Graph-Based Workflow Recommendation: On Improving Business Process Modeling

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1 Grph-Bs Workflow ommntion: On Improving Businss Pross Moling Bin Co Collg of Computr Sin Zhjing Univrsity Hngzhou Chin 37 Dongjing Wng Collg of Computr Sin Zhjing Univrsity Hngzhou Chin 37 Jinwi Yin Collg of Computr Sin Zhjing Univrsity Hngzhou Chin 37 Zhohui Wu Collg of Computr Sin Zhjing Univrsity Hngzhou Chin 37 Shuigung Dng Collg of Computr Sin Zhjing Univrsity Hngzhou Chin 37 ABSTACT How to improv th moling ffiiny n ury hs om urning prolm. Th populriztion of rommntion thniqu in E-Commr provi us nw trjtoris tht n us for rssing th prolm. In this ppr, w propos grph-s workflow rommntion for improving usinss pross moling. Th strt point is so-ll workflow rpository inluing st of lry vlop pross mols. Grph mining mtho is us to xtrt th pross pttrns from th rpository. Bs on grph it istn (GED) [], w lult th istn twn pttrns n th prtil usinss pross, viw s rfrn mol, whih is unr moling n slt th nit nos with smllr istns for rommntion. Th prformn stuy show its fsiility for prtil uss. Ctgoris n Sujt Dsriptors H.4. [Informtion Systms Applitions]: Offi Automtion Workflow mngmnt Kywors Grph-Bs, Workflow ommntion, Businss Pross Moling, Grph Eit Distn. INTODUCTION With th mturity of workflow thnology, ntrpriss prfr to sri thir usinss oprtions in trms of usinss prosss. Dsriing usinss pross is pi of sign n moling work whih is th tivity of (r-)vluting n orgnizing tsks tht usinss pross is ompos of. Howvr, pross moling woul iffiult or vn Prmission to mk igitl or hr opis of ll or prt of this work for prsonl or lssroom us is grnt without f provi tht opis r not m or istriut for profit or ommril vntg n tht opis r this noti n th full ittion on th first pg. To opy othrwis, to rpulish, to post on srvrs or to ristriut to lists, rquirs prior spifi prmission n/or f. CIKM, Otor 9 Novmr,, Mui, HI, USA. Copyright ACM //...$5.. impossil whn omin knowlg is missing or prosss r to sri y mturs in th fil. Furthrmor, morn ommr lso rings forwr highr rquirmnt on th ffiiny n ury of usinss pross moling. Effiiny. Th usinss pross usully follows mrkt mns whih might hng frquntly. It is hr for molrs to figur out th hng mns within limit tim, whih woul l to rs ffiiny for moling. Aury. Th usinss oprtions r oming mor n mor omplit. Dsigning suh prosss rlis hvily on tit omin knowlg n prsonl xprins whih th molrs might not hv. An th prosss mol y thm r proly not suitl. Nowys, muh work is fousing on improving th usinss pross moling. Bs on vnt logs, workflow mining [] n isovr th tul usinss prosss whih r not proly s priv y th mngmnt n it n hlp molrs improv pross moling with isovr pross mols. Pross rtrivl [3, 4] n lso hlp molrs improv th moling y rtriving th similr frgmnts from th workflow rpository. Howvr, on th sis of ths two thniqus, th onstrution of nw usinss pross is still rfrr to th pr-isovr tmplt mols whih n muh mnul work to nlyz. In [6], th uthors propos workflow rommntion thniqu ll Flowommnr whih lvrgs provnn of workflows to provi rommntion for th st no tht ns to hosn to omplt th workflow. Howvr, Flowommnr osn t support pttrns whih onsists of omplx strutur (.g. AND-join, O-join, t.) n it will fil in f of nit no with multipl influning upstrm su-pths. Bsis, th tul usinss prosss r fr yon th stright lin struturs n Flowommnr n t wily us in rl pplition. Sin th workflow rpository usully ontins lrg mount of usinss prosss n ths prosss r typilly mol in form of irt grphs, strting from th grph strutur of th usinss pross n orrowing th is from tritionl rommntion systms, w pln to pro ssoition rul mining twn usinss tivity nos n pross frgmnts (i.., sugrphs) within workflow rpository, n provi rlt ision support for moling prosss. 57

