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Randomized function evaluation on a ring

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Distributed Algorithms (WDAG 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 312))

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Abstract

Let R be a unidirectional asynchronous ring of n processors each with a single input bit. Let f be any cyclic non-constant function of n boolean variables. Moran and Warmuth [5] prove that any deterministic algorithm for R that evaluates f has communication complexity Ω(n log n) bits. They also construct a cyclic non-constant boolean function that can be evaluated in O(n log n) bits by a deterministic algorithm.

This contrasts with the following new results:

  1. 1.

    There exists a cyclic non-constant boolean function which can be evaluated with expected complexity O(n√log n) bits by a randomized algorithm for R.

  2. 2.

    Any nondeterministic algorithm for R which evaluates any cyclic non-constant function has communication complexity Ω(n√log n) bits.

(Preliminary Version)

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

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References

  1. K. Abrahamson, A. Adler, L. Higham, and D. Kirkpatrick. Probabilistic Solitude Detection I: Rings Size Known Approximately. Technical Report 87–8, University of British Columbia, 1987. submitted for publication.

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  2. K. Abrahamson, A. Adler, L. Higham, and D. Kirkpatrick. Probabilistic Solitude detection II: Rings Size Known Exactly. Technical Report 86–26, University of British Columbia, 1986. submitted for publication.

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  3. K. Abrahamson, A. Adler, L. Higham, and D. Kirkpatrick. Probabilistic solitude verification on a ring. In Proc. 5th Annual ACM Symp. on Principles of Distributed Computing, pages 161–173, 1986.

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  4. K. Abrahamson, A. Adler, L. Higham, and D. Kirkpatrick. Randomized Function Evaluation on a Ring. Technical Report 87–20, University of British Columbia, 1987. submitted for publication.

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  5. S. Moran and M. Warmuth. Gap theorems for distributed computation. In Proc. 5th Annual ACM Symp. on Principles of Distributed Computing, pages 131–140, 1986.

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Author information

Author notes

  1. Karl Abrahamson

    Present address: Computer Science Department, Washington State University, 99164-1210, Pullman, Washington, USA

Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, V6T 1W5, Vancouver, B.C., Canada

    Karl Abrahamson, Lisa Higham & David Kirkpatrick

  2. Department of Mathematics, University of British Columbia, V6T 1W5, Vancouver, B.C., Canada

    Andrew Adler

Authors
  1. Karl Abrahamson
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  2. Andrew Adler
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  3. Lisa Higham
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  4. David Kirkpatrick
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Editor information

J. van Leeuwen

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© 1988 Springer-Verlag Berlin Heidelberg

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Abrahamson, K., Adler, A., Higham, L., Kirkpatrick, D. (1988). Randomized function evaluation on a ring. In: van Leeuwen, J. (eds) Distributed Algorithms. WDAG 1987. Lecture Notes in Computer Science, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019812

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  • DOI: https://doi.org/10.1007/BFb0019812

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19366-1

  • Online ISBN: 978-3-540-39239-2

  • eBook Packages: Springer Book Archive

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