Parameterized Complexity on a New Sorting Algorithm: A Study in Simulation

TL;DR

This paper investigates a modified quicksort algorithm's performance across various probability distributions, emphasizing parameterized complexity and empirical modeling of its average sorting time.

Contribution

It provides an empirical analysis of the algorithm's sensitivity to input distributions and develops a model explaining its average sorting time based on parameters.

Findings

Algorithm sorts some distributions faster than others

Performance varies significantly with input distribution

Empirical model explains average sorting time based on distribution parameters

Abstract

Sundararajan and Chakraborty (2007) introduced a new sorting algorithm by modifying the fast and popular Quick sort and removing the interchanges. In a subsequent empirical study, Sourabh, Sundararajan and Chakraborty (2007) demonstrated that this algorithm sorts inputs from certain probability distributions faster than others and the authors made a list of some standard probability distributions in decreasing order of speed, namely, Continuous uniform < Discrete uniform < Binomial < Negative Binomial < Poisson < Geometric < Exponential < Standard Normal. It is clear from this interesting second study that the algorithm is sensitive to input probability distribution. Based on these pervious findings, in the present paper we are motivated to do some further study on this sorting algorithm through simulation and determine the appropriate empirical model which explains its average sorting time with special emphasis on parameterized complexity.