Analysis and Performance Measurement of Sorting Algorithms

Abstract: When using the visualize to compare algorithms, never forget that the visualize sorts only very small arrays. The effect of quadratic complexity (either a square number of moves or a square number of exchanges) is dramatic as the size of the array grows. For instance, dichotomic insertion, which is only marginally slower than quick sort on 100 items, becomes 10 times slower on 10000 items. We have investigated the complexity values researchers have obtained and observed that there is scope for fine tuning in present context. Strong evidence to that effect is also presented. We aim to provide a useful and comprehensive note to researcher about how complexity aspects of sorting algorithms can be best analyzed. Keywords: Algorithm analysis, Sorting algorithm, Empirical Analysis Computational Complexity notations. Title: Performance Comparison of Sorting Algorithms On The Basis Of Complexity Author: Mr. Niraj Kumar, Mr. Rajesh Singh International Journal of Computer Science and Information Technology Research ISSN 2348-120X (online), ISSN 2348-1196 (print) Research Publish Journals

International Journal of Scientific Research in Computer Science, Engineering and Information Technology, 2023

In today's era, the development of information technology is increasingly rapid. This is because human life is currently very dependent on the needs of information technology. This can be proven by the number of human interactions with various gadgets, such as laptops, cellphones, computers, and so on. The development of information technology has made IT activists such as companies and programmers compete in making good applications. One of the most basic things that are mastered in making an application is making algorithms. Currently, there are many types of algorithms. One of them is the data sorting algorithm. In this study, we will try to examine 3 data sorting algorithms, namely Insertion Sort, Quick Sort, and Merge Sort. These three algorithms will be used to sort random data ranging from 1000 to 20,000 data. The three algorithms will be compared in terms of execution time. The results show that the Insertion Sort algorithm is a data sorting algorithm that has the fastest execution time compared to other algorithms, while the Merge Sort algorithm is the most time consuming algorithm compared to other algorithms.

— An algorithm is precise specification of a sequence of instruction to be carried out in order to solve a given problem. Sorting is considered as a fundamental operation in computer science as it is used as an intermediate step in many operations. Sorting refers to the process of arranging list of elements in a particular order. The elements are arranged in increasing or decreasing order of their key values. This research paper presents the different types of sorting algorithms of data structure like Bubble Sort, Selection Sort, Insertion Sort, Merge Sort and Quick Sort and also gives their performance analysis with respect to time complexity. These five algorithms are important and have been an area of focus for a long time but still the question remains the same of " which to use when? " which is the main reason to perform this research. Each algorithm solves the sorting problem in a different way. This research provides a detailed study of how all the five algorithms work and then compares them on the basis of various parameters apart from time complexity to reach our conclusion. I. INTRODUCTION Algorithm is an unambiguous, step-by-step procedure for solving a problem, which is guaranteed to terminate after a finite number of steps. In other words algorithm is logical representation of the instructions which should be executed to perform meaningful task. For a given problem, there are generally many different algorithms for solving it. Some algorithms are more efficient than others, in that less time or memory is required to execute them. The analysis of algorithms studies time and memory requirements of algorithms and the way those requirements depend on the number of items being processed. Sorting is generally understood to be the process of rearranging a given set of objects in a specific order and therefore, the analysis and design of useful sorting algorithms has remained one of the most important research areas in the field. Despite the fact that, several new sorting algorithms being introduced, the large number of programmers in the field depends on one of the comparison-based sorting algorithms: Bubble, Insertion, Selection sort etc. Hence sorting is an almost universally performed and hence, considered as a fundamental activity. The usefulness and significance of sorting is depicted from the day to day application of sorting in real-life objects. For instance, objects are sorted in: Telephone directories, income tax files, tables of contents, libraries, dictionaries. The methods of sorting can be divided into two categories: INTERNAL SORTING: If all the data that is to be sorted can be adjusted at a time in main memory, then internal sorting methods are used. EXTERNAL SORTING: When the data to be sorted can " t be accommodated in the memory at the time and some has to be kept in auxiliary memory (hard disk, floppy, tape etc) , then external sorting method are used. The complexity of a sorting algorithm measures the running time of function in which " n " numbers of items are sorted. The choice of which sorting method is suitable for a problem depends on various efficiency considerations for different problem. Three most important of these considerations are:  The length of time spent by programmer in coding a particular sorting program.  Amount of machine time necessary for running the program.  The amount of memory necessary for running program.  Stability-does the sort preserve the order of keys with equal values.

Sorting is the basic operation in most of the applications of computer science. Sorting means to arrange data in particular order inside computer. In this paper we have discussed performance of different sorting algorithms with their advantages and disadvantages. This paper also represents the application areas for different sorting algorithms. Main goal of this paper is to compare the performance of different sorting algorithms based on different parameters.

In modern days we see disciplines like data sciences, data Analytics, and machine learning are emerging to promote Information Technology and in bringing up Internet of things. Algorithms like sorting and searching plays a important role, as efficient sorting with searching is important for other algorithms. The emerging areas are using Python and Java languages for its implementation and have become most popular ones than C and C++. Also it is seen less asymptotic analysis is made on popular sorting algorithms using Python and Java. Sufficient asymptotic analysis and results using C/C++ are seen in research articles. This paper makes performance measures by implementing Popular Sorting Algorithms(PSAs) using Java, Python and C++ languages. We conducted our experiments on random data to make average case analysis and on ordered data to make worst case analysis. Our results have shown Merge sort performing well for Python implementation than Quick sort. Quick sort remains excellent in performance for Java implementation for random data. C++ implementation verified the behaviors of PSAs. Finally, we have indicated the miss behaviors made by Java and Python as observed in the results.

