Abstract
In this paper, we present the first leader election protocol in the population protocol model that stabilizes within \(O(\log n)\) parallel time in expectation with \(O(\log n)\) states per agent, where n is the number of agents. Given a rough knowledge m of the population size n such that \(m \ge \log _2 n\) and \(m=O(\log n)\), the proposed protocol guarantees that exactly one leader is elected and the unique leader is kept forever thereafter.
This work was supported by JSPS KAKENHI Grant Numbers 17K19977, 18K18000, 19H04085, and 19K11826 and JST SICORP Grant Number JPMJSC1606.
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- 1.
Recall that \(\mathcal {S}_{P_{LL}}\) is the set of configurations such that, for any configuration \(C \in \mathcal {S}_{P_{LL}}\), exactly one agent outputs L (i.e., is a leader) in C and no agent changes its output in execution \(\varXi _{P_{LL}}(C,\gamma )\) for any schedule \(\gamma \).
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Sudo, Y., Ooshita, F., Izumi, T., Kakugawa, H., Masuzawa, T. (2019). Logarithmic Expected-Time Leader Election in Population Protocol Model. In: Ghaffari, M., Nesterenko, M., Tixeuil, S., Tucci, S., Yamauchi, Y. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2019. Lecture Notes in Computer Science(), vol 11914. Springer, Cham. https://doi.org/10.1007/978-3-030-34992-9_26
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