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IJCCS (Indonesian Journal of Computing and Cybernetics Systems)
Vol.x, No.x, July xxxx, pp. 1~5
ISSN (print): 1978-1520, ISSN (online): 2460-7258
DOI: 10.22146/ijccs.xxxx ◼ 1
Received June 1st,2012; Revised June 25th, 2012; Accepted July 10th, 2012
The Application of the Rabin-Karp Algorithm with the
Synonym Recognition Approach to Detect Plagiarism in
Student Assignments
Irma Handayani 1*, Anita Fira Waluyo *2
1,2 University of Technology Yogyakarta
Siliwangi Street (Ringroad Utara), Jombor, Sleman, D.I.Yogyakarta, Indonesia
e-mail: *1irma.handayani@staff.uty.ac.id, 2 anitafira@uty.ac.id
Abstrak
Kemajuan teknologi yang pesat telah mempermudah segala hal, termasuk dalam bidang
pendidikan. Namun, kecanggihan ini juga mengakibatkan penyalahgunaan teknologi, khususnya
dalam hal duplikasi atau plagiarisme. Masalah ini tidak hanya terjadi pada tugas esai tetapi juga
kode program. Untuk mengatasi hal ini, telah dilakukan penelitian untuk mendeteksi plagiarisme
pada tugas mahasiswa dengan menggunakan metode Rabin-Karp dan pendekatan Synonym
Recognition. Penelitian ini menemukan bahwa tingkat kemiripan terkecil adalah 20%, sedangkan
yang terbesar adalah 76%. Penelitian ini bertujuan untuk memberikan solusi yang cepat dan
akurat untuk mencegah maraknya aktivitas plagiarisme di bidang akademik.
Kata kunci: Algoritma rabin karp, plagiarisme, kesamaan, tugas mahasiswa
Abstract
Rapid technological advances have made everything easier, including in the field of
education. However, this sophistication has also resulted in misuse of technology, especially in
terms of duplication or plagiarism. This problem does not only occur in essay assignments but
also in program code. To overcome this, research has been conducted to detect plagiarism in
student assignments using the Rabin-Karp method and the Synonym Recognition approach. This
study found that the smallest similarity level was 20%, while the largest was 76%. This study aims
to provide a fast and accurate solution to prevent the rampant activity of plagiarism in the
academic field.
Keywords : Rabin karp algorithm, plagiarism, similarity, student assignments
1. INTRODUCTION
Along with the very rapid development of technology today, especially in the fields of
technology and the internet, many positive impacts have been reaped from technological progress.
This progress has led to swift development in the digital realm [1]. However, it has also ushered
in several inevitable negative impacts, one of the most significant being plagiarism, a major issue
in the academic world [2]. In today's digital era, easy access to information via the internet has
accelerated the exchange of knowledge in various fields, including education. Yet, this ease also
presents significant challenges, such as an increase in plagiarism cases among students, not only
in essay assignments but also in program code [3]. Plagiarism is an unethical practice involving
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the use of someone else’s work as one’s own without appropriate credit, often facilitated by the
ease of duplicating text and materials provided by sophisticated technology [4]. Previous research
has identified and developed various methods for detecting plagiarism, from manual to
algorithmic approaches [5]. Algorithms such as Winnowing and Jaro-Winkler have been widely
used to detect text similarities, but these methods often fall short in recognizing more complex
forms of plagiarism that involve synonyms or substantially changed text structures [6]. Despite
advances in plagiarism detection technology, there remains a significant gap in the ability to
identify plagiarism involving synonyms and text restructuring [6]. This study aims to address this
gap by using a modified Rabin-Karp algorithm with a synonym recognition approach, which has
not been widely explored in previous literature [7]. The main contribution of this study is the
development of a method that can efficiently improve the accuracy of plagiarism detection, speed
up the checking process, and ultimately improve academic integrity [8]. The purpose of this study
is to develop and validate a plagiarism detection system that can accurately identify text
similarities, including the use of synonyms, in students' academic documents [9]. This system is
expected to be used by educational institutions to proactively reduce plagiarism incidents and
support educational efforts in teaching good academic ethics to students [10]. The modified Rabin
Karp algorithm has been shown to select the best K-Gram values, showing highest performance
with k = 3 achieving interpretations of 1-14% (Little degree of similarity) and 15-50% (Medium
level of similarity) which significantly enhances the method's efficacy [9]. Moreover, when
combined with the Jaro-Winkler algorithm in tests, the accuracy of text similarity identification
has been greatly increased, as evidenced by a study on Indonesian text [10]. Further tests have
shown that the system's average document similarity test result was 24.13, with an accuracy rate
of 94.7% [11]. After analyzing ten documents with a k-gram 1 value, the Rabin-Karp algorithm
was implemented to detect plagiarism in web-based text document files, finding the greatest
percentage of similarity at 57.14%, while the lowest was 28.57% [12]. The Indonesian text
document similarity detection system uses both confix-stripping and Rabin-Karp algorithms [13].
