SUGISAKAMASANORI

Journal of Advances in Artificial Life Robotics
Vol. 1(4); March (2021), pp. 187–192
ON LINE ISSN 2435-8061; ISSN-L 2435-8061
https://alife-robotics.org/jallr.html

Research Article

Identification of Redundant Test Cases by Using Similarity
Measurement Method for Test Suite Evaluation
Mochamad Chandra Saputra1, Tetsuro Katayama1, Yoshihiro Kita2, Hisaaki Yamaba1, Kentaro Aburada1, Naonobu
Okazaki1

Interdisciplinary Graduate School of Agriculture and Engineering, University of Miyazaki, 1-1 Gakuen-Kibanadai Nishi, Miyazaki, 889-2192 Japan
Department of Information Security, Faculty of Information Systems, Siebold Campus, University of Nagasaki, 1-1-1 Manabino, Nagayo-cho, NishiSonogi-gun, Nagasaki, 851-2195 Japan
1
2

ARTICLE INFO
Article History
Received 10 November 2019
Accepted 13 November 2020
Keywords
Euclidean distance
Redundant test cases
Test suite evaluation

ABSTRACT

Evaluating the test suite that contains redundant test cases is necessary to ensure the efficiency of
the testing and reducing the cost of testing. The principle of redundant test cases on this research
is any test cases on a similar path executed with a similar high value of normalized Euclidean
distance. The first, the similarity calculated between the test cases and path coverage uses
Euclidean distance. The value of the Euclidean distance on the test case with the lowest value of
distance indicating highly similar and possibly executing similar lines of code. The normalized
Euclidean distance is using to normalize the value from Euclidean distance result. The experimentuses two java programs. Each redundancy score is 0.37 and 0.67, respectively. It means 37% and
67% of the test cases should be avoided because there are inefficiency test cases on the test suite.
The research confirms redundant test cases can be identified by Euclidean distance andnormalized Euclidean distance to evaluate the test suite.

© 2022 The Author. Published by Sugisaka Masanori at ALife Robotics Corporation Ltd.
This is an open access article distributed under the CC BY-NC 4.0 license(http://creativecommons.org/licenses/by-nc/4.0/).

testing is to test every method or class by applying the test
cases on the unit testing. Using unit testing which applied
test cases helps to find the code coverage information as
one of the valuable information in the white-box testing[1].
The oldest and one of the most popular approaches in the
structural testing technique is basis path testing. Basis pathtesting is based on the control structure of a program. Basispath testing steps are drawing flow graph then finding all
possible paths (independent path) covered and the last, due
to the testing all those paths are must be executed [2]. This
research uses the basis path testing approach especially togenerate the flow graph for considering the code coverage.
IEEE has the definition of the test case is a set of test inputs,
execution conditions, and expected results developed for aparticular objective, such as to exercise a particular
program path or to verify compliance with a specific

1. Introduction
The software contains the series of instruction which
execute several tasks to achieve the objective. The several
representations of the instruction on the view of thesoftware developer are the action to objects able to workon several tasks and applied to the programming languageas the method or class. The testing is important forassessing the method or class run as well as required.
Testing helps to increase the source code stability and toensure that the release version of the software is stable andno impacted user by the mistake on code development.
One of testing technique is structural testing or called
white box testing. The white-box testing uses the internal
structure of the software under test. The white-box testing
is to analyze the source code which concerns the internal
structure of source code. The basic principle on white-box

