Finding extrema with unary predicates

We consider the problem of determining the maximum and minimum elements of a setX={x1...,xn}, drawn from some finite universeU of real numbers, 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 an arbitrary set of numbers held by distinct processors.