Probabilistic Analysis of the Dual-Pivot Quicksort “Count”

Abstract

Recently, Aumüller and Dietzfelbinger proposed a version of a dual-pivot quicksort, called "Count", which is optimal among dual-pivot versions with respect to the average number of key comparisons required. In this note we provide further probabilistic analysis of "Count". We derive an exact formula for the average number of swaps needed by "Count" as well as an asymptotic formula for the variance of the number of swaps and a limit law. Also for the number of key comparisons the asymptotic variance and a limit law are identified. We also consider both complexity measures jointly and find their asymptotic correlation.

Accelerating Database Systems Using FPGAs: A Survey

“…Quicksort and variations are currently preferred on CPUs. Optimisations of quicksort can be found in the Oracle database implementation [18] and this research area is still fairly active. Other uses of sorting on databases include the analytics-related queries, hence the tau notation in relational algebra which represents sorting.…”