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Time and Space Optimal Exact Majority Population Protocols

Abstract

In this paper we study population protocols governed by the {\em random scheduler}, which uniformly at random selects pairwise interactions between nn agents. The main result of this paper is the first time and space optimal {\em exact majority population protocol} which also works with high probability. The new protocol operates in the optimal {\em parallel time} O(logn),O(\log n), which is equivalent to O(nlogn)O(n\log n) sequential {\em pairwise interactions}, where each agent utilises the optimal number of O(logn)O(\log n) states. The time optimality of the new majority protocol is possible thanks to the novel concept of fixed-resolution phase clocks introduced and analysed in this paper. The new phase clock allows to count approximately constant parallel time in population protocols.

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