Time and Space Optimal Exact Majority Population Protocols

Gąsieniec, Leszek, Stachowiak, Grzegorz and Uznański, Przemysław
(2020) Time and Space Optimal Exact Majority Population Protocols.

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Abstract

In this paper we study population protocols governed by the {\em 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 {\em exact majority population protocol} which also works with high probability. The new protocol operates in the optimal {\em parallel time} $O(\log n),$ which is equivalent to $O(n\log n)$ sequential {\em 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.

Item Type: Article We combined this paper with arXiv:2012.15800 and have a new updated version at arXiv:2106.10201 cs.DC, cs.DC, cs.DS Symplectic Admin 07 Dec 2020 08:51 30 Apr 2022 20:10 Author https://livrepository.liverpool.ac.uk/id/eprint/3109201