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Message terminate algorithms for anonymous rings of unknown size

  • Israel Cidon
  • Yuval Shavitt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 647)

Abstract

We consider a ring of unknown number of anonymous processors. We restrict ourselves to algorithms that are message terminate, i.e. the algorithm terminates when no more messages are present in the system but the processors may lack the ability to detect this situation. The work addresses algorithms (both deterministic and probabilistic) that always terminate with the correct result. We show the following:
  • A deterministic algorithm for orientation that requires a symmetry breaking marking on the links and uses O(n log2n) bits for communication and O(n) time. A Las-Vegas version of this algorithm that uses probability to break symmetry has the same average communication and time cost.

  • A deterministic algorithm for pattern searching that uses O(n · ¦S¦) communication bits for a pattern of length ¦S¦. Computing AND and OR are simple cases of that algorithm.

  • A probabilistic algorithm for dividing an even ring to pairs that uses O(n log n) communication bits and time.

  • The impossibility of computing a class of functions called nonsym-metric that includes: leader election, XOR and finding the ring size. The same technique can be applied to prove the impossibility of dividing an odd ring to a maximal number of pairs.

Keywords

Deterministic Algorithm Unknown Number Maximum Match Ring Size Leader Election 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Israel Cidon
    • 1
  • Yuval Shavitt
    • 1
  1. 1.Electrical Engineering Dept.Technion - Israel Institute of TechnologyHaifaIsrael

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