2 W ll it grph-s workflow rommntion. A usinss pross frgmnt whih is unr moling is viw s rfrrn mol, n th pttrns r ll th influning upstrm sugrphs of th tivity nos tht trmin th ourrn of ths nos in th workflows. Th ssoition rul mining minly rfr to pttrn xtrtion whih is th fountion of workflow rommntion. Bs on msuring similrity n lulting istn twn rfrn mol n pross pttrns, this thniqu oul rommn pproprit nos for molrs to utomt th onstrution of usinss prosss. As rsult, it n not only Sp up th usinss pross moling y ruing th lirtion tim whih is n whn omin knowlg is inqut, ut lso provi guin for hoosing th most likly tsks y minimizing th rrors tht r possily m in usinss pross moling. In this ppr, w us grph mining thniqu to xtrt th pttrns from th workflow rpository. An s on th grph it istn (GED), w propos 3-imnsitonl istn lultion mtri for srhing th most rlvnt pttrns s th rommntion fountion. Thn w slt th orrsponing nos of thos pttrns n trmin whthr ths nos oul rommn to th molrs.. DISTANCE CALCULATION Firstly, w fin wht usinss pross grph is. Thr r mny moling mthos for usinss prosss. Diffrnt moling mtho hs iffrnt rprsnttion of workflow struturs, whih uss th onfusion of unrstning th ovrll strutur of usinss pross. Thus, w fin usinss pross grph in n strt viw. Dfinition. (Businss Pross Grph). Lt T st of no typs n L finit lpht of lls for nos. A usinss pross is onnt grph not y tupl P =(N,α, β) whr: (i)n is th finit st of nos; (ii) α : N T is th no typing funtion; (iii) β : N L is th no lling funtion. Lt E = N N st of irt gs n x N,y N. A no x is n input no of nothr no y iff thr is irt g from x to y (i.., (x, y) E). No x is n output no of y iff (y,x) E. Strt nos r nos without ny input n n nos r thos without ny output. In orr to pprntly sri th omplx struturs of pross mol, funtion α is us to istinguish twn no typs. Tk Ptri-nt for xmpl, pl ( p ) n trnsition ( t ) r two iffrnt no typs. As shown in Fig., th uppr mols r stnr workflow pttrns (i.., AND-split, AND-join, O-split, O-join) rprsnt y Ptri-nt n th lowr row shows orrsponing usinss pross grphs. Eh no is nnott with pir initingthnotypnthnoll. Dfinition. (Cnit No St, Upstrm Sugrph). Lt P =(N,α,β) np =(N,α,β )two usinss pross grphs. N <P,n> rprsnts th n nos of pross P, whih r ll nit nos. P is n upstrm sugrph for nit no st N <P,n> if (i) N <P > = N N <P,n> ; (ii) P is usinss pross sugrph of P. From Dfinition it follows tht, h usinss pross grph or sugrph oul ivi into two prts whih (t, ) (p, ) (p, ) (p, ) (p, ) (t, ) AND-split AND-join O-split O-join (p, ) (t, ) (t, ) (t, ) (t, ) (p, ) Figur : Ptri-nt mol n its pross grphs r nit no st n its orrsponing upstrm sugrph. Convrsly, h pir of thm orrspons to usinss pross grph or sugrph. In workflow rpositoris, thr r mny pirs n it oftn hppns tht on upstrm sugrph or nit no st my ppr in mor thn on pirs. Thus, w vlut th orrltion of nit no st n its upstrm sugrphs through th msur of onfin whih fin s follows. Dfinition 3. (Confin). Lt nit no st n u n upstrm sugrph. frq(, u) rprsnts th frquny tht n u our togthr. frq() rprsnts th frquny tht ours lon. Th onfin of givn u is: Conf(, u) = frq(,u) frq() Th nit no st n upstrm sugrph within pross grph or sugrph whih is of low frquny might proly orrlt strongly. If support msur of tritionl ssoit ruls is us, suh orrltions will limint n rommntions s on ths usinss prosss r impossil. Thrfor, w only lvrg th onfin in our work n support is not suppos to us. Bs on th Dfinition 3, w prsnt following finition. Dfinition 4. (Influning Upstrm Sugrph). Lt θ Conf onfin thrshol. For givn nit no st n its orrsponing upstrm sugrph u, u is influning iff: Conf(, u) θ Conf. In workflow rpositoris, influning upstrm sugrph trmins th ourrn