A note on multipivot Quicksort

TL;DR

This paper analyzes a generalized version of Quicksort that uses multiple pivots, deriving the expected cost and computing constants with Vandermonde matrices, providing insights into its efficiency.

Contribution

It introduces a detailed analysis of multipivot Quicksort, including expected cost calculations and the use of Vandermonde matrices for constant computation.

Findings

Expected cost formulas for multipivot Quicksort

Use of Vandermonde matrices to compute integration constants

Insights into efficiency of multi-pivot partitioning

Abstract

We analyse a generalisation of the Quicksort algorithm, where k uniformly at random chosen pivots are used for partitioning an array of n distinct keys. Specifically, the expected cost of this scheme is obtained, under the assumption of linearity of the cost needed for the partition process. The integration constants of the expected cost are computed using Vandermonde matrices.