Review on Sorting Algorithms A Comparative Study

Khalid Suleiman Al-Kharabsheh, Ibrahim Mahmoud AlTurani, Abdallah Mahmoud Ibrahim AlTurani & Nabeel
Imhammed Zanoon
International Journal of Computer Science and Security (IJCSS), Volume (7) : Issue (3) : 2013 120
Review on Sorting Algorithms
A Comparative Study
Khalid Suleiman Al-Kharabsheh khalidkh@bau.edu.jo
Aqaba College , Balqa Applied University
Aqaba, Jordan
Ibrahim Mahmoud AlTurani Traini111@bau.edu.jo
Aqaba, Jordan
Abdallah Mahmoud Ibrahim AlTurani Traini2001@yahoo.com
IT college,Jordan University of Science and Technology
Irbid,Jordan
Nabeel Imhammed Zanoon Dr.nabeel@bau.edu.jo
Aqaba, Jordan
Abstract
There are many popular problems in different practical fields of computer sciences, database
applications, Networks and Artificial intelligence. One of these basic operations and problems is
sorting algorithm; the sorting problem has attracted a great deal of research. A lot of sorting
algorithms has been developed to enhance the performance in terms of computational
complexity. there are several factors that must be taken in consideration; time complexity,
stability, memory space. Information growth rapidly in our world leads to increase developing sort
algorithms.a stable sorting algorithms maintain the relative order of records with equal keys This
paper makes a comparison between the Grouping Comparison Sort (GCS) and conventional
algorithm such as Selection sort, Quick sort, Insertion sort , Merge sort and Bubble sort with
respect execution time to show how this algorithm perform reduce execution time.
Keywords: Sort, Grouping Comparison Sort, Quick Sort, Merge Sort, Time Complexity.
1. INTRODUCTION
Sorting is a process of rearrangement a list of elements to the correct order since handling the
elements in a certain order more efficient than handling randomize elements [1].Sorting and
searching are among the most common programming processes, as an example take database
applications if you want to maintain the information and ease of retrieval you must keep
information in a sensible order, for example, alphabetical order, ascending/descending order and
order according to names, ids, years, departments, etc.
Information growth rapidly in our world leads to increase developing sort algorithms. Developing
sort algorithms through improved performance and decreasing complexity, it has attracted a great
deal of research; because any effect of sorting algorithm enhancement of the current algorithms
or product new algorithms that reflects to optimize other algorithms. Large number of algorithms
developed to improve sorting like merge sort, bubble sort, insertion sort, quick sort ,selection sort
and others, each of them has a different mechanism to reorder elements which increase the
performance and efficiency of the practical applications and reduce time complexity of each one.
When comparing between various sorting algorithms, there are several factors that must be taken
in consideration; first of them is the time complexity, the time complexity of an algorithm
determined the amount of time that can be taken by an algorithm to run [3][7][27]. This factor

Imhammed Zanoon
different from sorting algorithm to another according to the size of data that we want to reorder,
some sorting algorithm inefficient and too slow. The time complexity of an algorithm is generally
written in form big O(n) notation, where the O represents the complexity of the algorithm and a
value n represent the number of elementary operations performed by the algorithm [8].The
second factor is the stability[26], means; algorithm keeps elements with equal values in the same
relative order in the output as they were in the input. [2][3][9]. Some sorting algorithms are stable
by its nature such as insertion sort, merge sort, bubble sort, while some sorting algorithms are
not, such as quick sort, any given sorting algorithm which is not stable can be modified to be
stable [3]. The third factor is memory space, algorithm that used recursive techniques need more
copies of sorting data that affect to memory space [3][9].Many previous researches have been
suggested to enhance the sorting algorithm to maintain memory and improve efficiency. Most of
these algorithms are used comparative operation between the oldest algorithm and the newest
one to prove that.
2. PERFORMANCE IN AVERAGE CASE BETWEEN SORTING AlGORITHMS
the following studies are previous study on the same research which make a comparative
between different type of sorting algorithms:
(Pooja Adhikari,2007) The performance of any computation depends upon the performance of
sorting algorithms.Like all complicated problems, there are many solutions that can achieve the
same results. This paper choose two of the sorting algorithms among them selection sort and
shell sort and compares the various performance factor among them.
(Davide Pasetto Albert Akhriev,2011) In this paper we provide a qualitative and quantitative
analysis of the performance of parallel sorting algorithms on modern multi-core hardware. We
consider several general-purpose methods,which are widely regarded among the best algorithms
available, with particular interest in sorting of database records and very large arrays (several
gigabytes and more), whose size far exceed L2/L3 cache.
(ADITYA DEV MISHRA & DEEPAK GARG,2008)Many different sorting algorithms have been
developed and improved to make sorting fast. As a measure of performance mainly the average
number of operations or the average execution times of these algorithms have been investigated
and 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
This paper implemented of Selection sort, Quick sort, Insertion sort , Merge sort ,Bubble sort and
GCS algorithms using C++ programming language, and measure the execution time of all
programs with the same input data using the same computer. The built-in function (clock ()) in
C++ is used to get the elapsed time of the implementing algorithms, execution time of a program
is measured in milliseconds [6].The performances of GCS algorithm and a set of conventional
sort algorithms are comparatively tested under average cases by using random test data from
size 10000 to 30000. The result obtained is given in Table 1 to Table 6 for each Algorithm and the
curves are shown in figure 1.
Selection sort
Selection sorts the simplest of sorting techniques. It's work very well for small files, also It's has a
quite important application because each item is actually moved at most once [4]. It has O (n2)
time complexity, making it inefficient on large lists. Selection sort has one advantage over other
sort techniques[15][16]. Although it does many comparisons, it does the least amount of data
moving. That means, if your data has small keys but large data area, then selection sorting may
be the quickest.[8] .In Table 1 the execution time and number of elements as follow:

Imhammed Zanoon
Number of elements Running time (ms)
10000 2227
20000 5058
30000 8254
TABLE 1: Running Time for Selection Sort.
Insertion sort
Insertion sort is very similar to selection sort. It is a simple sorting algorithm that builds the final
sorted list one item at a time[18]. It has O (n2) time complexity, It is much less efficient on large
lists than more advanced algorithms such as quick sort, heap sort, or merge sort. However,
insertion sort provides several advantages Simple implementation and, Efficient for small data
sets [10][17] .In Table 2 the execution time and number of elements as follow:
10000 1605
20000 3678
30000 6125
TABLE 2: Running Time for Insertion Sort.
Merge sort
Merge sort is a divide and conquer algorithm .It's Divide the list into two approximately equal sub
lists, Then Sort the sub lists recursively[19]. It has an O (n log n) Time complexity .merge sort is a
stable sort, parallelizes better, and is more efficient at handling slow-to-access sequential media.
Merge sort is often the best choice for sorting a linked list [11][20]. In Table 3 the execution time
and number of elements as follow:
10000 728
20000 1509
30000 2272
TABLE 3: Running time for merge sort
Quick sort
In this sort an element called pivot is identified and that element is fixed in its place by moving all
the elements less than that to its left and all the elements greater than that to its right. Since it
partitions the element sequence into left, pivot and right it is referred as a sorting by partitioning.
It's an O (n log n) Time complexity in average case[21][22]. In Table 4 the execution time and
number of elements as follow:
10000 489
20000 1084
30000 1648
TABLE 4: Running Rime for Quick Sort.

Imhammed Zanoon
Bubble sort
Bubble sort is a simple sorting algorithm that works by repeatedly; it's comparing each pair of
adjacent items and swapping them if they are in the wrong order. This passing procedure is
repeated until no swaps are required, indicating that the list is sorted [13][23]. It has a O (n2)
Time complexity means that its efficiency decreases dramatically on lists of more than a small
number of elements [12][24]. In Table 4 the execution time and number of elements as follow:
10000 1133
20000 3103
30000 5730
TABLE 5: Running Time for Bubble Sort.
Grouping Comparison sort
In this sort we divide the list of elements into groups; each group contains three elements that
compare with the first element of next groups. Performance has been decreased by GCS
algorithm, mainly if the input size more than 25000 elements that returned increasing number of
comparison, the performance have been improved when size of input is less than 25000
elements. It has a time complexity O (n2) [14]. In Table 6 the execution time and number of
elements as follow:
10000 1124
20000 3374
30000 6687
TABLE 6: Running Time for Comparison Sort.
3. COMPARATIVE STUDY AND DISCUSSION
All the six sorting algorithms (Selection Sort, Insertion sort, Merge sort, Quick sort, Bubble Sort
and Comparison sort) were implemented in C++ programming languages and tested for the
random sequence input of length 10000, 20000, 30000, All the six sorting algorithms were
executed on machine Operating System having Intel(R) Core(TM) 2 Duo CPU E8400 @ 3.00
GHz (2 CPUs) and installed memory (RAM) 2038 MB. The Plot of length of input and CPU time
taken (ms) is shown in figure 1. Result shows that for small input the performance for the six
techniques is all most nearest, but for the large input Quick sort is the fastest and the selection
sort the slowest. the grouping comparison sort for small input (10000) is the third sort and in the
large input (30000) is the fifth sort in order between the six sorting algorithms.