International Journal of Computer Applications, 2020

Sorting is one of the most important task in many computer applications. Efficiency becomes a big problem when the sorting involves a large amounts of data. There are a lot of sorting algorithms with different implementations. Some of them sort data by comparison while others don't. The main aim of this thesis is to evaluate the comparison and noncomparison based algorithms in terms of execution time and memory consumption. Five main algorithms were selected for evaluation. Out of these five, three were comparison based algorithms (quick, bubble and merge) while the remaining two were non-comparison based (radix and counting). After conducting an experiment using array of different data sizes (ranging from 1000 to 35000), it was realized that the comparison based algorithms were less efficient than the noncomparison ones. Among the comparison algorithms, bubble sort had the highest time complexity due to the swapping nature of the algorithm. It never stops execution until the largest element is bubbled to the right of the array in every iteration. Despite this disadvantage, it was realized that it is memory efficient since it does not create new memory in every iteration. It relies on a single memory for the swapping array operation. The quick sort algorithm uses a reasonable amount of time to execute, but has a poor memory utilization due to the creation of numerous sub arrays to complete the sorting process. Among the comparison based algorithms, merge sort was far better than both quick and bubble. On the average, merge sort utilized 32.261 seconds to sort all the arrays used in the experiment while quick and bubble utilized 41.05 and 165.11 seconds respectively. The merge algorithm recorded an average memory consumption of 5.5MB for all the experiment while quick and bubble recorded 650.792MB and 4.54MB respectively. Even though the merge sort is better than both quick and bubble, it cannot be compared to the non-comparison based algorithms since they perform far better than the comparison based ones. When the two groups were evaluated against execution time, the comparison based algorithms recorded an average score of 476.757 seconds while the non-comparison obtained 17.849 seconds. With respect to the memory utilization, the non-comparison based algorithms obtained 27.12MB while the comparison ones obtained 1321.681MB. This clearly reveals the efficiency of the non-comparison based algorithms over the comparison ones in terms of execution time and memory utilization.

International Journal of Emerging Trends in Engineering Research (IJETER), 2021

In the era of new technology, we have huge amount of data to deal with arranging the huge amount of data has remained a big challenge. This research paper includes two types of sorting algorithm, Heap Sort and Insertion Sort and also their performance analysis on thebasis of running time along with their complexity. This paper includes the algorithms and theirimplementation in Java programming language. For theresults of this research study,the comparison ofthese two sorting algorithms with different type of the data at running time such as Large, Average, and Small. In Large,data pass100 integers in the array. For Average data pass 50integers in the array and for Small data pass10 integers in the array. It checks that,which sorting technique is efficient according to the input data. Then identifiesthe efficiency of these algorithms according to this data three cases used that is Best, Average and Worst Case. The result of this analysis is showing with the help of graphs to show that how much time both algorithms take while given the desired outpu

Sorting is nothing but alphabetizing, categorizing, arranging or putting items in an ordered sequence. It is a key fundamental operation in the field of computer science. It is of extreme importance because it adds usefulness to data. In this papers, we have compared five important sorting algorithms (Bubble, Quick, Selection, Insertion and Merge). We have developed a program in C# and experimented with the input values 1-150, 1-300 and 1-950. The performance and efficiency of these algorithms in terms of CPU time consumption has been recorded and presented in tabular and graphical form.

International Journal of Modern Education and Computer Science, 2013

Sorting allows information or data to be put into a meaningful order. As efficiency is a major concern of computing, data are sorted in order to gain the efficiency in retrieving or searching tasks. The factors affecting the efficiency of shell, Heap, Bubble, Quick and Merge sorting techniques in terms of running time, memory usage and the number of exchanges were investigated. Experiment was conducted for the decision variables generated from algorithms implemented in Java programming and factor analysis by principal components of the obtained experimental data was carried out in order to estimate the contribution of each factor to the success of the sorting algorithms. Further statistical analysis was carried out to generate eigenvalue of the extracted factor and hence, a system of linear equations which was used to estimate the assessment of each factor of the sorting techniques was proposed. The study revealed that the main factor affecting these sorting techniques was time taken to sort. It contributed 97.842%, 97.693%, 89.351%, 98.336% and 90.480% for Bubble sort, Heap sort, Merge sort, Quick sort and Shell sort respectively. The number of swap came second contributing 1.587% for Bubble sort, 2.305% for Heap sort, 10.63% for Merge sort, 1.643% for Quick sort and 9.514% for Shell sort. The memory used was the least of the factors contributing negligible percentage for the five sorting techniques. It contributed 0.571% for Bubble sort, 0.002% for Heap sort, 0.011% for Merge sort, 0.021% for Quick sort and 0.006% for Shell sort.

2009

Since the dawn of computing, the sorting problem has attracted a great deal of research. In past, many researchers have attempted to optimize it properly using empirical analysis. We have investigated the complexity values researchers have obtained and observed that there is scope for fine tuning in present context. Strong evidence to that effect is also presented. We aim to provide a useful and comprehensive note to researcher about how complexity aspects of sorting algorithms can be best analyzed. It is also intended current researchers to think about whether their own work might be improved by a suggestive fine tuning. Our work is based on the knowledge learned after literature review of experimentation, survey paper analysis being carried out for the performance improvements of sorting algorithms. Although written from the perspective of a theoretical computer scientist, it is intended to be of use to researchers from all fields who want to study sorting algorithms rigorously.