On selecting thek largest with median tests

LetW itk(n) be the minimax complexity of selecting thek largest elements ofn numbersx 1,x 2,...,x n by pairwise comparisonsx i :x j . It is well known thatW 2(n) =n−2+ [lgn], andW k (n) = n + (k−1)lg n +O(1) for all fixed k ≥ 3. In this paper we studyW′ k (n), the minimax complexity of selecting thek largest, when tests of the form “Isx i the median of {x i ,x j ,x t }?” are also allowed. It is proved thatW′2(n) =n−2+ [lgn], andW′ k (n) =n + (k−1)lg2 n +O(1) for all fixedk≥3.