Time and Space Optimal Exact Majority Population Protocols

11/14/2020

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by   Leszek Gasieniec, et al.

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In this paper we study population protocols governed by the random scheduler, which uniformly at random selects pairwise interactions between n agents. The main result of this paper is the first time and space optimal exact majority population protocol which also works with high probability. The new protocol operates in the optimal parallel time O(log n), which is equivalent to O(nlog n) sequential pairwise interactions, where each agent utilises the optimal number of 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.