Doty, David, Eftekhari, Mahsa, Gasieniec, Leszek 
ORCID: 0000-0003-1809-9814, Severson, Eric, Uznanski, Przemyslaw and Stachowiak, Grzegorz
(2022)
A time and space optimal stable population protocol solving exact majority.
2021 IEEE 62ND ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS 2021), 2022-F.
pp. 1044-1055.
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Abstract
We study population protocols, a model of distributed computing appropriate for modeling well-mixed chemical reaction networks and other physical systems where agents exchange information in pairwise interactions, but have no control over their schedule of interaction partners. The well-studied *majority* problem is that of determining in an initial population of $n$ agents, each with one of two opinions $A$ or $B$, whether there are more $A$, more $B$, or a tie. A *stable* protocol solves this problem with probability 1 by eventually entering a configuration in which all agents agree on a correct consensus decision of $\mathsf{A}$, $\mathsf{B}$, or $\mathsf{T}$, from which the consensus cannot change. We describe a protocol that solves this problem using $O(\log n)$ states ($\log \log n + O(1)$ bits of memory) and optimal expected time $O(\log n)$. The number of states $O(\log n)$ is known to be optimal for the class of polylogarithmic time stable protocols that are "output dominant" and "monotone". These are two natural constraints satisfied by our protocol, making it simultaneously time- and state-optimal for that class. We introduce a key technique called a "fixed resolution clock" to achieve partial synchronization. Our protocol is *nonuniform*: the transition function has the value $\left \lceil {\log n} \right \rceil$ encoded in it. We show that the protocol can be modified to be uniform, while increasing the state complexity to $\Theta(\log n \log \log n)$.
| Item Type: | Article |
|---|---|
| Additional Information: | Applied FOCS reviewers' comments |
| Uncontrolled Keywords: | majority, population protocols, stable |
| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 25 Jun 2021 09:29 |
| Last Modified: | 18 Jan 2023 21:37 |
| DOI: | 10.1109/FOCS52979.2021.00104 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3127681 |
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