Sorting Algorithms – A Comparative Study

— 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.

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.

Sorting essential, especially in the software engineering process is considered. Sorting is used as an immediate step as a piece of different processes. Sorting to track refers to the list of segments in the association of a specific request by ascending or descending order by means of a key description. There are many sorting algorithms have been made accordingly. There are different sorting algorithms like Bubble Sort, Selection Sort, Insertion Sort, Merge Sort, Heap Sort and Quick Sort. In this research paper, we discuss a bubble sort algorithm and two new algorithms sorting, to improved selection sort and improved bubble Sort techniques. Improved selection sort is a provide details regarding the selection sort by advancement it quicker and never stable sort algorithm. Improved bubble Sort is in the request of progress all through the bubble sort and selection sort strategies with O (nlgn) finish as opposed to O (n2) to the bubble sort and selection sort algorithms. They explore ...

International Journal of Computer Applications, 2013

Ordering is a very important for mankind .If anything is in unordered then it will not easily understand by anyone but if it is in order then it will easily understand and used by anyone. So ordering is a very important issue in computer science also. In computer science many programming applications use ordering to solving a problem either it is in ascending or descending order. In this paper we discuss four sorting algorithms which are already existed named as Insertion Sort, Bubble Sort, Selection Sort, Merge Sort and we design a new sorting algorithm named as index sort also. In this paper we check the performance and comparison of all five sorting algorithm on the basis of increasing the no of elements in bulk. We check how much processing time is taken by all four sorting algorithms with Index Sort and compared them and finding which sorting algorithm takes less time to sort the elements like 10, 100, 1000, 10000 . If any algorithm takes less processing time it means that it sorts the element faster than others. The processing time of a sorting algorithm is based on the processing speed of a Processor as well as internal memory (RAM) used by the system.

2011 3rd International Conference on Computer Research and Development, 2011

Today implementation of sort leads to lower and easier order time. Our purpose in this article are trying to introduce an algorithm with lower cost of Bubble sort and nearly same as Selection sort. A way is in orderly inserting of elements in another array. Sort is an algorithm that arranges all elements of an array, orderly. This algorithm has sequential form. The order of Selection sort complexity is nearly least than Bubble sort.

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.

— sorting of elements is an important task in computation that is used frequently in different processes. For accomplish task in reasonable amount of time efficient algorithm is needed. Different types of sorting algorithms have been devised for the purpose. Which is the best suited sorting algorithm can only be decided by comparing the available algorithms in different aspects. In this paper a comparison is made for different sorting algorithms used in computation. Keywords— best sorting algorithm, bubble sort algorithms, quick sort algorithms, sorting algorithms, efficient sorting

One of the fundamental issues in computer science is ordering a list of items. Although there is a huge number of sorting algorithms, sorting problem has attracted a great deal of research; because efficient sorting is important to optimize the use of other algorithms. This paper presents two new sorting algorithms, enhanced selection sort and enhanced bubble Sort algorithms. Enhanced selection sort is an enhancement on selection sort by making it slightly faster and stable sorting algorithm. Enhanced bubble sort is an enhancement on both bubble sort and selection sort algorithms with O(nlgn) complexity instead of O(n 2) for bubble sort and selection sort algorithms. The two new algorithms are analyzed, implemented, tested, and compared and the results were promising.

Research Journal of Applied Sciences, Engineering and Technology, 2014

In everyday life there is a large amount of data to arrange because sorting removes any ambiguities and make the data analysis and data processing very easy, efficient and provides with cost less effort. In this study a set of improved sorting algorithms are proposed which gives better performance and design idea. In this study five new sorting algorithms (Bi-directional Selection Sort, Bi-directional bubble sort, MIDBiDirectional Selection Sort, MIDBidirectional bubble sort and linear insertion sort are presented. Bi-directional Selection Sort and MIDBiDirectional Selection Sort are the enhancement on basic selection sort while Bidirectional bubble sort and MIDBidirectional bubble sort are the enhancement on basic bubble sort by changing the selection and swapping mechanism of data for sorting. Enhanced sorting algorithms reduced the iteration by half and quarter times respectively. Asymptotically complexities of these algorithms are reduced to O (n 2 /2) and O (n 2 /4) from O (n 2). Linear insertion sort is the enhancement of insertion sort by changing the design of algorithm (convert two loops to one loop). So asymptotically this algorithm is converted to linear time complexity from quadratic complexity. These sorting algorithms are described using C. The proposed algorithms are analyzed using asymptotic analysis and also using machine-running time and compared with their basic sorting algorithms. In this study we also discuss how the performance and complexity can be improved by optimizing the code and design.

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.

2020

The problem of sorting is a problem that arises frequently in computer programming and though which is need to be resolved. Many different sorting algorithms have been developed and improved to make sorting optimized and fast. As a measure of performance mainly the average number of operations or the average execution times of these algorithms have been compared. There is no one sorting method that is best for every situation. Some of the factors to be considered in choosing a sorting algorithm include the size of the list to be sorted, the programming effort, the number of words of main memory available,the size of disk or tape units, the extent to which the list is already ordered, and the distribution of values.

Sorting is one of the fundamental issues in computer science. Sorting problem gain more popularity, as efficient sorting is more important to optimize other algorithms e.g. searching algorithms. A number of sorting algorithms has been proposed with different constraints e.g. number of iterations (inner loop, outer loop), complexity, and CPU consuming problem. This paper presents a comparison of different sorting algorithms (Sort, Optimized Sort, Selection Sort, Quick Sort, and Merge Sort) with different data sets (small data, medium data, and large data), with Best Case, Average Case, and worst case constraint. All six algorithms are analyzed, implemented, tested, compared and concluded that which algorithm is best for small, average, and large data sets, with all three constraints (best case, average case, and worst case).

2013

Sorting is an operation to arrange the elements of a data structure in some logical order. In our daily lifes, without knowing about sorting we are doing works in sorted order. So that’s why everybody must need an efficient sorting technique which will solve sorting problem with in limited time. So We have discussed about various existing sorting algorithms with their advantage and disadvantage. In this paper, we have proposed a new sorting algorithm which overcomes some common disadvantage of some traditional existing algorithms by properly utilizing the memory. Here, we have compared our algorithm with traditional existing algorithms by using some factors. KeywordsVarious sorting algorithms. Bubble sort, Selection sort, Insertion sort and Quick sort

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.

2020

Sorting algorithm in the computational process makes it easy for users when the data sorting process because the data is sorted by the process quickly and automatically. In addition to speed in sorting data, memory efficiency must also be considered. In this research, a retesting of two sorting methods is conducted, namely the bubble sort method and the insertion sort method based on the comparison of two programming languages, Java with Visual Basic 2010 using the decision tree method. This research aims to find out which algorithm has lower memory consumption in the sorting process using Java or Visual Basic 2010. The results of the comparison show, in Visual Basic 2010. insertion sort algorithm which has the lowest average memory consumption of 4.3243KB for .vb extensions and 2.0145KB for .exe extensions. while the bubble sort method with a consumption amount of 4.4358KB for the .vb extension and 2.0352 for extension.exe. Furthermore, if you use the Java programming language. So ...