Word similarity detection using the Rabin Karp algorithm, based on the findings of the tests that
have been performed using 10 abstract document data in the thesis, it produces an accuracy rate
of 95.08% and the time to process the tested documents is an average of 11.8 seconds [14]. One
benefit of the Rabin-Karp algorithm is its ability to search long pattern strings. The text
preprocessing stages of the Rabin-Karp algorithm in this system include case folding, tokenizing,
filtering or stopword removal, and stemming. Meanwhile, Synonym Recognition is the detection
of plagiarism through a synonym approach [15].
2. METHODS
A. System Description
This study faces several important limitations to consider. The dataset used is limited to
only assignment documents from informatics students at Universitas Teknologi Yogyakarta,
which may affect the generalizability of the results due to the lack of variety of academic
documents from other disciplines or institutions. This study relies heavily on the Rabin-Karp
algorithm to detect text similarity, but this algorithm may not be completely effective in
identifying all types of plagiarism, especially those involving heavily altered or rearranged text.
In addition, implementing the Rabin-Karp algorithm with a synonym recognition approach can
add complexity and require longer processing times, especially for very long documents or large
datasets. The variability in the performance of the Rabin-Karp algorithm, which can change
depending on the k-gram value used, suggests that there is a trade-off between speed and accuracy
that must be carefully managed, with smaller k-gram values tending to produce better accuracy.
The system is designed to detect plagiarism in student assignments using the Rabin Karp
algorithm with the Synonym Recognition approach. The process applied to the system is divided
into 4 stages, namely Preprocessing, Synonym Recognition, Rabin Karp modeling dan Dice
Similarity Coefficient. Figure 1 below illustrates the system flow in further detail. [16].
IJCCS ISSN (print): 1978-1520, ISSN (online): 2460-7258 ◼
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Figure 1. System Flow
B. Data Collection
This stage is the first step to starting research. Data obtained by collecting primary data, namely data on
assignment documents from Informatics students, UTY. The dataset used is text data and not a file that can
be uploaded.
C. Data Processing
The dataset used is an assignment document for students majoring in Informatics, UTY. Examples of
data used in this research are 10 student assignment documents and 1 document is used as a dataset which is
then used to compare and look for words that contain similarities, after which the value or level of similarity
is calculated.
D. Preprocessing
The first step in the text mining process is preprocessing. It is utilized to convert unstructured textual data
into organized textual data [17]. Preprocessing is the process of taking a document's unnecessary text and
removing it from the document so that it won't cause noise during the next step. Three separate steps comprise
preprocessing: tokenizing, filtering, and case folding [18]. Case Folding is the stage of changing capital
letters to lower case [19]. Only letters a to z are accepted. Characters other than letters are omitted and are
considered delimiters [20]. Tokenizing is the process of breaking down a document into groups of words
[21]. Furthermore, tokenization eliminated all numbers, symbols, and punctuation because they had no
distinct score and had nothing to do with the string that needed to be processed [22]. Words that have no
meaning are eliminated during the filtering process. Stopwords are a common term for the meaningless
words. Stopwords include phrases like "juga," "dan," "untuk," and "adalah." [23]. These stopwords must be
removed because they significantly reduce the text similarity percentage and affect the text similarity
method's accuracy when conjunctions are used frequently in sentences [24]. In a text document, the stemming
process helps to eliminate affixes from words so that the word taken is the root word. It was carried out in
order to make the next procedure easier. Affixes include things like "mem," "kan," "ber," "pun," and "mem-
an" [25]. The acquired root words were employed as tokens in every text passage to improve syntactic
matching precision and efficiency. For example, the words "belajar" and "mengajar" were found in document
1 and document 2, respectively. The word "belajar dan mengajar" became "ajar" following the stemming
process since "ajar" is the root of both "belajar" and "mengajar." [22].
E. Synonym Recognition
One technique for identifying instances of text plagiarism using the synonym approach is synonym
recognition. [15]. To say that the degree of similarity is more accurate in this instance, words that contain
synonyms are found when comparing two documents. The Synonym Recognition stage is carried out during
the preprocessing stage. Figure 2 below shows the process of recognizing synonyms.
