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Uniform self-stabilizing rings

  • Distributed Computing
  • Conference paper
  • First Online:
VLSI Algorithms and Architectures (AWOC 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 319))

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Abstract

A self-stabilizing system has the property that it eventually reaches a legitimate configuration when started in any arbitrary configuration. Dijkstra originally introduced the self-stabilization problem and gave several solutions for a ring of processors [Dij74]. His solutions, and others that have appeared, use a distinguished processor in the ring, which can help to drive the system toward stability. Dijkstra observed that a distinguished processor is essential if the number of processors in the ring is composite [Dij82]. We show that there is a self-stabilizing system with no distinguished processor if the size of the ring is prime. Our basic protocol use Θ(n2) states in each processor, where n is the size of the ring. We also give a refined protocol which uses only Θ(n2/ln n) states.

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada grant A0952. Authors' current addresses: James E. Burns, School of Information and Computer Science, Georgia Institute of Technology, Atlanta, GA 30332-0280. Jan Pachl, IBM Research Laboratory, Saumerstrasse 4, 8803 Ruschlikon, Switzerland.

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Authors and Affiliations

  1. Georgia Institute of Technology, USA

    James E. Burns

  2. University of Waterloo, USA

    Jan Pachl

Authors
  1. James E. Burns
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  2. Jan Pachl
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John H. Reif

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© 1988 Springer-Verlag Berlin Heidelberg

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Burns, J.E., Pachl, J. (1988). Uniform self-stabilizing rings. In: Reif, J.H. (eds) VLSI Algorithms and Architectures. AWOC 1988. Lecture Notes in Computer Science, vol 319. Springer, New York, NY. https://doi.org/10.1007/BFb0040406

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  • DOI: https://doi.org/10.1007/BFb0040406

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96818-6

  • Online ISBN: 978-0-387-34770-7

  • eBook Packages: Springer Book Archive

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