Abstract
A population protocol is one of distributed computing models for passively-mobile systems, where a number of agents change their states by pairwise interactions between two agents. In this paper, we investigate the solvability of the self-stabilizing leader election in population protocols without any kind of oracles. We identify the necessary and sufficient condition to solve the self-stabilizing leader election in population protocols from the aspects of local memory complexity and fairness assumptions. This paper shows that under the assumption of global fairness, no protocol using only nāāā1 states can solve the self-stabilizing leader election in complete interaction graphs, where n is the number of agents in the system. To prove this impossibility, we introduce a novel proof technique, called closed-set argument. In addition, we propose a self-stabilizing leader election protocol using n states that works even under the unfairness assumption. This protocol requires the exact knowledge about the number of agents in the system. We also show that such knowledge is necessary to construct any self-stabilizing leader election protocol.
This work is supported in part by the Japan Society for the Promotion of Science: Grant-in-Aid for Young Scientists(B)(19700058), the Japan Society for the Promotion of Science: Grant-in-Aid for Scientific Research(C)(21500013) and Hori Information Science Promotion Foundation.
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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. Distributed ComputingĀ 18(4), 235ā253 (2006)
Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. In: Anderson, J.H., Prencipe, G., Wattenhofer, R. (eds.) OPODIS 2005. LNCS, vol.Ā 3974, pp. 103ā117. Springer, Heidelberg (2006)
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.Ā 3560, pp. 63ā74. Springer, Heidelberg (2005)
Angluin, D., Aspnes, J., Eisenstat, D.: Stably computable predicates are semilinear. In: Proc. 25th Annual ACM Symposium on Principles of Distributed Computing, pp. 292ā299 (2006)
Angluin, D., Aspnes, J., Eisenstat, D.: A simple protocol for fast robust approximate majority. In: Pelc, A. (ed.) DISC 2007. LNCS, vol.Ā 4731, pp. 20ā32. Springer, Heidelberg (2007)
Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. Distributed ComputingĀ 20(4), 279ā304 (2007)
Aspnes, J., Ruppert, E.: An introduction to population protocols. Bulletin of the EATCSĀ 93, 98ā117 (2007)
Beauquier, J., Clement, J., Messika, S., Rosaz, L., Rozoy, B.: Self-stabilizing counting in mobil sensor networks. In: Pelc, A. (ed.) DISC 2007. LNCS, vol.Ā 4731, pp. 63ā76. Springer, Heidelberg (2007)
Canepa, D., Potop-Butucaru, M.G.: Stabilizing leader election in population protocols (2007) (unpublished)
Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Ruppert, E.: When birds die: Making population protocols fault-tolerant. In: Gibbons, P.B., Abdelzaher, T., Aspnes, J., Rao, R. (eds.) DCOSS 2006. LNCS, vol.Ā 4026, pp. 51ā66. Springer, Heidelberg (2006)
Fischer, M.J., Jiang, H.: Self-stabilizing leader election in networks of finite-state anonymous agent. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol.Ā 4305, pp. 395ā409. Springer, Heidelberg (2006)
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Cai, S., Izumi, T., Wada, K. (2010). Space Complexity of Self-stabilizing Leader Election in Passively-Mobile Anonymous Agents. In: Kutten, S., Žerovnik, J. (eds) Structural Information and Communication Complexity. SIROCCO 2009. Lecture Notes in Computer Science, vol 5869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11476-2_10
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DOI: https://doi.org/10.1007/978-3-642-11476-2_10
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