A Comparative Study on the Performance of Permutation Algorithms

TL;DR

This paper compares the performance of three permutation algorithms—Bottom-Up, Lexicography, and Johnson-Trotter—implemented with brute-force and divide-and-conquer approaches, by measuring execution times through computer simulations.

Contribution

It provides a comparative analysis of permutation algorithms with multiple implementation approaches, highlighting their efficiency differences.

Findings

Johnson-Trotter generally faster than others

Divide-and-conquer approach improves performance

Implementation details influence execution time

Abstract

Permutation is the different arrangements that can be made with a given number of things taking some or all of them at a time. The notation P(n,r) is used to denote the number of permutations of n things taken r at a time. Permutation is used in various fields such as mathematics, group theory, statistics, and computing, to solve several combinatorial problems such as the job assignment problem and the traveling salesman problem. In effect, permutation algorithms have been studied and experimented for many years now. Bottom-Up, Lexicography, and Johnson-Trotter are three of the most popular permutation algorithms that emerged during the past decades. In this paper, we are implementing three of the most eminent permutation algorithms, they are respectively: Bottom-Up, Lexicography, and Johnson-Trotter algorithms. The implementation of each algorithm will be carried out using two different approaches: brute-force and divide and conquer. The algorithms codes will be tested using a computer simulation tool to measure and evaluate the execution time between the different implementations.