Imhammed Zanoon
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
123
size * 10000
Timeinms
Selection sort
Insertion sort
Merge Sort
Quick sort
Bubble sort
Comparison sort
FIGURE 1 : Plot of Number of Input vs CPU.
3.1 Complexity Comparison between Typical sorting algorithms
The comparison of complexity between GCS and conventional sort algorithms are listed in table
7[5]. Table 6 determines the time complexity of new algorithm is equivalent to some conventional
sort algorithms[25][28]. GCS gave an additional method to manipulate information.
Algorithm Average case Worst case
Selection sort O ( n2 ) O ( n2 )
Insertion sort O ( n2 ) O ( n2 )
Merge Sort O ( n log n ) O ( n log n )
Quick sort O ( n log n ) O ( n2 )
Bubble sort O ( n2 ) O ( n2 )
Comparison Sort O ( n2 ) O ( n2 )
TABLE 7: Time Complexity of Typical Sorting Algorithms.
4. CONCLUSION AND FUTURE WORK
This paper discuss a comparison between the new suggested algorithm (GCS) and
selection sort, Insertion sort, merge sort, quick sort and bubble sort. It analysis the
performance of these algorithms for the same number of elements (10000, 20000,
30000). For small input the performance for the six techniques is all most nearest, but for
the large input Quick sort is the fastest and the selection sort the slowest. Comparison sort
in average and worst case have the same time complexity with selection, Insertion and bubble
sort This research is initial step for future work; in the future we will improve our algorithms
Grouping Comparison Sort algorithms (GCS) to optimize software’s in searching method and
retrieve data.
5. REFERENCES
[1] P.Adhikari, Review on Sorting Algorithms, "A comparative study on two sorting algorithm",
Mississppi state university, 2007.

Imhammed Zanoon
[2] T. Cormen, C.Leiserson, R. Rivest and C.Stein, Introduction To Algorithms, McGraw-Hill,
Third Edition, 2009,pp.15-17.
[3] M. Goodrich and R. Tamassia, Data Structures and Algorithms in Java,John wiley & sons
4th edition, 2010,pp.241-243.
[4] R. Sedgewick and K. Wayne, Algorithms,Pearson Education, 4th Edition, 2011,pp.248-249.
[5] T. Cormen, C.Leiserson, R. Rivest and C.Stein,Introduction to Algorithms, McGraw Hill,
2001,pp.320-330.
[6] H. Deitel and P. Deitel, C++ How to Program, Prentice Hall, 2001,pp.150-170
[7] M. Sipser, Introduction to the Theory of Computation,Thomson,1996,pp.177-190.
[8] S. Jadoon , S.Solehria, S.Rehman and H.Jan.( 2011,FEB). " Design and Analysis of
Optimized Selection Sort Algorithm".11. (1),pp. 16-21.
Available: http://www.ijens.org/IJECS%20Vol%2011%20Issue%2001.html.
[9] Aditya Dev Mishra & Deepak Garg.(2008,DEC). “Selection of Best Sorting Algorithm ",
International journal of intelligent information Processing. II (II).pp. 363-368.
Available: http://academia.edu/1976253/Selection_of_Best_Sorting_Algorithm.
[10] http://en.wikipedia.org/wiki/Insertion_sort
[11] http://en.wikipedia.org/wiki/Merge_sort
[12] http://en.wikipedia.org/wiki/Bubble_sort
[13] http://www.techopedia.com/definition/3757/bubble-sort
[14] I. trini, k. kharabsheh, A. trini, (2013,may)."Grouping Comparison Sort", Australian Journal
of Basic and Applied Sciences.pp221-228.
[15] R. Sedgewick, Algorithms in C++, Addison–Wesley Longman,1998,pp 273–274.
[16] A. Levitin, Introduction to the Design & Analysis of Algorithms, Addison–Wesley Longman,
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[17] http://corewar.co.uk/assembly/insertion.htm
Third Edition, 2009,pp.15-21
[19] Katajainen, Jyrki; Pasanen, Tomi; Teuhola, Jukka (1996,MAR). "Practical in-place
mergesort". Nordic Journal of Computing. (3). pp. 27–40.
[20] Kronrod, M. A. (1969). "Optimal ordering algorithm without operational field". Soviet
Mathematics - Doklady (10). pp. 744.
Third Edition, 2009,pp.145-164.
[22] A. LaMarca and R. E. Ladner.(1997), "The Influence of Caches on the Performance of
Sorting." Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete
Algorithms,. pp. 370–379.
[23] D.Knuth, The Art of Computer Programming,Addison-Wesley,Third Edition 1997,pp. 106–
110 .

Imhammed Zanoon
[24] http://www.sorting-algorithms.com/bubble-sort.
[25] T.Niemann, Sorting and Searching Algorithms:A Cookbook, 2008 , pp.11-14.
[26] H.Ahmed,H.Mahmoud, N.Alghreimil,” A Stable Comparison-based Sorting Algorithm with
worst Case complexity of O(n log n) Comparisons and O(n) Moves” ,World Academy of
Science, Engineering and Technology(22),pp.970-975.
[27] C.Cook , D.Kim. “Best sorting algorithm for nearly sorted lists". Commun. ACM,
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[28] D.Garg,” Selection O. Best Sorting Algorithm”, International Journal of Intelligent Information
Processing 2(2),pp.363-368.
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