Visualization of performance of bubble sort in worst case in personal computer using polynomial curve fitting technique

Abstract

Bubble sort is one of the simple sorting algorithms. In this study, the researchers had used polynomial curve fitting technique to visualize the performance of Bubble sort in the worst case in a personal computer. To identify the best fit (i) R square, (ii) Adjusted R square, (iii) Root mean square error, (iv) Akaike information criterion (AIC) and (v) Bayesian information criterion (BIC) had been used. The Bubble sort algorithm in the worst case had been implemented using C programming language and the algorithm had been run for data size two thousand five hundred (2500) to data size twenty thousand (20000) with an interval of five hundred (500). For each data size one hundred (100) observations (execution time in seconds) had been recorded and for each data size the median value of the observations (execution time in seconds) had been calculated. Thus, the researchers had calculated thirty six (36) data points (data size versus median value of execution time in seconds). The polynomial curve fitting had been tried and tested on these thirty six (36) data points (data size versus median value of execution time in seconds). In total twenty four (24) models starting from linear model to polynomial of degree 24 had been employed in this study to identify the best model and among these models “Polynomial of degree 2” model had been identified as the best model.