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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-30347-0_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30346-3
Online ISBN: 978-3-642-30347-0
eBook Packages: Computer ScienceComputer Science (R0)