Partition Sort Revisited: Reconfirming the Robustness in Average Case and much more!

TL;DR

This paper reexamines the robustness of Partition Sort's average-case complexity, confirming its stability across various distributions, including those with undefined expectations, and explores its sensitivity to input distribution parameters.

Contribution

It provides empirical evidence that Partition Sort maintains O(nlogn) average complexity even with Cauchy inputs and investigates its parameterized complexity with Binomial inputs.

Findings

Partition Sort is robust for Cauchy distribution inputs.

Algorithm shows sensitivity to input distribution parameters.

Encouraging results for Binomial inputs suggest broader applicability.

Abstract

In our previous work there was some indication that Partition Sort could be having a more robust average case O(nlogn) complexity than the popular Quick Sort. In our first study in this paper, we reconfirm this through computer experiments for inputs from Cauchy distribution for which expectation theoretically does not exist. Additionally, the algorithm is found to be sensitive to parameters of the input probability distribution demanding further investigation on parameterized complexity. The results on this algorithm for Binomial inputs in our second study are very encouraging in that direction.