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Figure 2.Synonym Recognition Process
F. Rabin Karp Modeling
This algorithm looks for possible patterns in the input text using the hash function. The average and best-
case running times for the text length n and pattern p of mutual length m are O (n+m) in space O (p), and
the worst-case time is O (nm) in space O(m) [26]. The Rabin-Karp algorithm employs hashing and K-
Gram, among other features. The preprocessing phase is completed before implementing the Rabin-Karp
algorithm [11]. The pseudocode for the Rabin-Karp algorithm in Table 1 is as follows.
Table 1. Pseudocode Rabin-Karp Algorithm
The phases of the Rabin-Karp algorithm are as follows:
a) K-Gram
A k-gram is a long sequence of tokens of length k. This K-Gram method takes pieces of letter characters
with k values from a text which are continuously read from the beginning of the source text to the end of the
source text [11]. An example of a K-Gram with a value of k = 3 can be seen in Table 2.
Table 2. K-Gram Example
Sentence
Rabin Karp Algorithm
Preprocessing
rabinkarpalgorithm
K-Gram
{rab} {ink} {arp}{alg} {ori} {thm}
b) Hash
Hashing is a way to convert string characters into integers called hash values. The process of converting
it into a hash value uses the rolling hash function. The rolling hash equation can be seen in equation 1 [27].
(1)
Function
Rabin-Karp (input s: s [1..m], text: string [1..n] boolean
{Searching string s in text strings with the Rabin-Karp
algorithm}
Declaration
i : integer found = boolean
Algorithm
found false
hs hash (s[1..m])
hsub hash (text [1..i+m-1])
for i 1 to n do
if hsub = hs then
if text [i..i+m-1] = s then
found true
else
hsub hash (text [i+1..i+m])
end for
return found
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Information:
h: substring
c: ASCII value per character
b: constant prime number
k: many characters
q: modulo prime number
The following is an example of a rolling hash number for a substring with a K-Gram value of 4 seen in
table 3. Table 3. Example of Hash Calculation
Atribut
Nilai Array
Rolling Hash ke 1
[0] => maka
m = 109, a = 97, k = 107, a=97, basis=11,
mod = 10007
H=c_m*b^(k-1)+c_a*b^(k-2)+c_k*b^(k-
3)+c_a*b^(k-4)
H=109*11^3+97*11^2+107*11^1+97*11^0
H=145079+11737+1177+97
H=158090 Mod 10007
H= 7985
Rolling Hash ke 2
[1] => akan
a = 97, k = 107, a = 97, n = 110, basis = 11,
mod = 10007
H=c_a*b^(k-1)+c_k*b^(k-2)+c_a*b^(k-
3)+c_n*b^(k-4)
H=97*11^3+107*11^2+97*11^1+110*11^0
H=129107+12947+1067+110
H=143231 Mod 10007
H= 3133
c) Dice’s Coefficient Similarity
Dice’s Similarity Coefficient is an algorithm used to calculate the level of similarity between two objects
by multiplying by 2 the number of intersection values between the document and the query, then dividing it
by the number of document values and the query value [28]. The application of Dice's Similarity Coefficient
in calculating similarity values using the k-gram approach is in equation 2 as follows.
x 100 (2)
Information:
S: similarity value
A dan B: the sum of the sets of kgrams in text 1 and text 2
C: the number of similar k-grams from the texts being compared
To determine the type of plagiarism between the documents tested, there are 5 types of percentage
assessment, as follows:
1) 0%: A test result of 0% indicates that the content and overall sentence structure of the two
documents are entirely different.
2) < 15%: A test result of 15% indicates a low degree of similarity between the two documents.
3) 15–50%: A score of 15–50% indicates that there is moderate plagiarism in the document.
4) >50%: A test result of more than 50% indicates that the document may be on the verge of being
plagiarized.
5) 100%: Because the content is exactly the same throughout, a test result of 100% indicates that the
document is plagiarized.
From the assessment percentage above, the tolerance level for pelagiarism is 50% or means indicating that
the document includes moderate level plagiarism.
3. RESULTS AND DISCUSSION
A. Process of Compiling Student Assignment Data
The data used to detect plagiarism is 10 student assignment data with k-gram values = 4 and 5
and prime numbers = 7.
B. Calculation Example
There are two documents entered into the system, namely training data and test data or Text A
and Text B, as seen in Figure 3 and Figure 4 below.
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Figure 3 Example of Text Data A
Figure 4 Example of Text Data B
C. Preprocessing Stage
After entering the Text A and Text B documents, the next step is preprocessing, which consists of case
folding or changing uppercase letters to lowercase, tokenizing or the process of separating words based on
word order, and the filtering process. The results of the preprocessing stage are shown in table 4 below.
