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

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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