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 conditions 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 n−1 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 is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distrib. Comput. 18(4), 235–253 (2006)
Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. In: Proc. 9th International Conference on Principles of Distributed Systems (OPODIS). LNCS, vol. 3974, pp. 103–117 (2005)
Angluin, D., Aspnes, J., Chan, M., Fischer, M.J., Jiang, H., Peralta, R.: Stably computable properties of network graphs. In: Proc. International Conference on Distributed Computing in Sensor Systems (DCOSS). LNCS, vol. 3560, pp. 63–74 (2005)
Angluin, D., Aspnes, J., Eisenstat, D.: Stably computable predicates are semilinear. In: Proc. 25th Annual ACM Symposium on Principles of Distributed Computing, pp. 292–299 (2006)
Angluin, D., Aspnes, J., Eisenstat, D.: A simple protocol for fast robust approximate majority. In: Proc. 21st International Symposium on Distributed Computing (DISC). LNCS, vol. 4731, pp. 20–32 (2007)
Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. Distrib. Comput. 20(4), 279–304 (2007)
Aspnes, J., Ruppert, E.: An introduction to population protocols. Bull. Eur. Assoc. Theor. Comput. Sci. 93, 98–117 (2007)
Beauquier, J., Clement, J., Messika, S., Rosaz, L., Rozoy, B.: Self-stabilizing counting in mobil sensor networks. In: Proc. 21st International Symposium on Distributed Computing (DISC). LNCS, vol. 4731, pp. 63–76 (2007)
Canepa, D., Gradinariu Potop-Butucaru, M.: Stabilizing leader election in population protocols. In: Proc. of the 3rd ACM SIGOPS/SIGACT Workshop on Reliability, Availability, and Security WRAS, July 2010
Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Ruppert, E.: When birds die: making population protocols fault-tolerant. In: Proc. 2nd IEEE International Conference on Distributed Computing in Sensor Systems (DCOSS). LNCS, vol. 4026, pp. 51–66 (2006)
Fischer, M.J., Jiang, H.: Self-stabilizing leader election in networks of finite-state anonymous agent. In: Proc. 10th International Conference on Principle of Distributed Systems (OPODIS). LNCS, vol. 4305, pp. 395–409 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cai, S., Izumi, T. & Wada, K. How to Prove Impossibility Under Global Fairness: On Space Complexity of Self-Stabilizing Leader Election on a Population Protocol Model. Theory Comput Syst 50, 433–445 (2012). https://doi.org/10.1007/s00224-011-9313-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00224-011-9313-z