EPS2WAY: AN EFFICIENT PAIRWISE TEST DATA GENERATION STRATEGY

8/12/2019 EPS2WAY: AN EFFICIENT PAIRWISE TEST DATA GENERATION STRATEGY

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EPS2Way: An Efficient Pairwise Test Data Generation Strategy

K.F. Rabbi1, Sabira Khatun

1, Che Yahaya Yaakub

1and M. F. J. Klaib

2

1Faculty of Computer Systems & Software Engineering, Universiti Malaysia Pahang,

Pahang, Malaysia.2Faculty of Science and Information Technology, Jadara University, Jordan.

Corresponding E-mail:[email protected]

ABSTRACT

Testing is a very important task to developerror free software. The funds and release

time of a software product is limited, thus, itis nearly hard to execute the exhaustive test

i.e., to test all combinations of input data.Pairwise (2 way) test data generationstrategy maintains higher reduction of

exhaustive numbers at the same time, it isalso a low cost solution to test any software

product thoroughly. Usually, in software,faults are caused by unusual combination ofinput data. Hence, optimization in terms ofnumber of generated test-cases andexecution time is in demand. This paper

proposes an efficient pairwise searchapproach (EPS2Way) of input values for

optimum test data generation. This approachsearches the most coverable pairs by pairing

parameters and adopts one-test-at-a-time to

construct final test suites. EPS2Way iseffective in terms of number of generated

test cases and execution time compared toother existing strategies.

KEYWORDS

Combinatorial interaction, Software testing,Pairwise testing, Pairwise search approach,Test case generation.

1 INTRODUCTION

In the process of software engineering,

software testing and debugging is still

very labor-intensive and expensive [1].

Approximately 50% of project money

goes under software testing. Thus, the

focus is to find an automatic and cost-effective software testing and debugging

strategy to ensure high quality software

release [2]. Nowadays research andinvestigations on software testing

focuses on test coverage criterion design,

test-case generation problem, test oracleproblem, regression testing problem and

fault localization problem [1]. Among

these problems test-case generation

problem is a valuable one and come

forth in producing error free software[1]. To solve this problem, Pairwise

strategy (i.e. two-way interaction) hasbeen renowned as an effective test case

reduction strategy and able to detect

from 60 to 80 percent of the faults [3, 4].

For example, the proofing tab under

option dialog in Microsoft excel

(Figure 1), there are 6 possible

configurations needed to be tested. Eachconfiguration takes two values (checked

or unchecked) and on top of that the

French modes takes 3 possible valuesand Dictionary language takes 54

possible values. So to test this proofing

tab exhaustively, the number of testcases need to be executed is 2

6x 54 x 3

i.e. 10,368. Assuming each test case may

International Journal on New Computer Architectures and Their Applications (IJNCAA) 1(4): 1099-1109

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consume 4 minutes to execute; results

around 28 days to complete the

exhaustive test of this proofing tab [3,4].

Figure 1: Microsoft Excel Proofing Option

Similarly, for a hardware product whichhas 30 on/off switches, to test allpossible combination may need 230 =1,073,741,824 test cases, and consume10,214 years by considering 5 minutesduration for each single test case [4].Nowadays, research work incombinatorial strategy aims to generatesmallest amount of performable test suits

[5]. The solution of this challenge isknown as non-deterministic polynomial-time hard (NP-hard) [6]. So far manyapproaches have been proposed to solvethis problem for last few decades [5-8,10-14] but yet optimum one is indemand. This paper introduces anefficient pairwise search approach fortest data generation. This strategycombines two parameters collectively (apair) and searches for another parameter

combination to generate test suits fromthe parameter pairs in terms of optimumsize and time consumption.

The paper is organized as follows. Therelated work detail is presented inSection 2. Followed by the proposedEPS2Way strategy, the developed

EPS2Way prototype tool, the empiricalresults with its efficiency and

comparison, and finally the conclusion.

2 RELATED WORKS

Observed facts show that lack of testingfor both functional and nonfunctional isone of the major sources of software andsystems bug/errors [7, 8]. NationalInstitute of Standard and Technology(NIST) estimated that the cost ofsoftware failure to the US economy at $6

X 1010

, which was the 0.6 percent ofGDP [9, 10]. Around one-third of thiscost can be reduced by improvingsoftware testing structure. Hence,automatic testing is one of the criticalconcerns [11]. Through systemautomation, software developmentprocess may become more practical andscalable. However, the automatedgeneration and reduction of test cases arechallenging [12]. The underlying

problem is known as NP-hard thusresearchers have focused on thetechniques that search to find nearoptimal test sets in a reasonable time[13, 14].

