Realtime Detection and Coloring of Matching Operator Nodes in Workflow Nets

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Operator Nodes in Workow Nets

AndreasEckleder

NeroDevelopment&ServicesGmbH,Karlsbad,Germany

[email protected]

ThomasFreytag

CooperativeStateUniversityKarlsruhe,Germany

[email protected]

JanMendling

Humboldt-UniversitätzuBerlin,Germany

[email protected]

HajoA. Reijers

EindhovenUniversityofTechnology,TheNetherlands

[email protected]

Abstract

Thisworkdescribestheimplementationofanalgorithmtoidentifyand

colorizematchingsplit/join-operatorpairsinworkownetbasedprocess

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 akeyrequirementforsuccessfulvi-

sualprocessmodellingresults. In[2,3]itwasinvestigatedhowtheunderstand-

ability ofworkownetscan 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

withaspecicsemanticsfasterthanotherelementsofvisualization.

Foragivenpairofnodesinaworkownet,thenumberofindependentpaths

leadingfromtheonenodetotheothercanbecalculatedwiththemax-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 workow net and therefore suitable to

provewhether wellhandledness appliesornot. Inparticular thetechniquesfor

ndingmatching operatornodesin aworkownetcanalso 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 besketchedanddemon-

strated. Finally,aconclusionwill begivenwithideastoenhance theproposed

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Ourdenition ofapairofmatchingnodesisageneralizationof theconceptof

PT/TP-handlesasusedto denewell-handlednessin [5, 6].

Inawell-handledWF-netPN,twonodesx andy arecalledmatchingoper-

ator nodes i

•

^x îsânÂND-splitând^y ânÂND-joinôr^x îsân^XOR-splitôrâ^place,ând

y anXOR-joinoraplace

•

^there îs â^pair ôf êlementary ^paths^C1 ând^C2 ^leading^from ^x ^to ^y^such

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,todetectallmatchingoperatornodesofagivenworkownet,

allpairsofnodes

{n ₁ , n ₂ } ∈ (A s ×A j )∪(X s × X j )∪ (X s ×S)∪ (S ×X j ) ∪(S ×S

⁾

where

A _s/j

^stands^for ^the^nodes^of ^typeAND-split/joinrespectivelyand

X _s/j

standsforthenodesof typeXOR-split/join respectively,must be checked. As

onlynodeswith 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

^. ^Whenever^the^max-ow^/^min-cutâlgorithmîs^reportingâ^maximum

ow>1foranygivenpairofnodes,thatpairismarkedasamatchingoperator

node. Once all matching operator pairsof agivenworkownetare 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

matchingoperatorpairis notmutually exclusive,so agivennodecanbepart

ofmorethanonematch.

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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 workownets sup-

portingthewell-established"vanderAalst"notation[6]. Thetoolismaintained

via Sourceforge, a common platform for the distributed development of free

softwareprojects. Severalpublications haveaccompanied theemerging devel-

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toggle button on the toolbar. When coloring is switched on, each cluster of

matchingoperatorsis assignedoneof thecolorsfrom aselectionpalette. The

paletteitselfcanbecreatedwithinasettingsdialog(seegure4)andlledwith

arbitrarycolorvalues.

Figure4: A settingsdialogallowsthecongurationofopticalappearance

There is a special neutral color (usually white) that is used for all nodes

thathavenotbeenidentiedasmembersofanypairorclusterbythealgorithm.

Theirgraphicalrepresentationmatchesthatofstandardnodeswhenthecoloring

featureisdisabled.

Inenabled mode,theworkownetgraphisconstantlymonitoredforuser-

inicted 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

representationoftheworkownetisupdatedusingthenewcolors. Toenhance

thevisualfeedbackofcorrectmodelling,onlynodepairsthatdonotviolatethe

rulesofwell-handlednessareconsideredforcoloring.