Corresponding author’s E-mail: chandra@earth.cs.miyazaki-u.ac.jp, kat@cs.miyazaki-u.ac.jp, kita@sun.ac.jp, yamaba@cs.miyazaki-u.ac.jp,
aburada@cs.miyazaki-u.ac.jp, oka@cs.miyazaki-u.ac.jp187requirement [3]. The test case is applied to unit testing
considers individual components are tested to ensure they
operate correctly [4]. The programmer uses the unit testing
to test individual program units, such as procedures,functions, methods, or classes.
Evaluating the test suite is necessary to ensure theefficiency of the testing and reducing the cost of testing.
Test cases on the test suite are a strong element to evaluate
to increase efficiency [5]. Reducing the cost of testing is
associated with a test process that includes the cost ofdesigning, maintaining, and executing test cases [6]. Test
suite may contain redundant, ambiguous, vague, and unfit
test cases [7]. Therefore, evaluate the test suite is criticalto find the redundant test cases that should be avoided tohave better efficiency and the cost of testing.
Testing a software system contains a various set of test
cases which capable of examining several parts of thesource code. The test cases are redundant if the test case
executing similar lines of code, the path of source code, or
the test case already covering by another at the current
testing. This research tries to identify the redundant test
case on the test suite by using the test case similarity basedon code coverage information and then calculates theredundancy score for the test suite to evaluate it.
The Euclidean distance is used to calculate many cases ofsimilarity. The distance similarity between the test caseswith the same length can be calculated by summing theordered point-to-point distance [8]. This research iscomparing the lines of code executed by the test case andthe lines must be executed by the basis path testing
approach on calculating the similarity. The code coverageneeds to check to confirm that each line of code executedon the testing process [9].

Figure 1. The concept of redundant test cases

by using the percentage approach. The percentage
calculation is conducting by dividing the number of
redundant test cases on the test suite with the number oftest cases. The degree of redundancy represents several
redundant test cases in the test suite and the range the scoreis from 0 to 1. The formula such as follow.
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 =∑𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐∑𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐(1)

where redundant test cases are the number of test cases thathave the highest normalized Euclidean distance result andsimilar to the other test cases at a similar path that should
be avoiding. The redundancy score calculated by dividing
the number of redundant test cases with the number of test
cases on the test suite.
3. Similarity
The similarity measurement is a process to quantified thesimilarity between two objects. Commonly, thequantification of similarity is using the distancecalculation algorithm. One of the distance calculation
algorithms is Euclidean distance. This paper uses the
Euclidean distance to measure the similarity between test
case coverage and path coverage [11]. The coverage is thenumber of lines of code executed when the test cases areused in testing. The similarity between the test case andpath coverage is measured based on the coverage line. The
principle of similar in this research is when the result from
Euclidean distance between the path and test case coverage
has the lowest value of similarity. The lowest Euclidean
distance value means that the test cases have highly similar.

2. The Principle of Redundant on Test Case
The consequence of redundant test cases is many test caseswith not suitable to use. The redundancy will increase thetesting effort, cost, and time of testing [10]. The test casesin the test suite may examine overlapping or similar code
coverage. Figure 1 uses to illustrate the concept of
redundancy. The example, there are test case A, test caseB, and path-1. The redundant test cases exist when either
two test cases serve the same purpose related to the same
path. The principle of redundant test cases in this researchis in case some test cases have a similar path with asimilarly high value of normalized Euclidean distance toother test cases.
The redundancy score is needed to know the degree of test
suite redundancy. The redundant score is calculated

Similar test cases in the test suite will through the same
path. Using the Euclidean distance, the similarity between
the test case and path coverage is described as follows. Let
be two object x as path and y test case vectors of the length188

a similar path with a similarly high value of normalized
Euclidean distance to other test cases.

of index n, and 𝑥𝑥𝑖𝑖 and 𝑦𝑦𝑖𝑖 the 𝑖𝑖 th index of the line of code
executed from x and y, respectively. This condition
presents distance functions used in Euclidean as follows.
𝑑𝑑(𝑥𝑥, 𝑦𝑦) = �∑𝑛𝑛𝑖𝑖=1(𝑥𝑥𝑖𝑖 − 𝑦𝑦𝑖𝑖 )2(2)

Table 1. The result of the test case executed on Student Grades

The result from the Euclidean distance shows how similar
the test case and path. The Euclidean distance result is not
scalable. Because of this condition, the result from
Euclidean distance is needed to normalize for morescalable on similarity. Normalizing the Euclidean distanceresult is to change the values to a common scale without
distorting differences in the ranges of values. The range ofvalue between 0 to 1. The normalized Euclidean distanceis calculated as follows.
Normalized Euclidean distance =1

1+𝑑𝑑(𝑥𝑥,𝑦𝑦)