Pairwise testing is a significant approachfor software testing as it providesefficient error detection at a very lowcost. It shows a good balance by linkingthe magnitude and effectiveness of

combinations. It requires, combinationof any two parameter values has to becovered by at least one test case [14, 15].From the point of pairwise there aresome pre-defined rules to calculate thetest cases directly from the mathematicalfunctions, which are known as algebraicstrategy [4]. On the other side,



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computational approaches are based on

the calculation of coverage of generated

pairs, followed by an iterative or randomsearch technique to create test cases.

IRPS algorithm [6] uses the

computational approach. It is adeterministic strategy which generates

all pairs and then stores it to the linked

list. Finally it searches the entire list,

select best list and empties the list. Whenall list become empty, the collection of

best list is determined as the final test

suite.

The Automatic Efficient Test Generator

(AETG) [16] and its deviation mAETG[6] generate pairwise test data using

computational approach. This approach

uses the Greedy technique to build test

cases based on covering as much aspossible uncovered pairs. AETG uses a

random search algorithm [17]. Genetic

Algorithm (GA) and Ant Colony

Algorithm (ACA) are the variants ofAETG [18, 19]. Genetic algorithm [18]

creates an initial population of

individuals (test cases) and then thefitness of those individuals is calculated.

Then it starts discarding the unfit

individuals by the individual selectionmethods. The genetic operators such as

crossover and mutation are applied on

the selected individuals and this

continues until a set of best individuals

found. Ant Colony Algorithm [18]candidate solution is associated with the

start and end points. When an antchooses one edge among the different

edges, it would choose the edge with a

large amount of pheromone which givesthe better result with the higher

probability.

The In-Parameter-Order (IPO) [12]

strategy starts with an empty test set andadds one test at a time for pairwise

testing. It creates the test cases by

combination of the first two parameters,

then add third and calculate how manypair is been covered and so on until all

the values of each parameter is checked.

This approach is deterministic approach.

AllPairs [20] algorithm can generate test

suites covering all pairwise interactions

within a reasonable time. The strategyseems to be deterministic strategies since

the same test suite are generated every

run time.

The Simulated Annealing (SA) [21]

algorithm is also a deterministic strategy

with the same generated test suite forevery run time.

Generalization of Two Way test data

(G2Way) [22] is one of the excellenttools based on computational and

deterministic strategy. It is based on

backtracking algorithm and usescustomized markup language to describe

base data. The G2Way backtracking

algorithm tries to combine generatedpairs so that it covers highest pairs.

Finally after covering all the pairs, the

test case treats as a final test suite.

One of the recent algorithms is effectiverandom search based pairwise test data

generation algorithm named R2Way tooptimize the number of test cases [23].

R2Way takes a random number from 0

to maximum possible exhaustive

number of test cases and creates a testcase based on some binary calculations.



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Java program was used to test the

performance of R2Way. It is able to

support both uniform and non-uniformvalues effectively with near optimum

performance in terms of number of

generated test cases and time

consumption.

3 PROPOSED EPS2Way

STRATEGY

The proposed efficient pairwise test data

generation strategy works in three (3)steps as follows:

I. Firstly, it generates pairparameters and their values.

II. Then, the value of one pair iscombined with another pair bycalculating the highest possible

coverable pairs. In this way it

constructs a test case and adds to

the final test suit.

III. Finally, it constructs the testcases from uncovered pairsthrough an adjustment algorithm.

To make this easily understandable, ascenario is presented in terms of

example as follows:

3.1 Pair Generation

EPS2Way strategy/algorithm first takes

the parameters and corresponding valuesto make the 2 way combinations. The

combinations stored into the memory.

As an example, suppose, there are six (6)parameters A, B, C, D, E, and F, each

with 2 values as shown in Table 1.

Table 1: Example parameters with values

Parameters A B C D E F

Valuesa1 b1 c1 d1 e1 f1

a2 b2 c2 d2 e2 f2

EPS2Way first generates header pairparameters which are AB, CD, EF and

then calculates the possible values of all

the pairs as shown in Table 2. In this

example, each of AB, CD and EF paircontains 2 x 2 = 4 pair of values and

stored in the memory respectively. The

expression can be expressed as follows:

NP = [V1 * V2] (1)

Where, NP = Number of Pairs, V1 =Value of Parameter 1, V2 = Value of

Parameter 2.

Table 2: Generated header pair parameters and

all possible values

Pair

ParametersAB CD

EF

Generated

all possibletest cases

[a1, b1] [c1, d1] [e1, f1]

[a1, b2] [c1, d2] [e1, f2]

[a2, b1] [c2, d1] [e2, f1]

[a2, b2] [c2, d2] [e2, f2]

3.2 Test Case Generation

At the beginning, each AB pair tries tocombine with one of the CD pairs. If

combined pairs give highest or

maximum coverage, then it tries tocombine with the values of EF pairs. Sothe test case generation approach is in

greedy mode and constructs test cases

one at a time.

