Uniform self-stabilizing rings

  • Authors:
  • J. E. Burns;Jan K. Pachl

  • Affiliations:
  • Georgia Institute of Technology, Atlanta;Zurich Research Lab, Rüschlikon, Switzerland

  • Venue:
  • ACM Transactions on Programming Languages and Systems (TOPLAS)
  • Year:
  • 1989

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Abstract

A self-stabilizing system has the property that, no matter how it is perturbed, it eventually returns to a legitimate configuration. Dijkstra originally introduced the self-stabilization problem and gave several solutions for a ring of processors in his 1974 Communications of the ACM paper. His solutions use a distinguished processor in the ring, which effectively acts as a controlling element to drive the system toward stability. Dijkstra has observed that a distinguished processor is essential if the number of processors in the ring is composite. We show, by presenting a protocol and proving its correctness, that there is a self-stabilizing system with no distinguished processor if the size of the ring is prime. The basic protocol uses &THgr; (n2) states in each processor when n is the size of the ring. We modify the basic protocol to obtain one that uses &THgr; (n2/ln n) states.