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In population protocols, the underlying distributed network consists of $n$nodes (or agents), denoted by $V$, and a scheduler that continuously selectsuniformly random pairs of nodes to interact. When two nodes interact, theirstates are updated by applying a state transition function that depends only onthe states of the two nodes prior to the interaction. The efficiency of apopulation protocol is measured in terms of both time (which is the number ofinteractions until the nodes collectively have a valid output) and the numberof possible states of nodes used by the protocol. By convention, we considerthe parallel time cost, which is the time divided by $n$.  In this paper we consider the majority problem, where each node receives asinput a color that is either black or white, and the goal is to have all of thenodes output the color that is the majority of the input colors. We design apopulation protocol that solves the majority problem in $O(\log^{3/2}n)$parallel time, both with high probability and in expectation, while using$O(\log n)$ states. Our protocol improves on a recent protocol of Berenbrink etal. that runs in $O(\log^{5/3}n)$ parallel time, both with high probability andin expectation, using $O(\log n)$ states.

An $O(\log^{3/2}n)$ Parallel Time Population Protocol for Majority with $O(\log n)$ States