Analysis of multiple quickselect variants

Abstract

Multiple Quickselect is an algorithm that uses the idea of Quicksort to search for several order statistics simultaneously. In order to improve the efficiency of Quicksort, one can use the median of 2 t+1 randomly chosen elements as pivot element in the partitioning stage. Such a median of 2 t+1 partition can also be applied to Multiple Quickselect to reduce the number of comparisons. Here we give an analysis of such Multiple Quickselect variants that use median of 2 t+1 partition and describe for these algorithms the asymptotic behaviour of the expected number of required comparisons to find p-order statistics in a data set of size n for n→∞ and fixed p.