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Loosely-Stabilizing Leader Election with Polylogarithmic Convergence Time

Authors Yuichi Sudo, Fukuhito Ooshita, Hirotsugu Kakugawa, Toshimitsu Masuzawa, Ajoy K. Datta, Lawrence L. Larmore

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Author Details

Yuichi Sudo
  • Graduate School of Information Science and Technology, Osaka University, Japan
Fukuhito Ooshita
  • Graduate School of Science and Technology, Nara Institute of Science and Technology, Japan
Hirotsugu Kakugawa
  • Graduate School of Information Science and Technology, Osaka University, Japan
Toshimitsu Masuzawa
  • Graduate School of Information Science and Technology, Osaka University, Japan
Ajoy K. Datta
  • Department of Computer Science, University of Nevada, Las Vegas, USA
Lawrence L. Larmore
  • Department of Computer Science, University of Nevada, Las Vegas, USA

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Yuichi Sudo, Fukuhito Ooshita, Hirotsugu Kakugawa, Toshimitsu Masuzawa, Ajoy K. Datta, and Lawrence L. Larmore. Loosely-Stabilizing Leader Election with Polylogarithmic Convergence Time. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.OPODIS.2018.30

Abstract

A loosely-stabilizing leader election protocol with polylogarithmic convergence time in the population protocol model is presented in this paper. In the population protocol model, which is a common abstract model of mobile sensor networks, it is known to be impossible to design a self-stabilizing leader election protocol. Thus, in our prior work, we introduced the concept of loose-stabilization, which is weaker than self-stabilization but has similar advantage as self-stabilization in practice. Following this work, several loosely-stabilizing leader election protocols are presented. The loosely-stabilizing leader election guarantees that, starting from an arbitrary configuration, the system reaches a safe configuration with a single leader within a relatively short time, and keeps the unique leader for an sufficiently long time thereafter. The convergence times of all the existing loosely-stabilizing protocols, i.e., the expected time to reach a safe configuration, are polynomial in n where n is the number of nodes (while the holding times to keep the unique leader are exponential in n). In this paper, a loosely-stabilizing protocol with polylogarithmic convergence time is presented. Its holding time is not exponential, but arbitrarily large polynomial in n.

Subject Classification

ACM Subject Classification
  • Theory of computation → Self-organization
Keywords
  • Loose-stabilization
  • Population protocols
  • and Leader election

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