Partitioning schemes for quicksort and quickselect

TL;DR

This paper explores various partitioning schemes for quicksort and quickselect, including ternary schemes that efficiently handle keys equal to the pivot, with theoretical and experimental analysis of their performance.

Contribution

It introduces new partitioning schemes, especially ternary schemes, and provides estimates and experimental validation of their efficiency in quicksort and quickselect.

Findings

Ternary schemes effectively identify all keys equal to the pivot with minimal additional cost.

Different partitioning schemes vary in the number of swaps they perform.

Experimental results support the efficiency of ternary schemes in practical scenarios.

Abstract

We introduce several modifications of the partitioning schemes used in Hoare's quicksort and quickselect algorithms, including ternary schemes which identify keys less or greater than the pivot. We give estimates for the numbers of swaps made by each scheme. Our computational experiments indicate that ternary schemes allow quickselect to identify all keys equal to the selected key at little additional cost.