A Comparative Analysis of Sorting Algorithms with focus on Merge Sort

Abstract

In our thesis work, we try to find out the efficiency of several sorting algorithms and generate a comparative report according to performance, based on experimental data size and data order for all algorithm. To do this we have researched, analyzed about 9 different types of well-known sorting algorithms. We convert the algorithms to programable code, compile and run with different set of data. We keep the sorting algorithm’s description as it is. We give focus on, how the algorithms work, considering their total operation count (assignment count, comparison count) and complexity based on our same data set for all algorithm. We write programming code for each sorting algorithm in C programming language. In our investigation, we have also worked with big and small data for different cases (ordered, preordered, random, disordered) and put their result in different tables. We show the increasing ratio to compare the result. we also show the data in graphical chart for view comparative report in same window. We mark their efficiency with point and ranked them. At last we discussed their result of efficiency in a single table. We modify the merge sort and try to make an improved tri-merge sorting algorithm that is more efficient than marge sort. Theoretically if we divide and conquer with higher number its result is better, some paper exists on it, but to manage the algorithm, there cost lot of operations count. Like, if we consider quadratic divide-conquer, its manage complexly is huge than binary divide-conquer that why we generally use binary merge. We found trimerge is theoretically and practically true based on investigation data set. Tri-marge take some more compare operation for manage and sort when data remain 1 or 2 at last stage, whereas binary merge don’t need such compare. But for big data size tri-merge gain lot of operation count that give significant result that declare tri-merge is more efficient than merge sort algorithm. We also experiment with penta-merge algorithm which give more better result but algorithm and implementation is too complex. We shall try to define the tri-merge algorithm so that it can be used to implement in any programming language. It will help students, researchers to use the algorithm, as like we got the various algorithm structure over the internet.