In Table 2, EPS2Way tries to combine

[a1, b1] pair with four possible values of



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CD which are: [c1, d1], [c1, d2], [c2,

d1], [c2, d2]. The first combined AB-CD

pair with the highest coverage looks forthe available pairs again from EF header

pair among: [e1, f1], [e1, f2], [e2, f1],

[e2, f2] as shown in Table 3. Finally, the

combined AB-CD-EF pair with highestcoverage is then added to the final test

suit.

Table 3 shows, one of AB pairs [a1, b1]searches for the best pairs among the

available pairs of CD and its output

should be only one, which is [a1, b1, c1,d1] as the first uncovered final test-case

with full coverage. Again, generated pair

[a1, b1, c1, d1] search for the availablepairs of EF and the generated output is

[a1, b1, c1, d1, e1, f1]. Same procedure

is followed by other AB pair parameters

to generate other final test cases. Thehighest coverable pairs are stored in the

final test set.

Table 3: Example of pair search and final test

case generation

Initi

al

pairs

Avai

lable

pairs

Best

uncover

ed pairs

Available

Pairs

Bestuncove

red

pairs

[a1,b1]

[c1,

d1]

[a1, b1,c1, d1]

[e1,

f1]

[a1, b1,

c1, d1,

e1, f1]

[c1,

d2]

[e1,

f2]

[c2,

d1]

[e2,

f1]

[c2,

d2]

[e2,

f2]

[a1,b2]

[c1,

d1][a1, b2,c1, d2]

[e1,

f1] [a1, b2,

c1, d2,

e1, f2]

[c1,

d2]

[e1,

f2]

[c2, [e2,

d1] f1]

[c2,

d2]

[e2,

f2]

[a2,

b1]

[c1,

d1]

[a2, b1,

c2, d1]

[e1,

f1]

[a2, b1,

c2, d1,e2, f1]

[c1,

d2]

[e1,

f2]

[c2,

d1]

[e2,

f1]

[c2,

d2]

[e2,

f2]

[a2,

b2]

[c1,

d1]

[a2, b2,

c2, d2]

[e1,

f1]

[a2, b2,

c2, d2,e2, f2]

[c1,d2]

[e1,f2]

[c2,d1]

[e2,f1]

[c2,d2]

[e2,f2]

3.3 Pair Covering & Test Case

Adjustment

At this stage, the adjustment algorithm

performs an exhaustive search for allpossible uncovered pairs and tries to

adjust all uncovered pairs. When an

adjustment is done it is added to the finaltest set. Figure 2 shows the test case

generation adjustment algorithm and

Figure 3 shows the flowchart of the

strategy.

Adjustment Algorithm to Generate Test Suits ()Begin

Let PP= {} represents the set of

all possible pairs

Let PS= {} represents the pairs

where all the PSstores in PP

Let PB= {} represents the best

pairs set which cover highest

pairs

Let PF= {} as empty set



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represents the Final test suits

Let CBas number = 0 represents

the best covering number

Let CCas number = 0 represents

the current covering number

For each PSas P1in PP

For each next PSas P2in PP

Add P1with P2and

put in P

CC= Get coverage

pair number of P

IF CBis less or

equal to CC

Put CCinto CB

Put P2into PB

End IF

End ForAdd P1with PBand store to PF

End For

End

Figure 2: EPS2Way pseudo code for test case

generation from uncovered pairs.

Figure 3: Flow chart of the EPS2way strategy

4 EPS2Way PROTOTYPE TOOL

A prototype tool is developed withsimple GUI to investigate EPS2Wayperformance in terms of the number of

generated test cases & execution time.

The tool accepts both uniform and non-uniform values and shows the required

number of test cases. Figures 4 to 7

shows the screen shot of PS2Way

prototype tool.

Figure 4: Generator Window

Figure 5: Same parameter & value window



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Figure 6: Different Parameter and Value window

Figure 7: Generated Test cases

Figure 4 shows the initial windows

containing two buttons. The value of the

T-way field is 2 (un-editable) as thecurrent algorithm supports pairwise (2-

way) testing. The buttons Same Params

& Values and Differ Params and

Values are for uniform and non-uniform input values respectively.

Clicking on the Same Params &

Values opens input popup windows

shown in Figure 5. The Number ofParameter field takes the required

number of parameters as input and the

Number of values for each parametertakes input values for each parameter.

