Finding percentile elements

We describe an algorithm for selecting the αn-th largest element (where 0<α<1), out of a totally ordered set of n elements, using at most (1+(1+o(1))H(α))·n comparisons, where H(α) is the binary entropy function and the o(1) stands for a function that tends to 0 as α tends to 0. This, for small α´s, is almost best possible as there is a lower bound of about (1+H(α))·n comparisons. The algorithm obtained beats the global 3n upper bound of Schonhage, Paterson and Pippenger (1976) for α<1/3