of nit no st n w ll thm pttrns. Nxt, w prsnt our finition of pttrn tl whih is th input for istn lultion n no rommntion. Dfinition 5. (Pttrn Tl). Th pttrn tl is tupl T =(I,C,f)whr: (i)i is th finit st of influning upstrm sugrphs; (ii) C is th finit st of nit no sts; (iii) f : I C is surjtiv mpping. Th nit no sts in pttrn tl ontins th no(s) whih is(r) to rommn. In orr to pik th orrt nit no st, mthing th rfrn mol, whih is unr onstrution, with th influning upstrm sugrphs is rquir. Thus, GED (grph it istn []) oul us for this purpos. Th si i of GED is to sum th ost of lmntry rror-orrting oprtions: no sustitution, no insrtion/ltion, g insrtion/ltion. An th miniml ost tkn ovr ll oprtions is th it istn twn two grphs. Th smllr th it istn, th mor similr th two grphs. Howvr, GED oul not th only mtri for usinss pross grphs omprison unr th irumstn of workflow rommntion. Suppos tht thr is pross unr onstrution:? whr? rprsnts th 58

3 i iv 4 3 ii iii (4,3) Figur : An illustrtion for kwr lotion unknown no tht is to rommn. Two pttrns (, ) in pttrn tl r mth n thir orrsponing nit no st is {} n {f}. Th GED vlus for givn pross frgmnt ginst ov two pttrns r proly sm. Tht is to sy, th proility for rommning no n f is qul. In ft, no f shoul rommn inst of no. Bus th pttrn is losr to th pl whr th no rommntion ours. Thus, pprntly, whr th pttrn lot in givn pross ontriuts to rommntion ury. Dfinition 6. (Bkwr Lotion of A No). Lt P =(N,α,β) rfrn mol n ( N = ) st of rommntion nos for P. In P, i(x) no(x) rsptivly rprsnt th input nos st n output nos st of x (x (N )). N rprsnts th numr of th st N. x, y, z (N ), th kwr lotion of no x is: Lo n(x) = x Lo n(y)+ x i(y), o(i(y)) = mx(lo n(z)+) z o(i(x)), o(i(x)) > W illustrt Dfinition 6 in Fig.. Th pross in frm i is rfrn mol unr onstrution n rprsnts th st of rommntion nos. Two irt pths in frm ii r sugrphs of th pross in frm i. For h pth, th kwr lotion of h no is mrk ov. As for th lft sugrph in frm iii, no is th input of n (i.., i() n i()) n nos n r th output of (i..,, o()). Not tht, sin thr r two prlll pths for th pross in frm i, no hs two lotion vlus whih r 4 n 3. In this s, w hoos th mximum vlu. Thn w gt th finl kwr lotions of nos shown in frm iv. Dfinition 7. (Pttrn Lotion, Common Nos Numr). LtP =(N,α,β) pttrn from th pttrn tl T n P =(N,α,β ) rfrn mol unr onstrution. N rprsnts th numr of th st N. IfN N n x (N N ),α(x) =α (x),β(x) =β (x): Th lotion of P in P is: Lo p(p, P )=min(lo n(x)), x (N N ). Th numr of th ommon nos of P n P is: 3 Co n(p, P )= N N. As Dfinition 7 shows, pttrn lotion is ssign y th minimum kwr lotion of ll nos, whih oth xist in pttrn n th rfrn mol. Suppos tht thr is rfrn mol ( ) n two pttrns {( ),( )}. Gnrlly, ( ) is mor influning thn ( ) whn onsiring rommntion. An pttrn lotions for thm r n, whih mns th smllr lotion is th mor liklihoo to rommn. Somtims, th pttrn ing ompr hs th sm GED n pttrn lotion. In this s, w introu th thir msur of ommon nos numr to inrs th rommntion ury. Th mor ommon nos twn pttrn n usinss pross thr r, th mor similr thy r. Dfinition 8. (Distn Btwn Prosss). LtP = (N,α, β) rfrn mol, n P =(N,α,β ) pttrn from pttrn tl T. GED(P,P ) rprsnts th grph it istn twn P n P. mx n(p, P )rprsnts th mximum nos numr of P n P. φ, ϕ n ψ r wights for GED, pttrn lotion n ommon nos numr rsptivly. If x (N N ),α(x) =α (x),β(x) = β (x), th istn twn P n P is: Dist(P, P )=φ GED(P, P )+ϕ Lo p(p, P )+ ψ (mx n(p, P ) Co n(p, P )) As fin in Dfinition 8, w wights for ll msurs. Th omplx struturs n lrg volum of workflow rpository us th istn lultion vry omplit prolm in rl pplitions. As for rtin usinss pross, iffrnt msurs hv iffrnt ontriution to rommntion ury. Bsis, pross molrs my hv iffrnt is to iffrnt msurs. In our work, w lult th istn