Test case
Test case coverage
name
TC-1
0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0;
TC-2
0,0,0,0,0,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0;
TC-3
0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0;
TC-4
0,0,0,0,0,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0;
TC-5
0,0,0,0,0,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0;
TC-6
0,0,0,0,0,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0;
TC-7
0,0,0,0,0,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0;
TC-8
0,0,0,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0;
Table 2. The result of the test case executed on Quadratic
Function(3)

Test case
name
TC-1
TC-2
TC-3
TC-4
TC-5
TC-6
TC-7
TC-8
TC-9

Where 𝑑𝑑(𝑥𝑥, 𝑦𝑦) is the result of Euclidean distance. The
highest normalized Euclidean distance result means thattwo objects have highly similar.
4. Methodology
The objective of this research is to evaluate the test suiteby identified the redundant test cases. Student grades andquadratic function, which are java programs with each test
suite, are used in this research. The test cases and flow
graph are generated directly from the java source codes.

Test case coverage
0,0,0,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0;
0,0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,1,0,0;
0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0;
0,0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,1,0,0;
0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0;
0,0,0,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0;
0,0,0,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0;
0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0;
0,0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,1,0,0;

D. Calculate The Redundancy Score

This research collects information from the test case
executed as the lines of code executed by the test case. The
values lines of code are 1 for the executed lines by the test
case and 0 for line not executed. The information the lines
of code executed for the path coverage also observe basedon the independent path.

The number of redundant test cases on the test suite is
identified by using the normalized Euclidean distanceresult, and then the redundant score is calculated byformula (1). The test cases are redundant when the test
cases have similar highest value from normalized
Euclidean distance result at a similar path. The number of
redundant test cases refers to the number of avoiding test
cases on the test suite. The redundancy score represents thedegree of an inefficiency test case on the test suite.

A. Similarity Calculation
The Euclidean distance formula (2) calculation on thisresearch uses lines executed from path and test case. The
result from this calculation is distance value indicating thedegree of similarity.

5. The Experiment
The experiment has two java source codes: student gradesand quadratic function and also test suite for them. The test
suite for student grades consists of 8 test cases and 9 test
cases for a quadratic function. The information fromexecuting the test cases uses in the experiment is lines
executed as shown in Table 1 and Table 2. The 0 value on
test case coverage information means that the line of code
is not executed and 1 is executed.
The experiment generated the flow graph based on the java
source code as shown in Figure 2 and 3. Based on the flow
graph that has been drawing then calculated the value of
cyclomatic complexity related to the number of

B. Normalized Euclidean Distance
The normalized Euclidean distance on formula (3) uses theresult of Euclidean distance to change the Euclidean
distance value more scalable for similarity. The value 1means that the path and test case is similar. The lowest
value means that the similarity is low.
C. Identify The Redundant Test Cases
The identification of redundant test cases in this researchuses the result from the normalized Euclidean distance.
The redundant test cases are when several test cases have189

executed and 1 is executed. The information for the lines
of code executed that refers to the path coverage gain by
Table 4. The result from Euclidean distance for student grades

Table 3. Path coverage
Java
SourceCodeStudent
GradesQuadratic
Function

Path

Path coverage

P1
P2
P3
P4
P5
P1
P2
P3

0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0;
0,0,0,0,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0;
0,0,0,0,0,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0;
0,0,0,0,0,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,1,0;
0,0,0,0,0,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0;
0,0,0,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0;
0,0,0,0,1,1,1,1,1,1,1,0,0,0,1,1,1,1,0,1,0,0;
0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0;Path 1
Path 2Path 3
Path 4
Path 5

TC-1
0.00
1.73
2.00
2.24
2.45

TC-2
2.45
2.24
2.00
1.73
0.00

TC-3
0.00
1.73
2.00
2.24
2.45

TC-4
2.00
1.73
0.00
1.73
2.00

TC-5
2.24
2.00
1.73
0.00
1.73

TC-6
2.45
2.24
2.00
1.73
0.00

TC-7
2.45
2.24
2.00
1.73
0.00

TC-8
1.73
0.00
1.73
2.00
2.24

Table 5. The result from Euclidean distance for quadratic
function.
TC-1 TC-2 TC-3 TC-4 TC-5 TC-6 TC-7 TC-8 TC-9
Path-1 0.00 2.45 3.00 2.45 3.00 0.00 0.00 3.00 2.45
Path-2 2.45 0.00 2.65 0.00 2.65 2.45 2.45 2.65 0.00
Path-3 3.00 2.65 0.00 2.65 0.00 3.00 3.00 0.00 2.65
Table 6. The result from normalized Euclidean distance forstudent grades
TC-1

