In this article, we present the first leader election protocol in the population protocol model that stabilizes within O(logn) parallel time in expectation with O(logn) states per agent, where n is the number of agents. Given a rough knowledge m of lg n such that m ≥ lg n and m = O(logn), the proposed protocol guarantees that exactly one leader is elected and the unique leader is kept forever thereafter. This protocol is time-optimal because it was recently proven that any leader election protocol requires Ω(logn) parallel time.
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Sudo et al. (2020) studied this question.
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