Finding the αn-TH largest element

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