TC-2

TC-3

TC-4

TC-5

TC-6

TC-7

TC-8

Path 1

1.00

0.29

1.00

0.33

0.31

0.29

0.29

0.37

Path 2

0.37

0.31

0.37

0.37

0.33

0.31

0.31

1.00

Path 3

0.33

0.33

0.33

1.00

0.37

0.33

0.33

0.37

Path 4

0.31

0.37

0.31

0.37

1.00

0.37

0.37

0.33

Path 5

0.29

1.00

0.29

0.33

0.37

1.00

1.00

0.31

Table 7. The result from normalized Euclidean distance for thequadratic function
TC-1 TC-2 TC-3 TC-4 TC-5 TC-6 TC-7 TC-8 TC-9

Figure 2. Flow graph of the Student Grades

Path-1

1.00

0.29

0.25

0.29

0.25

1.00

1.00

0.25

0.29

Path-2

0.29

1.00

0.27

1.00

0.27

0.29

0.29

0.27

1.00

Path-3

0.25

0.27

1.00

0.27

1.00

0.25

0.25

1.00

0.27

observing every path and java source code. The next stepis calculating the similarity by using Euclidean distance.
The result calculation by using Euclidean distance show inTable 4 and Table 5. The result from Euclidean distance isused to calculate the normalized Euclidean distance. The
normalized Euclidean distance allows the value of
Euclidean distance scalable.
The result of normalized Euclidean distance as shown on
Table 6 and 7 uses to identify the redundant test case. The
identification of redundant test cases is when the value
from normalized Euclidean distance on several test cases
has a similar path with a similarly high value to other test
cases. The result of redundant test cases shown in Table 8.
The number of redundant test cases is used to calculate theredundancy score by formula (1).

Figure 3. Flow graph of the Quadratic Function

independent path. The principle on basis path testing is that
all independent paths are exercised to ensure that allstatements in a method have been executed at least once.
One of the famous software quality metrics is cyclomatic
complexity which used to find the logical complexity ofsoftware by considering the flow graph on pseudocode orsource code [2]. The result of cyclomatic complexity fromstudent grades with 4 predicate nodes is 5 and for quadratic
function with 2 predicate node is 3. Based on this result the
number of the independent path for student grades is 5 andfor the quadratic function is 3.
Based on the flow graph, the path coverage related to thesource code is as shown in Table 3, the 0 value on pathcoverage information means that the line of code is not

6. Result and Discussion
The result from Euclidean distance confirms that several
test cases on the student grades and quadratic function
have high similarity with path coverage. The lowest valueof Euclidean distance indicates that high similarity. The

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normalized Euclidean distance calculation. The
redundancy score for student grades is 0.37 and 0.67 forthe quadratic function. The redundancy score can represent
the percentage of redundancy. The meaning of thepercentage is there are 37% of the test case on the student
grades test suite is redundant and 67% on the quadratic
function that should be avoided because there are
inefficiency test cases on the test suite.
Future research is needed to consider other evaluation
methods of test suite, for example the similarity in fault
detection capability, reusability of test cases or test suite,and so on.
References

result of Euclidean distance needs to scalable for easy
investigation on the redundant test cases.
Table 8. The result of the test case redundancy based on thenormalized Euclidean distance.
Sudent Grades
Quadratic Function
Path-1 contains TC-1 and TC-3.
Path-1 contains TC-1,TC-6 and TC-7
Path-2 contains TC-8.
Path-2 contains TC-2, TC-4 and TC-9
Path-3 contains TC-4.
Path-3 contains TC-3, TC-5 and TC-8
Path-4 contains TC-5.
Path-5 contains TC-2, TC-6, and TC-7.

