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Space-Optimal Counting in Population Protocols

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Distributed Computing (DISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9363))

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Abstract

In this paper, we study the fundamental problem of counting, which consists in computing the size of a system. We consider the distributed communication model of population protocols of finite state, anonymous and asynchronous mobile devices (agents) communicating in pairs (according to a fairness condition). This work significantly improves the previous results known for counting in this model, in terms of (exact) space complexity. We present and prove correct the first space-optimal protocols solving the problem for two classical types of fairness, global and weak. Both protocols require no initialization of the counted agents.

The protocol designed for global fairness, surprisingly, uses only one bit of memory (two states) per counted agent. The protocol, functioning under weak fairness, requires the necessary \(\log P\) bits (P states, per counted agent) to be able to count up to P agents. Interestingly, this protocol exploits the intriguing Gros sequence of natural numbers, which is also used in the solutions to the Chinese Rings and the Hanoi Towers puzzles.

The extended version of this paper can be consulted in [8].

J. Beauquier—The work of this author was partially supported by the Israeli-French Maimonide research project.

J. Burman—The work of this author was partially supported by the Israeli-French Maimonide and the INS2I PEPS JCJC research projects.

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Authors and Affiliations

  1. LRI - CNRS UMR-8623, Université Paris Sud, Orsay, France

    Joffroy Beauquier & Janna Burman

  2. PRiSM - CNRS FRE-3709, Université de Versailles, Versailles, France

    Simon Clavière & Devan Sohier

Authors
  1. Joffroy Beauquier
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  2. Janna Burman
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  3. Simon Clavière
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  4. Devan Sohier
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Corresponding author

Correspondence to Janna Burman .

Editor information

Editors and Affiliations

  1. Technion, Haifa, Israel

    Yoram Moses

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Beauquier, J., Burman, J., Clavière, S., Sohier, D. (2015). Space-Optimal Counting in Population Protocols. In: Moses, Y. (eds) Distributed Computing. DISC 2015. Lecture Notes in Computer Science(), vol 9363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48653-5_42

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  • DOI: https://doi.org/10.1007/978-3-662-48653-5_42

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  • Print ISBN: 978-3-662-48652-8

  • Online ISBN: 978-3-662-48653-5

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