Finding the alpha n-th largest element

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