time O(Dlogn) where D is the diameter of the network and n is the number of vertices.
Moreover, for complete graphs under some additional conditions (sense of direction, or α< 0.55) the remaining constant number of vertices can be informed in the same time, i.e. O(logn).
The research has been supported by grant APVV-0433-06.
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References
Ahlswede, R., et al.: Fault-tolerant minimum broadcast networks. Networks 27 (1996)
Bagchi, A., Hakimi, S.L.: Information dissemination in distributed systems with faulty units. IEEE Transactions on Computers 43(6), 698–710 (1994)
Berman, K.A., Hawrylycz, M.: Telephone problems with failures. SIAM Journal on Algebraic and Discrete Methods 7(1), 13–17 (1986)
Berman, P., Diks, K., Pelc, A.: Reliable broadcasting in logarithmic time with Byzantine link failures. Journal of Algorithms 22(2), 199–211 (1997)
Bjork, L.A.: Recovery scenario for a db/dc system. In: ACM’73: Proceedings of the annual conference, pp. 142–146. ACM Press, New York (1973)
Chang, J.-M., Maxemchuk, N.F.: Reliable broadcast protocols. ACM Transactions on Computer Systems 2(3), 251–273 (1984)
Chlebus, B., Diks, K., Pelc, A.: Broadcasting in synchronous networks with dynamic faults. Networks 27 (1996)
Chlebus, B.S., Diks, K., Pelc, A.: Optimal broadcasting in faulty hypercubes. In: FTCS, pp. 266–273 (1991)
Chung, F.R.K., et al.: On induced subgraphs of the cube. Journal of Combinatorial Theory Series A 49, 180–187 (1988)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)
Diks, K., Pelc, A.: Almost safe gossiping in bounded degree networks. SIAM Journal on Discrete Mathematics 5(3), 338–344 (1992)
Dobrev, S., et al.: On fractional dynamic faults with threshold. In: Flocchini, P., Gąsieniec, L. (eds.) SIROCCO 2006. LNCS, vol. 4056, pp. 197–211. Springer, Heidelberg (2006)
Dobrev, S., Vrto, I.: Optimal broadcasting in hypercubes with dynamic faults. Information Processing Letters 71(2), 81–85 (1999)
Dobrev, S., Vrto, I.: Dynamic faults have small effect on broadcasting in hypercubes. Discrete Applied Mathematics 137(2), 155–158 (2004)
Dolev, S.: Self-stabilization. MIT Press, Cambridge (2000)
Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. Journal of the ACM 32(2), 374–382 (1985)
Flocchini, P., Mans, B., Santoro, N.: On the impact of sense of direction on message complexity. Information Processing Letters 63(1), 23–31 (1997)
Santoro, N., Mans, B., Flocchini, P.: Sense of Direction in Distributed Computing. In: Kutten, S. (ed.) DISC 1998. LNCS, vol. 1499, pp. 1–15. Springer, Heidelberg (1998)
Fraigniaud, P.: Asymptotically optimal broadcasting and gossiping in faulty hypercube multicomputers. IEEE Transactions on Computers 41(11), 1410–1419 (1992)
Gasieniec, L., Pelc, A.: Broadcasting with linearly bounded transmission faults. Discrete Applied Mathematics 83(1-3), 121–133 (1998)
Hedetniemi, S., Hedetniemi, S., Liestman, A.: A survey of broadcasting and gossiping in communication networks. Networks 18, 319–349 (1988)
Královič, R., Královič, R., Ružička, P.: Broadcasting with many faulty links. In: Sibeyn, J.F. (ed) SIROCCO, of Proceedings in Informatics, vol. 17, pp. 211–222. Carleton Scientific (2003)
Královič, R., Královič, R.: Rapid almost-complete broadcasting in faulty networks. Technical report, arXiv:cs.DC/0703122 (2007)
Liptak, Z., Nickelsen, A.: Broadcasting in complete networks with dynamic edge faults. In: Butelle, F. (ed.) OPODIS, Studia Informatica Universalis, pp. 123–142. Suger, Saint-Denis, rue Catulienne, France (2000)
Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. Journal of the ACM 27(2), 228–234 (1980)
Pelc, A.: Broadcasting in complete networks with faulty nodes using unreliable calls. Information Processing Letters 40(3), 169–174 (1991)
Pelc, A., Peleg, D.: Feasibility and complexity of broadcasting with random transmission failures. In: PODC ’05: Proceedings of the twenty-fourth annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pp. 334–341. ACM Press, New York (2005)
Santoro, N., Widmayer, P.: Distributed function evaluation in the presence of transmission faults. In: Asano, T., et al. (eds.) SIGAL 1990. LNCS, vol. 450, pp. 358–367. Springer, Heidelberg (1990)
Stanoi, I., Agrawal, D., Abbadi, A.E.: Using broadcast primitives in replicated databases. In: ICDCS ’98: Proceedings of the The 18th International Conference on Distributed Computing Systems, pp. 148–155. IEEE Computer Society, Washington (1998)
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Královič, R., Královič, R. (2007). Rapid Almost-Complete Broadcasting in Faulty Networks. In: Prencipe, G., Zaks, S. (eds) Structural Information and Communication Complexity. SIROCCO 2007. Lecture Notes in Computer Science, vol 4474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72951-8_20
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DOI: https://doi.org/10.1007/978-3-540-72951-8_20
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