The redundant test case is investigated from normalized
Euclidean distance calculation on test cases and path.
When the result is 1, it means that highly similar. There areseveral test case which has a high value of normalized
Euclidean distance same with other test cases in the same
path. This condition is called redundant test cases. The
number of redundant test cases is shown in Table 8.
The redundant test cases on student grades found on path
1 and path 5. On quadratic function, there is a redundant
test case on path-1, path-2, and path-3. This research uses
an independent path in which one test case is required for
one path to guarantee the coverage of source codes. The
principle of software testing is to ensure one path executedat least once, so one test case adequate to test one path. By
using this principle, the redundant test case should be
avoided. The number of the redundant test case based on
the result normalized Euclidean distance which should
avoid on student grades is TC-3, TC-6, TC-7, and for thequadratic function is TC-4, TC-5, TC-6, TC-7, TC-8, TC9.
This research also calculates the redundancy score byusing the formula (1). The redundancy score for student
grades is 0.37 and 0.67 for the quadratic function. The
redundancy score can represent the percentage ofredundancy. The meaning of the percentage is there are
37% of the test case on the student grades test suite isredundant and 67% on the quadratic function that should
be avoided because there is an inefficiency test cases on
the test suite.

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7. Conclusion
This research confirms that the redundant test cases can be
identified by Euclidean distance and the normalized
Euclidean distance to evaluate the test suite. The Euclidean
distance is to measure the similarity between test casecoverage and path coverage. The normalization of the
Euclidean distance result is necessary for more scalable
value for test suite evaluation. The current research
identified the redundant test cases on the result from191

===============================

Dr. Kentaro Aburada
He received the B.S., M.S and Ph.D.
degrees in computer science andsystem engineering from the
University of Miyazaki, Japan, in
2003, 2005 and 2009, respectively.
He is currently an Associate
Professor with the Faculty ofEngineering,
UniversityofMiyazaki, Japan. His research interests include
computer network and security. He is a member of IPSJ
and IEICE.

Authors Introduction

Mr. Mochamad Chandra Saputra
He received the Master's Degreefrom the University of Miyazaki,
Japan, and Brawijaya University,
Indonesia on Double Degree
Program 0n 2014. From 2006 - 2014
also work in Brawijaya University
ICT Unit as System Analyst. Since
2015 has been a lecturer on the
Faculty of Computer Science, Brawijaya University.
Now continue the Doctoral Study at the University ofMiyazaki. The research interest includes software
testing, software quality, and software project
management.

Dr. Naonobu Okazaki
He received his B.S, M.S., and Ph.D. degrees inelectricalandcommunicationengineering from Tohoku University,
Japan, in 1986, 1988 and 1992,
respectively.
HejoinedtheInformation Technology Researchand Development Center, Mitsubishi
Electric Corporation in 1991. He iscurrently a Professor with the Facultyof Engineering, University ofMiyazaki since 2002. His research interests include
mobile network and network security. He is a memberof IPSJ, IEICE and IEEE.

Dr. Tetsuro Katayama
He received the Ph.D. degree inengineering from Kyushu University,
Fukuoka, Japan in 1996. From 1996
to 2000 he has been a Research
Associate at the Graduate School ofInformation Science, Nara Instituteof Science and Technology, Japan.
Since 2000 he has been an Associate
Professor at Faculty of Engineering, Miyazaki
University, Japan. He is currently a Professor with theFaculty of Engineering, University of Miyazaki, Japan.
His research interests include software testing andquality. He is a member of the IPSJ, IEICE, and JSSST
Dr. Yoshihiro Kita

authentication.

===============================He received a PhD degree in systems
engineering from the University ofMiyazaki, Japan, in 2011. He iscurrently an Associate Professor with
the Faculty of Information Systems,
University of Nagasaki, Japan. His
research interests include software
testingandbiometrics

Dr. Hisaaki Yamaba
He received the B.S. and M.S. degrees
in chemical engineering from theTokyo Institute of Technology, Japan,
in 1988 and 1990, respectively, and
the Ph D. degree in systems
engineering from the University ofMiyazaki, Japan, in 2011. He iscurrently an Assistant Professor with
the Faculty of Engineering, University of Miyazaki,
Japan. His research interests include network security
and user authentication. He is a member of SICE and
SCEJ.

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