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

  • Joffroy Beauquier
  • Peva Blanchard
  • Janna Burman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8304)


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.


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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