Table 4. Hash Calculation Example
Document
Name
Document Contents
Doc Text
A
algoritmarabinkarphasilpersentasekeberada
ankalimat
Doc Text B
hasilpersentasekeberadaankalimat
D. Parsing K-Gram
In parsing k-grams, use the example of K-gram 5 in each text A document as shown in table 5 and text
B document in table 6 below. This means that each sentence will take pieces of 5 or 6 letter characters from
a text. Table 5. Parsing K-gram 5 Document Text A
No
Hasil
No
Hasil
No
Hasil
1
algor
17
rphas
33
ekebe
2
lgori
18
phasi
34
keber
3
gorit
19
hasil
35
ebara
4
oritm
20
asilp
36
berad
5
ritma
21
silpe
37
erada
6
itmar
22
ilper
38
radaa
7
tmara
23
lpers
39
adaan
8
marab
24
perse
40
daank
9
arabi
25
ersen
41
aanka
10
rabin
26
rsent
42
ankal
11
abink
27
senta
43
nkali
12
binka
28
entas
44
kalim
13
inkar
29
ntase
45
alima
14
nkarp
30
tasek
46
limat
15
karph
31
aseke
16
arpha
32
sekeb
Table 6. Parsing K-gram 5 Document Text B
No
Hasil
No
Hasil
No
Hasil
1
hasil
13
ersen
25
erada
2
asilb
14
rsent
26
radaa
3
silbe
15
senta
27
adaan
4
ilber
16
entas
28
daank
5
lberu
17
ntase
29
aanka
6
berup
18
tasek
30
ankal
7
erupa
19
aseke
31
nkali
8
rupap
20
sekeb
32
kalim
9
upape
21
ekebe
33
alima
10
paper
22
keber
34
limat
11
apers
23
ebara
12
perse
24
berad
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E. String Matching Stages
a) Rolling Hash
Examples of words that will be used are the words “algor” and “lgori”. The ASCII graded decimal
results are shown in table 7 below, with the specified base value being 10.
Table 7. ASCII Value
Char
Dec
Char
Dec
A
97
l
108
L
108
g
103
G
103
o
111
O
111
r
114
R
114
i
105
Hashing calculations using equation 1 are as follows.
The value of hashing in the substring “algor” is 1089524.
The value of rolling hashing in the substring “lgori” is 1195345.
b) String Matching with the Rabin-Karp Algorithm
In this process, it will match the hash of text A document and the hash of text B document which
are the same. The results look like in table 8 for document Text A and table 9 for document text B.
Table 8. Rolling Hash Result Text A
No
Term
Hash
No
Term
Hash
1
algor
1089524
24
perse
1233651
2
lgori
1195345
25
ersen
1136620
3
gorit
1153566
26
rsent
1266316
4
oritm
1235769
27
senta
1263257
5
ritma
1257787
28
entas
1132685
6
itmar
1177984
29
ntase
1226951
7
tmara
1279937
30
tasek
1269617
8
marab
1199468
31
aseke
1096271
9
arabi
1094785
32
sekeb
1262808
10
rabin
1247960
33
ekebe
1128181
11
abink
1079707
34
keber
1181924
12
binka
1097167
35
ebara
1119337
13
inkar
1171784
36
berad
1093470
14
nkarp
1217952
37
erada
1134797
15
karph
1179624
38
radaa
1248067
16
arpha
1096337
39
adaan
1080780
17
rphas
1263485
40
daank
1107907
18
phasi
1234955
41
aanka
1079167
19
hasil
1149658
42
ankal
1091778
20
asilp
1096692
43
nkali
1217885
21
silpe
1267021
44
kalim
1178959
22
ilper
1170324
45
alima
1089687
23
lpers
1203355
46
limat
1196986
Table 9. Rolling Hash Result Text B
No
Term
Hash
No
Term
Hash
1
hasil
1149658
18
tasek
1269617
2
asilb
1096678
19
aseke
1096271
3
silbe
1266881
20
sekeb
1262808
4
ilber
1168924
21
ekebe
1128181
5
lberu
1189257
22
keber
1181924
6
berup
1093682
23
ebara
1119337
7
erupa
1136917
24
berad
1093470
8
rupap
1269282
25
erada
1134797
9
upape
1292921
26
radaa
1248067
10
paper
1229324
27
adaan
1080780
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11
apers
1093355
28
daank
1107907
12
perse
1233651
29
aanka
1099167
13
ersen
1136620
30
ankal
1091778
14
rsent
1266316
31
nkali
1217885
15
senta
1263257
32
kalim
1178959
16
entas
1132685
33
alima
1089687
17
ntase
1226951
34
limat
1196986
It can be seen that the string matching results between documents Text A and Text B contain the
same number of hashes of 24.
c) Calculating Similarity
The hash count of the test document ( ) = 34
Same hash count ( ) = 24
So, the calculation result of the similarity between the test document and the training document is
70.58%.
d) Same Sentence Matching Process
This process takes data from documents Text A and Text B by cutting paragraphs into sentences.
