Randomized selection in n+C+o(n) comparisons

Abstract

In this paper we present a randomized selection algorithm that with high probability 1−1/n^ρ, for any constant ρ>1 requires n+C+o(n) comparisons to determine the Cth order statistic of n keys thus matching a corresponding lower bound on the average number of comparisons required. Low order terms in the number of comparisons performed can also be reduced by extending the algorithm of Floyd and Rivest and analyzing its resulting performance more carefully.