Abstract
We investigate the hardness of establishing as many stable marriages (that is, marriages that last forever) in a population whose memory is placed in some arbitrary state with respect to the considered problem, and where traitors try to jeopardize the whole process by behaving in a harmful manner. On the negative side, we demonstrate that no solution that is completely insensitive to traitors can exist, and we propose a protocol for the problem that is optimal with respect to the traitor containment radius.
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References
Barbaro, N.: Diary of the Siege of Constantinople. Translation by John Melville-Jones, New York (1453)
Pease, M.C., Shostak, R.E., Lamport, L.: Reaching agreement in the presence of faults. J. ACM 27(2), 228–234 (1980)
Lamport, L., Shostak, R.E., Pease, M.C.: The byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382–401 (1982)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)
Dolev, S.: Self-stabilization. MIT Press (March 2000)
Tixeuil, S.: Self-stabilizing Algorithms. Chapman & Hall/CRC Applied Algorithms and Data Structures. In: Algorithms and Theory of Computation Handbook, 2nd edn., pp. 26.1–26.45. CRC Press, Taylor & Francis Group (November 2009)
Nesterenko, M., Arora, A.: Tolerance to unbounded byzantine faults. In: 21st Symposium on Reliable Distributed Systems (SRDS 2002), pp. 22–29. IEEE Computer Society (2002)
Hsu, S.C., Huang, S.T.: A self-stabilizing algorithm for maximal matching. Inf. Process. Lett. 43(2), 77–81 (1992)
Tel, G.: Maximal matching stabilizes in quadratic time. Inf. Process. Lett. 49(6), 271–272 (1994)
Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks. In: IPDPS, p. 162 (2003)
Manne, F., Mjelde, M., Pilard, L., Tixeuil, S.: A new self-stabilizing maximal matching algorithm. Theoretical Computer Science (TCS) 410(14), 1336–1345 (2009)
Ghosh, S., Gupta, A., Hakan, M., Sriram, K., Pemmaraju, V.: Self-stabilizing dynamic programming algorithms on trees. In: Proceedings of the Second Workshop on Self-Stabilizing Systems, pp. 11.1–11.15 (1995)
Blair, J.R.S., Manne, F.: Efficient self-stabilizing algorithms for tree network. In: ICDCS, pp. 20–26 (2003)
Goddard, W., Hedetniemi, S.T., Shi, Z.: An anonymous self-stabilizing algorithm for 1-maximal matching in trees. In: PDPTA, pp. 797–803 (2006)
Manne, F., Mjelde, M., Pilard, L., Tixeuil, S.: A self-stabilizing 2/3-approximation algorithm for the maximum matching problem. Theoretical Computer Science (TCS) 412(40), 5515–5526 (2011)
Dolev, S., Welch, J.L.: Self-stabilizing clock synchronization in the presence of byzantine faults. J. ACM 51(5), 780–799 (2004)
Daliot, A., Dolev, D.: Self-stabilization of Byzantine Protocols. In: Tixeuil, S., Herman, T. (eds.) SSS 2005. LNCS, vol. 3764, pp. 48–67. Springer, Heidelberg (2005)
Masuzawa, T., Tixeuil, S.: Stabilizing link-coloration of arbitrary networks with unbounded byzantine faults. International Journal of Principles and Applications of Information Science and Technology (PAIST) 1(1), 1–13 (2007)
Dubois, S., Masuzawa, T., Tixeuil, S.: The Impact of Topology on Byzantine Containment in Stabilization. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 495–509. Springer, Heidelberg (2010)
Dubois, S., Masuzawa, T., Tixeuil, S.: On Byzantine Containment Properties of the min + 1 Protocol. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds.) SSS 2010. LNCS, vol. 6366, pp. 96–110. Springer, Heidelberg (2010)
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Dubois, S., Tixeuil, S., Zhu, N. (2012). The Byzantine Brides Problem. In: Kranakis, E., Krizanc, D., Luccio, F. (eds) Fun with Algorithms. FUN 2012. Lecture Notes in Computer Science, vol 7288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30347-0_13
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DOI: https://doi.org/10.1007/978-3-642-30347-0_13
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