Exponential bounds for the running time of a selection algorithm - Devroye, Luc (Journal of computer and system sciences, 1984)
Hoare's selection algorithm for finding the kth-largest element in a set of n elements is shown to use C comparisons where 1. (i) E( C p ) ⩽ A p n p for some constant A p > 0 and all p ⩾ 1; 2. (ii) P( C n ⩾ u ) ⩽ ( 3 4 ) u(1 + o(1)) as u → ∞. Exact values for the “ A p ” and “ o(1)” terms are given.