Brief announcement: Fast graphical population protocols

Alistarh D-A, Gelashvili R, Rybicki J. 2021. Brief announcement: Fast graphical population protocols. 35th International Symposium on Distributed Computing. DISC: Distributed Computing , LIPIcs, vol. 209, 43.

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Department
Series Title
LIPIcs
Abstract
Let G be a graph on n nodes. In the stochastic population protocol model, a collection of n indistinguishable, resource-limited nodes collectively solve tasks via pairwise interactions. In each interaction, two randomly chosen neighbors first read each other’s states, and then update their local states. A rich line of research has established tight upper and lower bounds on the complexity of fundamental tasks, such as majority and leader election, in this model, when G is a clique. Specifically, in the clique, these tasks can be solved fast, i.e., in n polylog n pairwise interactions, with high probability, using at most polylog n states per node. In this work, we consider the more general setting where G is an arbitrary graph, and present a technique for simulating protocols designed for fully-connected networks in any connected regular graph. Our main result is a simulation that is efficient on many interesting graph families: roughly, the simulation overhead is polylogarithmic in the number of nodes, and quadratic in the conductance of the graph. As an example, this implies that, in any regular graph with conductance φ, both leader election and exact majority can be solved in φ^{-2} ⋅ n polylog n pairwise interactions, with high probability, using at most φ^{-2} ⋅ polylog n states per node. This shows that there are fast and space-efficient population protocols for leader election and exact majority on graphs with good expansion properties.
Publishing Year
Date Published
2021-10-04
Proceedings Title
35th International Symposium on Distributed Computing
Acknowledgement
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 840605.
Volume
209
Article Number
43
Conference
DISC: Distributed Computing
Conference Location
Freiburg, Germany
Conference Date
2021-10-04 – 2021-10-08
ISSN
IST-REx-ID

Cite this

Alistarh D-A, Gelashvili R, Rybicki J. Brief announcement: Fast graphical population protocols. In: 35th International Symposium on Distributed Computing. Vol 209. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.DISC.2021.43
Alistarh, D.-A., Gelashvili, R., & Rybicki, J. (2021). Brief announcement: Fast graphical population protocols. In 35th International Symposium on Distributed Computing (Vol. 209). Freiburg, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.DISC.2021.43
Alistarh, Dan-Adrian, Rati Gelashvili, and Joel Rybicki. “Brief Announcement: Fast Graphical Population Protocols.” In 35th International Symposium on Distributed Computing, Vol. 209. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.DISC.2021.43.
D.-A. Alistarh, R. Gelashvili, and J. Rybicki, “Brief announcement: Fast graphical population protocols,” in 35th International Symposium on Distributed Computing, Freiburg, Germany, 2021, vol. 209.
Alistarh D-A, Gelashvili R, Rybicki J. 2021. Brief announcement: Fast graphical population protocols. 35th International Symposium on Distributed Computing. DISC: Distributed Computing , LIPIcs, vol. 209, 43.
Alistarh, Dan-Adrian, et al. “Brief Announcement: Fast Graphical Population Protocols.” 35th International Symposium on Distributed Computing, vol. 209, 43, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.DISC.2021.43.
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2021-11-12
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