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International Conference on Concurrency Theory

CONCUR 2014: CONCUR 2014 – Concurrency Theory pp 342–356Cite as

A Nearly Optimal Upper Bound for the Self-Stabilization Time in Herman’s Algorithm

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8704))

Abstract

Self-stabilization algorithms are very important in designing fault-tolerant distributed systems. In this paper we consider Herman’s self-stabilization algorithm and study its expected self-stabilization time. McIver and Morgan have conjectured the optimal upper bound being 0.148N 2, where N denotes the number of processors. We present an elementary proof showing a bound of 0.167N 2, a sharp improvement compared with the best known bound 0.521N 2. Our proof is inspired by McIver and Morgan’s approach: we find a nearly optimal closed form of the expected stabilization time for any initial configuration, and apply the Lagrange multipliers method to give an upper bound of it.

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Author information

Authors and Affiliations

  1. Centre for Quantum Computation and Intelligent Systems, University of Technology Sydney, Australia

    Yuan Feng

  2. AMSS-UTS Joint Research Laboratory for Quantum Computation, Chinese Academy of Sciences, Beijing, China

    Yuan Feng

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Lijun Zhang

Authors
  1. Yuan Feng
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  2. Lijun Zhang
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Padova, Via Trieste, 63, 35121, Padova, Italy

    Paolo Baldan

  2. Department of Computer Science, University of Roma “La Sapienza”, Via Salaria, 113, 00198, Rome, Italy

    Daniele Gorla

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© 2014 Springer-Verlag Berlin Heidelberg

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Feng, Y., Zhang, L. (2014). A Nearly Optimal Upper Bound for the Self-Stabilization Time in Herman’s Algorithm. In: Baldan, P., Gorla, D. (eds) CONCUR 2014 – Concurrency Theory. CONCUR 2014. Lecture Notes in Computer Science, vol 8704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44584-6_24

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  • DOI: https://doi.org/10.1007/978-3-662-44584-6_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44583-9

  • Online ISBN: 978-3-662-44584-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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