Realtime detection and coloring of matching operator nodes in
workflow nets
Citation for published version (APA):
Eckleder, A., Freytag, T., Mendling, J., & Reijers, H. A. (2009). Realtime detection and coloring of matching
operator nodes in workflow nets. In T. Freytag, & T. Eckleder (Eds.), AWPN2009 Algorithmen und Werkzeuge
für Petrinetze (pp. 56-61). (CEUR Workshop Proceedings; Vol. 501). CEUR-WS.org.
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Published: 01/12/2009
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Operator Nodes in Work ow Nets
AndreasEckleder
NeroDevelopment&ServicesGmbH,Karlsbad,Germany
aeckleder@nero.com
ThomasFreytag
CooperativeStateUniversityKarlsruhe,Germany
freytag@dhbw-karlsruhe.de
JanMendling
Humboldt-UniversitätzuBerlin,Germany
jan.mendling@wiwi.hu-berlin.de
HajoA. Reijers
EindhovenUniversityofTechnology,TheNetherlands
h.a.reijers@tue.nl
Abstract
Thisworkdescribestheimplementationofanalgorithmtoidentifyand
colorizematchingsplit/join-operatorpairsinwork ownetbasedprocess
models within the open source software WoPeD [1]. The concept was
suggestedasapowerfulmeanstoenhancetheunderstandabilityofprocess
graphsin[2]. Theimplementeddetectionandcoloring methodworksin
realtime, i. e. process designers get immediate feedback on actual or
intendedediting activities.
1 Introduction
Theunderstandabilityofprocessgraphsis akeyrequirementforsuccessful
vi-sualprocessmodellingresults. In[2,3]itwasinvestigatedhowthe
understand-ability ofwork ownetscan besupported byseveral methods. Oneofthem is
to assign colors to matching pairsof control ow operators (splits and joins).
Theapproachmakesuse ofthe fact that colors arerecognized and associated
withaspeci csemanticsfasterthanotherelementsofvisualization.
Foragivenpairofnodesinawork ownet,thenumberofindependentpaths
leadingfromtheonenodetotheothercanbecalculatedwiththe
max- ow/min-cut algorithm of Ford and Fulkerson [4]. This approach is able to determine
all P/T and T/P handles of a given work ow net and therefore suitable to
provewhether wellhandledness appliesornot. Inparticular thetechniquesfor
ndingmatching operatornodesin awork ownetcanalso beappliedto nd
mismatching operator nodesand thus canhelp toperformstructural analysis,
e. g. to checktheexistenceortheviolationofwell-handledness.
In the followingsections, the algorithm for performing the required check
will be introduced along with its formal prerequisites. Afterwards, an
imple-mentationintheopensourceproductWoPeD [1]will besketchedand
Ourde nition ofapairofmatchingnodesisageneralizationof theconceptof
PT/TP-handlesasusedto de newell-handlednessin [5, 6].
Inawell-handledWF-netPN,twonodesx andy arecalledmatching
oper-ator nodes i
•
x isanAND-splitandy anAND-joinorx isanXOR-splitoraplace,and y anXOR-joinoraplace•
there is apair of elementary pathsC1 andC2 leadingfrom x to ysuch that:α(C
1
) ∩ α(C
2
)
={x, y}⇒ C
1
6= C
2
.TheFordandFulkersonalgorithmcanbeusedtoverifythatthereareindeedat
leasttwoelementarypathsleadingfromagivennodex toanothernodey. This
can bedone in analogyto theapproachdescribedin [5] to detectPT andTP
handles. However,todetectallmatchingoperatornodesofagivenwork ownet,
allpairsofnodes
{n
1
, n
2
} ∈ (A
s
×A
j
)∪(X
s
×X
j
)∪(X
s
×S)∪(S ×X
j
)∪(S × S
) whereA
s/j
standsfor thenodesof typeAND-split/joinrespectivelyandX
s/j
standsforthenodesof typeXOR-split/join respectively,must be checked. Asonlynodeswith at leasttwoelementsin theirpostsetcanserveasasplit and
only nodes with at least two elements in their preset canserveas a join, we
limitourselectionofpairstothecombinationsof
{n
1
, n
2
}
where|n
1
· | > 1
and| · n
2
| > 1
. Wheneverthemax- ow/min-cutalgorithmisreportingamaximum ow>1foranygivenpairofnodes,thatpairismarkedasamatchingoperatornode. Once all matching operator pairsof agivenwork ownetare detected,
their graphical representation can be colorized in a suitable way in order to
stressthesemantical relationbetweenthem. Figure1showsasimpleexample
ofthecoloringalgorithmappliedtoasingleAND-split/join handle.
