Abstract
Self-stabilization in a model of anonymous, asynchronous interacting agents deployed in a network of unknown size is considered. Dijkstra-style round-robin token circulation can be done deterministically with constant space per node in this model. Constant-space protocols are given for leader election in rings, local-addressing in degree-bounded graphs, and establishing consistent global direction in an undirected ring. A protocol to construct a spanning tree in regular graphs using O(logD) memory is also given, where D is the diameter of the graph. A general method for eliminating nondeterministic transitions from the self-stabilizing implementation of a large family of behaviors is used to simplify the constructions, and general conditions under which protocol composition preserves behavior are used in proving their correctness.
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References
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: Twenty-Third ACM Symposium on Principles of Distributed Computing, pp. 290–299 (2004)
Angluin, D., Aspnes, J., Chan, M., Fischer, M.J., Jiang, H., Peralta, R.: Stably computable properties of network graphs. In: Prasanna, V.K., Iyengar, S.S., Spirakis, P.G., Welsh, M. (eds.) DCOSS 2005. LNCS, vol. 3560, pp. 63–74. Springer, Heidelberg (2005)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17(11), 643–644 (1974)
Mayer, A., Ofek, Y., Ostrovsky, R., Yung, M.: Self-stabilizing symmetry breaking in constant-space (extended abstract). In: Proc. 24th ACM Symp. on Theory of Computing, pp. 667–678 (1992)
Itkis, G., Lin, C., Simon, J.: Deterministic, constant space, self-stabilizing leader election on uniform rings. In: Workshop on Distributed Algorithms, pp. 288–302 (1995)
Higham, L., Myers, S.: Self-stabilizing token circulation on anonymous message passing rings. Technical report, University of Calgary (1999)
Johnen, C.: Bounded service time and memory space optimal self-stabilizing token circulation protocol on unidirectional rings. In: Procedings of the 18th International Parallel and Distributed Processing Symposium, p. 52a (2004)
Herman, T.: Probabilistic self-stabilization. Information Processing Letters 35(2), 63–67 (1990)
Dolev, S., Israeli, A., Moran, S.: Uniform dynamic self-stabilizing leader election. IEEE Transactions on Parallel and Distributed Systems 8, 424–440 (1997)
Beauquier, J., Gradinariu, M., Johnen, C.: Memory space requirements for self-stabilizing leader election protocols. In: Eighteenth ACM Symposium on Principles of Distributed Computing, pp. 199–207 (1999)
Itkis, G., Levin, L.A.: Fast and lean self-stabilizing asynchronous protocols. In: Proceeding of 35th Annual Symposium on Foundations of Computer Science, pp. 226–239. IEEE Press, Los Alamitos (1994)
Griggs, J.R., Yeh, R.K.: Labeling graphs with a condition at distance two. Journal of Discrete Mathematics 5, 586–595 (1992)
Herman, T., Tixeuil, S.: A distributed TDMA slot assignment algorithm for wireless sensor networks. In: Nikoletseas, S.E., Rolim, J.D.P. (eds.) ALGOSENSORS 2004. LNCS, vol. 3121, pp. 45–58. Springer, Heidelberg (2004)
Gradinariu, M., Johnen, C.: Self-stabilizing Neighborhood Unique Naming under Unfair Scheduler. In: Sakellariou, R., Keane, J.A., Gurd, J.R., Freeman, L. (eds.) Euro-Par 2001. LNCS, vol. 2150, pp. 458–465. Springer, Heidelberg (2001)
Moscibroda, T., Wattenhofer, R.: Coloring unstructured radio networks. In: Proceedings of the 17th annual ACM symposium on Parallelism in algorithms and architectures, pp. 39–48. ACM Press, New York (2005)
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Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H. (2006). Self-stabilizing Population Protocols. In: Anderson, J.H., Prencipe, G., Wattenhofer, R. (eds) Principles of Distributed Systems. OPODIS 2005. Lecture Notes in Computer Science, vol 3974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11795490_10
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DOI: https://doi.org/10.1007/11795490_10
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