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On the Power of Oracle \(\varOmega ?\) for Self-Stabilizing Leader Election in Population Protocols

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Stabilization, Safety, and Security of Distributed Systems (SSS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10083))

Abstract

This paper considers the fundamental problem of self-stabilizing leader election (SSLE) in the model of population protocols. In this model an unknown number of asynchronous, anonymous and finite state mobile agents interact in pairs. SSLE has been shown to be impossible in this model without additional assumptions. This impossibility can be circumvented for instance by augmenting the system with an oracle (an external module providing supplementary information useful to solve a problem). Fischer and Jiang have proposed solutions to SSLE, for complete communication graphs and rings, using the oracle \(\varOmega ?\), called the eventual leader detector. In this paper, we investigate the power of \(\varOmega ?\) on larger families of graphs. We present two important results.

Our first result states that \(\varOmega ?\) is powerful enough to allow solving SSLE over arbitrary communication graphs of bounded degree. Our second result states that, \(\varOmega ?\) is the weakest (in the sense of Chandra, Hadzilacos and Toueg) for solving SSLE over rings. We also prove that this result does not extend to all graphs; in particular not to the family of arbitrary graphs of bounded degree.

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Notes

  1. 1.

    This is in contrast to the non-uniform solutions given to SSLE over rings in [4] that does not use oracles.

  2. 2.

    The input alphabet can be viewed as the set of possible values given to the agents from the outside environment, like sensed values, output values from another protocol or from an oracle. The output alphabet can be viewed as the set of values that the protocol itself outputs outside. X and Y are both the interface values of the protocol.

  3. 3.

    In [18], where \(\varOmega ?\) has been introduced, the oracle is defined in a rather informal way.

  4. 4.

    In this paper, we are only interested in comparing oracles as far as self-stabilization is concerned.

References

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Authors and Affiliations

  1. LRI, Universit Paris-Sud, Orsay, France

    Joffroy Beauquier & Janna Burman

  2. LPD, EPFL, Lausanne, Switzerland

    Peva Blanchard

  3. University of Calgary, Calgary, Canada

    Oksana Denysyuk

Authors
  1. Joffroy Beauquier
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  2. Peva Blanchard
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  3. Janna Burman
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  4. Oksana Denysyuk
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Corresponding author

Correspondence to Janna Burman .

Editor information

Editors and Affiliations

  1. McMaster University, Hamilton, Ontario, Canada

    Borzoo Bonakdarpour

  2. LIP6, INRIA, UPMC Sorbonne Universities, Paris, France

    Franck Petit

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Beauquier, J., Blanchard, P., Burman, J., Denysyuk, O. (2016). On the Power of Oracle \(\varOmega ?\) for Self-Stabilizing Leader Election in Population Protocols. In: Bonakdarpour, B., Petit, F. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2016. Lecture Notes in Computer Science(), vol 10083. Springer, Cham. https://doi.org/10.1007/978-3-319-49259-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-49259-9_3

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  • Online ISBN: 978-3-319-49259-9

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