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Optimization of Binary Interval Consensus

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Abstract

Motivated by binary interval consensus algorithm in [1], the bounds for the time of convergence of this type of consensus [4], and using the optimization techniques for doubly stochastic matrices [2, 3], we introduce a distributed way to optimize binary interval consensus. With binary consensus problem, each node initially chooses one of the states 0 or 1 and the goal for the nodes is to agree on the state which was initially held by the majority. Binary interval consensus is a specific type of binary consensus which uses two intermediate states along with 0 and 1 to reduce the probability of error to zero. We show that if the probability of the nodes contacting each other is defined by a doubly stochastic matrix, the optimization of binary interval consensus can be done by reducing the second largest eigenvalue of the rate matrix Q.

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Notes

  1. 1.

    1 is a vector of all ones.

References

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Acknowledgments

Moez Draief holds a Leverhulme Trust Research Fellowship RF/9/RFG/2010/02/08.

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Authors and Affiliations

  1. Intelligent Systems and Networks Group, Department of Electrical and Electronic Engineering, Imperial College London, London, UK

    Arta Babaee & Moez Draief

Authors
  1. Arta Babaee
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  2. Moez Draief
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Correspondence to Arta Babaee .

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Editors and Affiliations

  1. , Dept of Electrical and Electronics Eng'g, Imperial College, London, SW7 2BT, United Kingdom

    Erol Gelenbe

  2. , EEE Dept., Imperial College, Exhibition Rd., London, SW72AZ, United Kingdom

    Ricardo Lent

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© 2013 Springer-Verlag London

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Babaee, A., Draief, M. (2013). Optimization of Binary Interval Consensus. In: Gelenbe, E., Lent, R. (eds) Computer and Information Sciences III. Springer, London. https://doi.org/10.1007/978-1-4471-4594-3_29

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  • DOI: https://doi.org/10.1007/978-1-4471-4594-3_29

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4593-6

  • Online ISBN: 978-1-4471-4594-3

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