Time-space trade-offs in population protocols for the majority problem

Petra Berenbrink; Robert Elsässer; Tom Friedetzky; Dominik Kaaser; Peter Kling; Tomasz Radzik

doi:10.1007/s00446-020-00385-0

Time-space trade-offs in population protocols for the majority problem

Distrib Comput. 2021;34(2):91-111. doi: 10.1007/s00446-020-00385-0. Epub 2020 Aug 5.

Authors

Petra Berenbrink¹, Robert Elsässer², Tom Friedetzky³, Dominik Kaaser¹, Peter Kling¹, Tomasz Radzik⁴

Affiliations

¹ Universität Hamburg, Vogt-Kölln-Str. 3, 22527 Hamburg, Germany.
² University of Salzburg, Jakob-Haringer-Str. 2, 5020 Salzburg, Austria.
³ Durham University, Lower Mountjoy South Road, Durham, DH1 3LE United Kingdom.
⁴ King's College London, Strand Campus Bush House, London, WC2B 4BG United Kingdom.

Abstract

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.

Keywords: Distributed computing; Majority; Population protocols; Stochastic processes.