Finding the N-th Largest Element

We describe an algorithm for selecting the n-th largest element (where 0 < < 1), from a totally ordered set of n elements, using at most (1 + (1 + o(1))H())n comparisons, where H() is the binary entropy function and the o(1) stands for a function that tends to 0 as tends to 0. For small values of this is almost the best possible as there is a lower bound of about (1 + H())n comparisons. The algorithm obtained beats the global 3n upper bound of Schh onhage, Paterson and Pippenger for < 1=3.