Thecoloringalgorithm hasbeenimplemented ontopofasimplied repre-

sentationof thetransformedworkownet. This transformedrepresentationis

derived fromthe originalgraph

G = (S, T, F )

^by însertingâ^rst^node^n' ând

asecondnoden foreachnode

n ∈ S ∪ T

^,ând^then^creatingânârc^connecting

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insertedforall arcs

(x, y) ∈ F

^of^the ^original ^net. ^Theimplementation of the Fordand Fulkerson algorithmis derivedfrom theoneintroducedin [10], with

themodicationtoselectnodesbasedonbreadth-rst search. Thealgorithm

runsatpolynomialtime.

Buildingthenodeclusterswhoseindividualnodesaresharingonecolorhas

beenimplementedbyusingasimple,iterativealgorithmasfollows:

1. LetAbealistofsetsofnodes,eachsetconsistingofoneofthematching

nodepairsdetected

2. While

a ∩ b 6= ∅

^for^any

a, b ∈ A

^with

a 6= b

^,^set

A = A r {a, b} + {(a ∪ b)}

Theexemplaryworkownetshown in gure3showsatotalofthree operator

node 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 complexworkow netswith

moreexistingclustersthanpalettecolorentries.

Thecoloringalgorithmhasbeenimplementedinasucientlygenericwayas

toallowitsapplicationtothegeneralizedproblemofdetectingPT/TP-handles

andthuscontrol-owerrorsinworkownets. Ourimplementationthereforealso

replacesthestructuralworkownetanalysis functionalityof WoPeD, allowing

PT/TP-handledetectionwithoutfallingbacktoexternaltoolsasWoan.

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[1] WoPeDwebsite: www.woped.org,accessed onAug2,2009.

[2] M. D. Lara. Proano: Visual layout for drawing understandable Process

Models.Master'sthesis,TechnischeUniversiteitEindhoven,2008.

[3] J.Mendling,H.A.Reijers,andJorgeCardoso.WhatMakesProcessModels

Understandable? InG.Alonso,P.DadamandM.Rosemann,editors,Pro-

ceedingsofthe5thInternationalConferenceBusinessProcessManagement

(BPM2007),LectureNotesinComputerScience4714,48-63.SpringerVer-

lag, Berlin,2007.

[4] L.R.FordandD.R.Fulkerson: Maximalowthroughanetwork,Canad.

J.Math.8(1956),399-404.

[5] H. M.W.Verbeek: VericationofWFnets.PhDdissertation,Technische

UniversiteitEindhoven,2004.

[6] W. M.P.vanderAalstandK.vanHee: WorkowManagement: Models,

Methods,andSystems,2002.

[7] T. Freytag and S. I. Landes: PWFtool - aPetri net workow modelling

environment.AWPN2003-ResearchReport,CatholicUniversityofEich-

staett,2003.

[8] C. Flenderand T. Freytag: Visualizing theSoundnessof Workow Nets.

AWPN2006-ResearchReport,UniversityofHamburg,2006.

[9] A. Eckleder and T. Freytag: WoPeD 2.0 goes BPEL 2.0. AWPN 2008 -

ResearchReport,UniversityofRostock,2008.

[10] T. Ihringer: Diskrete Mathematik: Eine Einführung in Theorie und An-

wendungen,2002.

Realtime Detection and Coloring of Matching Operator Nodes in Workflow Nets

•

•

α(C 1 ) ∩ α(C 2 )

{x, y}⇒ C 1 6= C 2

{n 1 , n 2 } ∈ (A s ×A j )∪(X s × X j )∪ (X s ×S)∪ (S ×X j ) ∪(S ×S

A s/j

X s/j

{n 1 , n 2 }

|n 1 · | > 1

| ·n 2 | > 1

G = (S, T, F )

n ∈ S ∪ T

(x, y) ∈ F

a ∩ b 6= ∅

a, b ∈ A

a 6= b

A = A r {a, b} + {(a ∪ b)}

α(C ₁ ) ∩ α(C ₂ )

{x, y}⇒ C ₁ 6= C ₂

{n ₁ , n ₂ } ∈ (A s ×A j )∪(X s × X j )∪ (X s ×S)∪ (S ×X j ) ∪(S ×S

A _s/j

X _s/j

{n ₁ , n ₂ }

|n ₁ · | > 1

| ·n ₂ | > 1