Self-stabilizing Leader Election in Population Protocols over Arbitrary Communication Graphs

  • Joffroy Beauquier
  • Peva Blanchard
  • Janna Burman
Conference paper

DOI: 10.1007/978-3-319-03850-6_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8304)
Cite this paper as:
Beauquier J., Blanchard P., Burman J. (2013) Self-stabilizing Leader Election in Population Protocols over Arbitrary Communication Graphs. In: Baldoni R., Nisse N., van Steen M. (eds) Principles of Distributed Systems. OPODIS 2013. Lecture Notes in Computer Science, vol 8304. Springer, Cham

Abstract

This paper considers the fundamental problem of self-stabilizing leader election (\(\mathcal{SSLE}\)) in the model of population protocols. In this model, an unknown number of asynchronous, anonymous and finite state mobile agents interact in pairs over a given communication graph. \(\mathcal{SSLE}\) has been shown to be impossible in the original model. This impossibility can been circumvented by a modular technique augmenting the system with an oracle - an external module abstracting the added assumption about the system. Fischer and Jiang have proposed solutions to \(\mathcal{SSLE}\), for complete communication graphs and rings, using an oracle Ω?, called the eventual leader detector. In this work, we present a solution for arbitrary graphs, using a composition of two copies of Ω?. We also prove that the difficulty comes from the requirement of self-stabilization, by giving a solution without oracle for arbitrary graphs, when an uniform initialization is allowed. Finally, we prove that there is no self-stabilizing implementation of Ω? using \(\mathcal{SSLE}\), in a sense we define precisely.

Keywords

leader election self-stabilization population protocols global fairness oracles 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Joffroy Beauquier
    • 1
  • Peva Blanchard
    • 2
  • Janna Burman
    • 1
  1. 1.LRI, Paris-South 11 UniversityOrsayFrance
  2. 2.LRIOrsay CedexFrance

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