Regular Article
Optimal Algorithms for Probabilistic Solitude Detection on Anonymous Rings

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Abstract

Probabilistic algorithms are developed for a basic problem in distributed computation, assuming anonymous, asynchronous, unidirectional rings of processors. The problem, known as Solitude Detection, requires that a nonempty subset of the processors, calledcontenders, determine whether or not there is exactly one contender. Monte Carlo algorithms are developed that err with probability bounded by a specified parameter ε and exhibit either message or processor termination. The algorithms transmit an optimal expected number of bits, to within a constant factor. Their bit complexities display a surprisingly rich dependence on the kind of termination exhibited and on the processors' knowledge of the size of the ring. Two probabilistic tools are isolated and then combined in various ways to achieve all our algorithms.

References (17)

  • H. Attiya et al.

    Better computing on the anonymous ring

    J. Algorithms

    (1991)
  • P. Duris et al.

    Two lower bounds in asynchronous distributed computation

    J. Comput. Syst. Sci.

    (1991)
  • A. Itai et al.

    Symmetry breaking in distributed networks

    Informat. and Comput.

    (1990)
  • K. Abrahamson et al.

    The bit complexity of probabilistic leader election on a undirectional ring

    Distributed Algorithms on Graphs

    (1986)
  • K. Abrahamson et al.

    The bit complexity of randomized leader election on a ring

    SIAM J. Comput.

    (1989)
  • K. Abrahamson et al.

    Randomized function evaluation on a ring

    Distributed Comput.

    (1989)
  • K. Abrahamson et al.

    Probabilistic leader election on rings of known size

    Workshop on Algorithms and Data Structures

    (1991)
  • K. Abrahamson et al.

    Tight lower bounds for probabilistic solitude verification on anonymous rings

    J. Assoc. Comput. Mach.

    (1994)
There are more references available in the full text version of this article.

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This research was supported in part by the Natural Sciences and Engineering Research Council of Canada and the Killam Foundation.

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