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

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



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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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