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Time-Optimal Loosely-Stabilizing Leader Election in Population Protocols

Authors Yuichi Sudo , Ryota Eguchi, Taisuke Izumi, Toshimitsu Masuzawa

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Author Details

Yuichi Sudo
  • Hosei University, Tokyo, Japan
Ryota Eguchi
  • Nagoya Institute of Technology, Japan
Taisuke Izumi
  • Osaka University, Japan
Toshimitsu Masuzawa
  • Osaka University, Japan

Funding

This work was supported by JSPS KAKENHI Grant Numbers 19H04085 and 20H04140.

Acknowledgements

We truly thank anonymous reviewers for their constructive and helpful comments. We also thank Przemyslaw Uznanski and Eric Severson: The first author of this paper got one of the key ideas of this paper after the discussion with them at PODC 2019.

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Yuichi Sudo, Ryota Eguchi, Taisuke Izumi, and Toshimitsu Masuzawa. Time-Optimal Loosely-Stabilizing Leader Election in Population Protocols. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.DISC.2021.40

Abstract

We consider the leader election problem in the population protocol model. In pragmatic settings of population protocols, self-stabilization is a highly desired feature owing to its fault resilience and the benefit of initialization freedom. However, the design of self-stabilizing leader election is possible only under a strong assumption (i.e., the knowledge of the exact size of a network) and rich computational resource (i.e., the number of states). Loose-stabilization is a promising relaxed concept of self-stabilization to address the aforementioned issue. Loose-stabilization guarantees that starting from any configuration, the network will reach a safe configuration where a single leader exists within a short time, and thereafter it will maintain the single leader for a long time, but not necessarily forever. The main contribution of this paper is giving a time-optimal loosely-stabilizing leader election protocol. The proposed protocol with design parameter τ ≥ 1 attains O(τ log n) parallel convergence time and Ω(n^τ) parallel holding time (i.e., the length of the period keeping the unique leader), both in expectation. This protocol is time-optimal in the sense of both the convergence and holding times in expectation because any loosely-stabilizing leader election protocol with the same length of the holding time is known to require Ω(τ log n) parallel time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • population protocols
  • leader election
  • loose-stabilization
  • self-stabilization

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References

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