Then match the sentences. The results of the process of displaying the same sentences in matching
two documents can be seen in table 10 below.
Table 10. Similarity Matching Results
Document
Name
Document Contents
Doc Text
A
Algoritma yang digunakan adalah Rabin-
Karp. Hasil presentase dan keberadaan
kalimat.
Doc Text B
Hasil persentase dan keberadaan kalimat.
F. Implementation
a) Input Dataset
The first step in the plagiarism detection system is to enter the dataset that will be used to check
plagiarism in student assignments, an example dataset is as shown in Figure 3 below.
Figure 5 Example Dataset
b) Determining K-Gram Value
After entering the data set, the second step is to determine the k-gram values and prime numbers, as
shown in Figure 4 below.
Figure 6 K-Gram and Prime Number Settings
c) Student Assignment Data Input
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Then in the third step, enter the student assignment data which will be checked for the level of
similarity, as shown in Figure 5 below.
Figure 7 Student Assignment Data Input
d) Similarity Result
The following are the results of the similarity level of the plagiarism detection process using the
Rabin Karp Algorithm, as seen in Figure 6.
Figure 8 Similarity Result
4. DISCUSSION
The results of the similarity of student assignments from 10 data using k-gram value = 4 can be
seen in table 11 below:
Table 11. Similarity Result K-Gram = 4
Document
Name
K-Gram
Prime
Similarity
Result
Doc. Text 1
4
7
38%
Doc. Text 2
4
7
58%
Doc. Text 3
4
7
49%
Doc. Text 4
4
7
39%
Doc. Text 5
4
7
25%
Doc. Text 6
4
7
20%
Doc. Text 7
4
7
27%
Doc. Text 8
4
7
76%
Doc. Text 9
4
7
56%
Doc. Text 10
4
7
31%
It can be seen from the similarity results above that the lowest similarity value is in text document
6, which is 20% and the highest similarity value is in text document 8, which is 76%.
Furthermore, the results of the similarity of student assignments from 10 data using k-gram value
= 5, can be seen in table 12 below.
Tabel 12. Similarity Results K-Gram = 5
Document
Name
K-Gram
Prima
Similarity
Result
Doc. Text 1
5
7
28%
Doc. Text 2
5
7
39%
Doc. Text 3
5
7
37%
Doc. Text 4
5
7
29%
Doc. Text 5
5
7
19%
Doc. Text 6
5
7
15%
Doc. Text 7
5
7
21%
Doc. Text 8
5
7
72%
Doc. Text 9
5
7
42%
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Doc. Text 10
5
7
24%
It can be seen from the similarity results above that the lowest similarity value is in text document
6, which is 15% and the highest similarity value is in text document 8, which is 72%.
5. CONCLUSIONS
The effective implementation of the Rabin-Karp algorithm with the Synonym Recognition
approach in detecting plagiarism in student assignments at Universitas Teknologi Yogyakarta.
Through the application of this method, plagiarism checking on student documents can be done
quickly and accurately, which shows a significant improvement compared to traditional manual
checking methods. Key findings include the ability of the system to determine similarity in student
assignments with varying degrees of similarity efficiently. For example, the use of a k-gram value
of 4 produces similarity levels ranging from 20% to 76%, while a k-gram value of 5 produces
similarity levels from 15% to 72%. Therefore, it can be concluded that a smaller k-gram value
will produce better similarity value accuracy compared to a larger K-gram value. These results
underline the importance of the choice of k-gram value in influencing the accuracy of plagiarism
detection. Future improvements may include refining the Synonym Recognition feature to capture
a wider range of synonymous relationships and exploring the use of more sophisticated algorithms
to further reduce processing time and improve system scalability. In conclusion, this study not
only reaffirms the capability of the Rabin-Karp algorithm in detecting text similarity, but also
paves the way for its further improvement and application in educational settings to enforce
academic standards and prevent unethical practices such as plagiarism.
ACKNOWLEDGMENT
Thank you to the Directorate of Research, Technology and Community Service, Directorate
General of Higher Education, Research and Technology, Ministry of Education, Culture,
Research and Technology for funding the implementation of this research through the Research
Grant for the “Penelitian Dosen Pemula” Scheme for Fiscal Year 2023.
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