Figure1: Simplecoloringexample
If multiple distinct handles exist in thesame net, each matching operator
nodepairis assignedan individualcolor(see gure2). Whenassigning colors
tooperator nodepairs,it mustbeconsideredthat assigning anodetoagiven
Figure3: Handleclusteringexample
Since only onesingle colorcanbe assigned to each node at atime, away
mustbefoundtodetermineacommoncolorforoperatornodesthatarepartof
morethanonematching pair. Thisis donebybuildingnode clustersfrom the
list of matching operator node pairs, where a given cluster contains allnodes
ofall pairssharingat least onecommon node. Figure 3showsan application
exampleofthisclusteringalgorithm, resultingin thesamecolorbeingusedfor
multiplematchingoperatorhandles{t1,t7}, {t1,t5}and{t1,t10}.
3 Implementation
WoPeD is an open source, Java-based graphical editor for work ownets
sup-portingthewell-established"vanderAalst"notation[6]. Thetoolismaintained
via Sourceforge, a common platform for the distributed development of free
devel-toggle button on the toolbar. When coloring is switched on, each cluster of
matchingoperatorsis assignedoneof thecolorsfrom aselectionpalette. The
paletteitselfcanbecreatedwithinasettingsdialog(see gure4)and lledwith
arbitrarycolorvalues.
Figure4: A settingsdialogallowsthecon gurationofopticalappearance
There is a special neutral color (usually white) that is used for all nodes
thathavenotbeenidenti edasmembersofanypairorclusterbythealgorithm.
Theirgraphicalrepresentationmatchesthatofstandardnodeswhenthecoloring
featureisdisabled.
Inenabled mode,thework ownetgraphisconstantlymonitoredfor
user-in icted changes. If a relevant change is detected, the coloring algorithm is
executed,producing apossiblynewset of nodeclusters. Each clusterreceives
anindividualcolorfromthepaletteuntil allcolorsarein use. Ifthishappens,
colors must be re-used or the palette must be extended. Finally, the visual
representationofthework ownetisupdatedusingthenewcolors. Toenhance
thevisualfeedbackofcorrectmodelling,onlynodepairsthatdonotviolatethe
rulesofwell-handlednessareconsideredforcoloring.
Thecoloringalgorithm hasbeenimplemented ontopofasimpli ed
repre-sentationof thetransformedwork ownet. This transformedrepresentationis
derived fromthe originalgraph
G
= (S, T, F )
by insertinga rstnoden' and asecondnoden foreachnoden
∈ S ∪ T
,andthencreatinganarcconnectinginsertedforall arcs
(x, y) ∈ F
ofthe original net. Theimplementation of the Fordand Fulkerson algorithmis derivedfrom theoneintroducedin [10], withthemodi cationtoselectnodesbasedonbreadth- rst search. Thealgorithm
runsatpolynomialtime.
Buildingthenodeclusterswhoseindividualnodesaresharingonecolorhas
beenimplementedbyusingasimple,iterativealgorithmasfollows:
1. LetAbealistofsetsofnodes,eachsetconsistingofoneofthematching
nodepairsdetected
2. While
a
∩ b 6= ∅
foranya, b
∈ A
witha
6= b
,setA
= A r {a, b} + {(a ∪ b)}
Theexemplarywork ownetshown in gure3showsatotalofthree operatornode pairs, each with more than onedistinct node paths leadingfrom oneto
another. Eachpairisaddedtoaninitiallistofnodesets:
1. {t1,t7}
2. {t1,t5}
3. {t1,t10}
Inthe rstiteration, {t1, t7} and {t1, t5} are combinedto {t1, t5, t7}. The
secondandlastiterationcombines{t1,t5,t7}and{t1,t10}to{t1,t5,t7,t10}.
Allnodesbelongingtothesameset ofnodesaredrawnwiththesamecolor.
4 Conclusion
Oneshortcomingofourapproachisthefactthatthenumberofcolorsahuman
canclearlydistinguishfrom eachotherisfairlylimited. Apossiblesolutionfor
thiscouldinvolvetheassignmentofspecialpatternsinadditiontoplainpalette
colors(e. g. hatched, stripedorplaid). Suchpatterns couldbeusedto extend
theamount ofdistinguishable handle clusters for complexwork ow netswith
moreexistingclustersthanpalettecolorentries.
Thecoloringalgorithmhasbeenimplementedinasu cientlygenericwayas
toallowitsapplicationtothegeneralizedproblemofdetectingPT/TP-handles
andthuscontrol- owerrorsinwork ownets. Ourimplementationthereforealso
replacesthestructuralwork ownetanalysis functionalityof WoPeD, allowing
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(BPM2007),LectureNotesinComputerScience4714,48-63.Springer
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