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Time-space Trade-offs in Population Protocols for the Majority Problem

Research output: Contribution to journalArticlepeer-review

Petra Berenbrink, Robert Elsaesser, Tom Friedetzky, Dominik Kaaser, Peter Kling, Tomasz Radzik

Original languageEnglish
Number of pages23
Issue number2
Early online date5 Aug 2020
Accepted/In press22 Jul 2020
E-pub ahead of print5 Aug 2020

Bibliographical note

Funding Information: Open Access funding provided by Projekt DEAL. Robert Elsässer and Dominik Kaaser were partially supported by the Austrian Science Fund (FWF) under grant no. P 27613 (“Distributed Voting in Large Networks”). Tomasz Radzik’s work was supported by EPSRC grant EP/M005038/1 (“Randomized Algorithms for Computer Networks”). Publisher Copyright: © 2020, The Author(s).


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Population protocols are a model for distributed computing that is focused on simplicity and robustness. A system of n identical agents (finite state machines) performs a global task like electing a unique leader or determining the majority opinion when each agent has one of two opinions. Agents communicate in pairwise interactions with randomly assigned communication partners. Quality is measured in two ways: the number of interactions to complete the task and the number of states per agent. We present protocols for the majority problem that allow for a trade-off between these two measures. Compared to the only other trade-off result (Alistarh et al. in Proceedings of the 2015 ACM symposium on principles of distributed computing, Donostia-San Sebastián, 2015), we improve the number of interactions by almost a linear factor. Furthermore, our protocols can be made uniform (working correctly without any information on the population size n), yielding the first uniform majority protocols that stabilize in a subquadratic number of interactions.

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