Finding extrema with unary predicates
We consider the problem of determining the maximum and minimum elements of a set X=x1,...,x n of integers, drawn from the some universe U, using only unary predicates of the inputs. It is shown that Θ(n+log|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 a set of integers held by distinct processors.
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