Tight lower bounds for probabilistic solitude verification on anonymous rings

Authors:
Karl Abrahamson;Andrew Adler;Lisa Highám;David Kirkpatrick
Affiliations:
Washington State University, Pullman, Washington;University of British Columbia, Vancouver, B.C., Canada;University of Calgary, Calgary, Alberta, Canada;University of British Columbia, B.C., Canada
Venue:
Journal of the ACM (JACM)
Year:
1994

Citing 13
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Abstract

A model that captures communication on asynchronous unidirectional rings is formalized. Our model incorporates both probabilistic and nondeterministic features and is strictly more powerful than a purely probabilistic model. Using this model, a collection of tools are developed that facilitate studying lower bounds on the expected communication complexity of Monte Carlo algorithms for language recognition problems on anonymous asynchronous unidirectional rings. The tools are used to establish tight lower bounds on the expected bit complexity of the Solitude Verification problem that asymptotically match upper bounds for this problem. The bounds demonstrate that, for this problem, the expected bit complexity depends subtly on the processors' knowledge of the size of the ring and on whether or not processor-detectable termination is required.