model-based testing...model-based testing (dit848 / dat261) spring 2017 lecture 9 graph theory...
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![Page 1: Model-Based Testing...Model-Based Testing (DIT848 / DAT261) Spring 2017 Lecture 9 Graph Theory Techniques in MBT Gerardo Schneider Department of Computer Science and EngineeringEuler](https://reader035.vdocuments.net/reader035/viewer/2022081407/604e941511d0366f69715942/html5/thumbnails/1.jpg)
Model-Based Testing (DIT848 / DAT261)
Spring 2017 Lecture 9
Graph Theory Techniques in MBT
Gerardo Schneider Department of Computer Science and Engineering
Chalmers | University of Gothenburg 1
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Outline
� Graph Theory Techniques in Model-Based Testing,by,HarryRobinson
� Interac1veexercises
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Euler Graph
f A
C
B b
a
c
d
e
g IsitanEulerGraph?Answer:No,notpossibletotraversealltheedgeswithoutrepe11on(nodesAandBhaveanoddnumberoflinks)
Groups 2-5 persons: 5 min 3
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Postman Problem
f A
C
B b
a
c
d
e
g
Finda“Chinese”Postman’ssolu1onAnswer:“Eulerize”thegraph(a1gca’de)
Groups 2-5 persons: 5-7 min
a’
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New York Street Sweeper
f A
C
B b
a
c
d
e
g
Answer:“Eulerize”theDigraphGroups 2-5 persons: 10 min
Note: Digraph
[-1]
[-1]
[+2]
FindaSweeper’ssolu1on
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New York Street Sweeper
f A
C
B b
a
c
d
e
g
“Proposal1”:a1hcgede’
Groups 2-5 persons: 10 min
Note: Digraph
h e’
FindaSweeper’ssolu1on
6 –>NOTASOLUTION!(weassumethereisanother“street”fromC1llB)
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New York Street Sweeper
f A
C
B b
a
c
d
e
g
SoluCon:a1gea’ce’de’’(weonlyuseexis1ng“streets”)Groups 2-5 persons: 10 min
Note: Digraph
a’
e’
FindaSweeper’ssolu1one’’
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Testing Combination of Actions
f A
C
B b
a
c
d
e
g
SoluCon:TransformthegraphusingdeBrujin’salgorithm(dualdigraph) Groups 2-5 persons: 10 min
Testlinkcombina+ons(2ac1ons:allpairsofadjacentac1ons)
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Testing Combination of Actions
a
c
b Solution
Groups 2-5 persons: 15 min
f
g
d e
Problems:-”Forgot”transi1onf->b-Needto“Eulerize”theresul1nggraph 9
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Testing Combination of Actions
a
c
b (Complete)
Solution
Groups 2-5 persons: 15 min
f
g
d e
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Testing under a Time Deadline
f A
C
B b
a
c
d
e
g
SoluCon1:5hs(notrepea1ngtests)
M1:a1e(4hs)M2:dhcge’(5hs)
Groups 2-5 persons: 7 min
AssumingtheaboveDigraph,parallelizefromini1alstate
h e’
Currentminimum1me:9hs(a1hcgede’) 11
SoluCon2:4hs(repea1ngsometests)
M1:afce(4hs)M2:acge(4hs)M3:dhbe(4hs)
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References � Readthepaper:GraphTheoryTechniquesinModel-BasedTesCng,byHarryRobinson(Presentedatthe1999Interna1onalConferenceonTes1ngComputerSo[ware)
� IfyouareinterestedyoucanvisittheChinesePostmanAlgorithmbyHaroldThimblebyhomepage.Itcontainsanimplementa1onandapaperdescribingit
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