Leader Election Requires Logarithmic Time in Population Protocols

In this paper, it is shown that every leader election protocol requires logarithmic stabilization time both in expectation and with high probability in the population protocol model. This lower bound holds even if each agent has knowledge of the exact size of a population and we can use an arbitrarily large number of agent states. This lower bound concludes that the protocol given in [Sudo et al., PODC 2019] is time-optimal in expectation.