Brief Announcement: Exact Size Counting in Uniform Population Protocols in Nearly Logarithmic Time

Doty, David; Eftekhari, Mahsa; Michail, Othon; Spirakis, Paul G.; Theofilatos, Michail

doi:10.4230/LIPIcs.DISC.2018.46

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Document Identifiers

DOI: 10.4230/LIPIcs.DISC.2018.46
URN: urn:nbn:de:0030-drops-98359

Author Details

David Doty

Department of Computer Science, University of California, Davis

Mahsa Eftekhari

Department of Computer Science, University of California, Davis

Othon Michail

Department of Computer Science, University of Liverpool, UK

Paul G. Spirakis

Department of Computer Science, University of Liverpool, UK and Computer Technology Institute & Press "Diophantus" (CTI), Patras, Greece

Michail Theofilatos

Department of Computer Science, University of Liverpool, UK

Cite AsGet BibTex

David Doty, Mahsa Eftekhari, Othon Michail, Paul G. Spirakis, and Michail Theofilatos. Brief Announcement: Exact Size Counting in Uniform Population Protocols in Nearly Logarithmic Time. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 46:1-46:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.DISC.2018.46

Abstract

We study population protocols: networks of anonymous agents whose pairwise interactions are chosen uniformly at random. The size counting problem is that of calculating the exact number n of agents in the population, assuming no leader (each agent starts in the same state). We give the first protocol that solves this problem in sublinear time. The protocol converges in O(log n log log n) time and uses O(n^60) states (O(1) + 60 log n bits of memory per agent) with probability 1-O((log log n)/n). The time to converge is also O(log n log log n) in expectation. Crucially, unlike most published protocols with omega(1) states, our protocol is uniform: it uses the same transition algorithm for any population size, so does not need an estimate of the population size to be embedded into the algorithm.

Subject Classification

ACM Subject Classification

Theory of computation → Distributed algorithms

Keywords

population protocol
counting
leader election
polylogarithmic time

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References

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