Figure 6 shows the popup window which

can take non uniform values. Here, thevalues can be added on the list box.

After clicking on the ok button the

number of test cases and the test case

suits are produced as shown in Figure 7.

5 EMPIRICAL RESULTS

To evaluate the efficiency of proposedEPS2Way, we have considered six (6)

different system configurations. Among

those the first three (3) are non-uniformparameterized values and the rest are

uniform as follows:

S1: 3 parameters with 3, 2 and 3 values.

S2: 3 parameters with 2, 1 and 3 values.

S3: 5 parameters with 3, 2, 1, 2 and 2

values.S4: 3 2-valued parameters

S5: 3 3-valued parameters

S6: 4 3-valued parameters.

The consideration of the parameters and

assumptions are according to some of



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the related existing algorithms that

support pairwise testing to compare our

results with those.

Table 4 shows the comparison of

generated test suite size by proposed

EPS2Way with others. The shadowed

cells indicate the best performance in

term of generated test case size. NA

indicates that data are not available. Itshows that proposed EPS2Way produces

the lowest number of test cases for each

configuration by showing its superiority.

Table 4: Comparison based on the generated test size

Sys AETG[16]

IPO[12]

TConfig[24]

Jenny[25]

TVG[26]

ALLPairs

[20]

G2Way[22]

R2Way[23]

ProposedEPS2Way

S1 NA 9 9 9 9 9 9 9 9

S2 NA 6 6 6 6 6 6 6 6

S3 NA 7 8 8 8 9 7 7 7S4 NA 4 4 5 6 4 4 4 4

S5 NA 10 9 9 10 10 10 10 9

S6 9 10 9 13 12 10 10 9 9

For a fair comparison of execution time

(i.e., complexity) among related test

strategies, either computing environment

should be same or need the source code(usually not available most of the cases).

All Pairs tool [20] is free to download

and can be executed using any platform.Also R2Way [23] is our proposedstrategy and have source code. Hence we

have compared the execution time of

EPS2Way with All Pairs and R2Wayusing the same platform as follows:

Intel P IV 3 GHz, 1 GB RAM, Java

programming language, and WindowsXP OS. For some of the other existing

strategies, the platform instances and

data are taken from References [22]. We

have managed to execute our EPS2Waystrategy using the following platform for

respective comparison with:

AETG [16], AETGm [6], SA [21]:Intel P IV 1.8 GHz, C++

programming language, Linux

Operating System.

IPO [12]: Intel P II 450 MHz, Javaprogramming language, Windows 98operating system.

GA [18], ACA [19]: Intel P IV 2.26GHz, C programming language,

Windows XP operating system.

G2Way [22]: Intel P IV 1.6 GHz, 1GB RAM, C++ programming

language, Windows XP operating

system.



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To compare the complexity, we have

assumed the following five (5)

configurations.

T1: 3 3-valued parameters,

T2: 4 3-valued parameters,

T3: 13 3-valued parameters,T4: 10 5-valued parameters,

T5: 1 5-valued parameters, 8 3-valued

parameters and 2 2-valued parameters.

Table 5 shows that in terms of executiontime, EPS2Way gives the better result

for first three system configurations T1,

T2 and T3. For the other two systems T4and T5 the execution time is also very

close to the lowest values with negligible

difference. Hence EPS2Wayoutperforms other existing strategies.

Table 5: Comparison Based on Execution Time (in seconds)

SysAETG[16]

AETGm[6]

IPO[12]

SA[21]

GA[18]

ACA[19]

ALLPairs[20]

G2Way[22]

R2Way[23]

ProposedEPS2Way

T1 NA NA NA NA NA NA 0.08 0.047 0.07 0.027

T2 NA NA NA NA NA NA 0.23 0.062 0.16 0.062

T3 NA NA NA NA NA NA 0.45 0.25 1.44 0.2

T4 NA NA 0.05 NA NA NA 1.02 0.687 20.3 0.06

T5 NA 58 NA 214 22 31 0.35 0.33 5 0.43

6 CONCLUSIONS

In this paper we have proposed pair

parameter based search algorithm forpairwise (2-way) test case generation.

The correctness of the proposed strategyis apparent. The algorithm is efficient interms of execution time and able to

generate highly reduced test suites to

fulfill the current demand by softwaredevelopment companies. The proposed

algorithms could be further extended to

support higher t-way interaction testingwhich is under investigation in

University Malaysia Pahang.

7 ACKNOWLEDGEMENTS

The authors would like to thanksUniversiti Malaysia Pahang for financial

support under University Research

Grants (RDU 100361) to finalize thiswork.



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EPS2WAY: AN EFFICIENT PAIRWISE TEST DATA GENERATION STRATEGY