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:
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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.
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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
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.
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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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.
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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© 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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