Probabilistic Analysis of MULTIPLE QUICK SELECT

Abstract

We investigate the distribution of the number of comparisons made by MULTIPLE QUICK SELECT (a variant of QUICK SORT for finding order statistics). By convergence in the Wasserstein metric space, we show that a limit distribution exists for a suitably normalized version of the number of comparisons. We characterize the limiting distribution by an inductive convolution and find its variance. We show that the limiting distribution is smooth and prove that it has a continuous density with unbounded support.