Abstract
This paper investigates the space complexity of a self stabilizing leader election in a mediated population protocol (SS-LE MPP). Cai, Izumi and Wada (2009) showed that SS-LE in a population protocol (SS-LE PP) for n agents requires at least n agent-states, and gave a SS-LE PP with n agent-states for n agents. MPP is a model of distributed computation, introduced by Chatzigiannakis, Michail and Spirakis (2009) as an extension of PP allowing an extra memory on every agents pair. While they showed that MPP is stronger than PP in general, it was not known if a MPP can really reduce the space complexity of SS-LE with respect to agent-states. We in this paper give a SS-LE MPP with (2/3)n agent-states and a single bit memory on every agents pair for n agents. We also show that there is no SS-LE MPP with any constant agent-states and any constant size memory on each agents-pair for general n agents.
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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 Computing 18, 235–253 (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. 3974, pp. 103–117. Springer, Heidelberg (2006)
Angluin, D., Aspnes, J., Eisenstat, D.: Stably computable predicates are semilinear. In: Prasanna, V.K., Iyengar, S.S., Spirakis, P.G., Welsh, M. (eds.) DCOSS 2005. LNCS, vol. 3560, pp. 63–74. Springer, Heidelberg (2005)
Aspnes, J., Ruppert, E.: An introduction to population protocols. Bulletin of the EATCS 93, 98–117 (2007)
Cai, S., Izumi, T., Wada, K.: Space complexity of self-stabilizing leader election in passively-mobile anonymous agents. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 113–125. Springer, Heidelberg (2010)
Canepa, D., Potop-Butucaru, M.G.: Stabilizing leader election in population protocols (2007) (unpublished), http://hal.archives-ouvertes.fr/docs/00/16/66/52/PDF/RR-6269.pdf
Chatzigiannakis, I., Michail, O., Spirakis, P.G.: Mediated population protocols. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 363–374. Springer, Heidelberg (2009)
Chatzigiannakis, I., Michail, O., Spirakis, P.G.: Recent advances in population protocols. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 56–76. Springer, Heidelberg (2009)
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. 4305, pp. 395–409. Springer, Heidelberg (2006)
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Mizoguchi, R., Ono, H., Kijima, S., Yamashita, M. (2010). Upper and Lower Bounds of Space Complexity of Self-Stabilizing Leader Election in Mediated Population Protocol. In: Lu, C., Masuzawa, T., Mosbah, M. (eds) Principles of Distributed Systems. OPODIS 2010. Lecture Notes in Computer Science, vol 6490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17653-1_35
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DOI: https://doi.org/10.1007/978-3-642-17653-1_35
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