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UBC CS TR-90-39 Summary

Finding Extrema With Unary Predicates, January 1990 Feng Gao, Leonidas J. Guibas, David G. Kirkpatrick, William T. Laaser and James Saxe

We consider the problem of determining the maximum and minimum elements {x_{1}, \ldots ,x_{n}}$, drawn from some finite universe $\cal U$ of real numbers, using only unary predicates of the inputs. It is shown that $\Theta (n + \log |{\cal U} |) $ unary predicate evaluations are necessary and sufficient, in the worst case. Results are applied to i) the problem of determining approximate extrema of a set of real numbers, in the same model, and ii) the multiparty broadcast communication complexity of determining the extrema of an arbitrary set of numbers held by distinct processors.

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