s on Dfinition 8. Apprntly, th smllr istn of pttrn mns th highr rommntion possiility for orrsponing nit no st. 3. ECOMMENDATION SCENAIOS Sin th rfrn mol my ontin mor thn on n no, thr r iffrnt rommntion rquirmnts. In this stion, w prsnt two rommntion snrios support in our work. Singl no s snrio is tht th rommntion rsult (i.., nit no st) is follow y on singl n no. It is triggr y rwing on g from on n no. Not tht, th nit no st whih woul rommn hr my ontin mor thn on no, th output of th n no, from whih nit no st is follow, is possily rnh strutur. Multipl nos s snrio is tht th rommntion rsult is follow y mor thn on no. It is triggr y rwing mor thn on g from svrl n nos. In this snrio, th molrs wnts to mrg th n nos of th rfrn mol to rommn no forming strutur lik AND-join, th no numr of nit no st hr shoul lwys on n w ovrlook thos sts whih ontin mor thn on no. For ths two snrios, mthing ll pths or sugrphs ginst pttrns in pttrn tl osts too muh n th istn lultion tim is intolrl. In ft, h xution pth hs its own usinss logi n th ownstrm no shoul in onformity with th logi of upstrm pth. Thrfor, w onsir th irt upstrm pth of th pl whr rommntion ours s th most importnt ftor. Ignoring othr pths(sugrphs), w only mth th upstrm xution pth or sugrph ginst th pttrns. As shown in Fig. 3, th no mrk rprsnts th pl whr rommntion ours n th right frms inluing singl no s n multipl nos s snrios prsnt thir orrsponing sugrphs for mthing. Apprntly, som xution pths r ignor. 59

4 f g j h i Singl no s Multipl nos s f g j Figur 3: A smpl of iffrnt snrios 4. POTOTYPE IMPLEMENTATION Th frmwork of grph-s workflow rommntion is shown in Fig. 4. In gnrl, thr r thr mouls in this frmwork n thy r frm y th ott lin in Fig. 4. Th first two mouls (i.., prprossing, pttrn isovry) r prform offlin whil th lst moul (i.., workflow rommntion) is onut onlin. Prprossing. In orr to filitt th pttrn xtrtion, rmoling usinss prosss mol y iffrnt nottions to uniform mols, whih r support y th high-lvl mouls in th frmwork, is nssry. Bs on th rmoling rsult, w us th ffiint grph mining lgorithm (.g. gspn [5]) to onut sugrph mining. Through this wy, w nlyz n min frgmnts of ll th usinss pross grph mols in workflow rpository. Not tht, th frquny hr is st to whih mns ll th sugrphs of ll th pross mols r foun. Th rson is tht no mttr how low-frquny th sugrph is, th nos in it might orrlt so strongly tht w n t ignor. Th output of this moul is st of sugrphs n thir own frqunis. Pttrn isovry. In this moul, firstly, h min sugrph is ompos to two prts whih r nit no st n upstrm sugrph (i.., Dfinition ). Th nit no st is us to xtn or omplt th rfrn mol unr onstrution whn rommntion ours, n th upstrm sugrph hr is us s th provnn for pttrn xtrtion. Thn, s on Dfinition 3 n Dfinition 4, w onut pttrn xtrtion slting th influning upstrm sugrphs. At lst, th slt pttrns n thir orrsponing nit no sts r rgistr into th pttrn tl (Dfinition 5), mking ry for susqunt workflow rommntion moul. Workflow rommntion. This moul gnrts th most likly tsks for pross molrs to xtn or omplt th usinss pross unr onstrution. Sin it is prform onlin, ompring with ov two mouls, its ury n ffiiny is mor onrn in prti. Th tils of th whol prour is shown in Algorithm. Thr r minly two omputtion stps in this moul. Th first stp hppns whn on of th rommntion snrios in- h i Algorithm Th lgorithm for workflow rommntion Input: A st of n nos E of th rfrn mol; th pttrn tl T ; wights for istn: φ, ϕ, ψ Output: Svrl nit no sts for rommntion : initiliz tl CNS =(C, D) whrd rprsnts istn vlus for C : P E gt th upstrm xution pth of E 3: for h ror (p, ) T o 4: if th th input t typ of nit no st mths th output t typ of E thn 5: S n(p, P E) gt th sm no numr 6: if S n(p, P E)! = thn 7: Lo p(p, P E) gt th pttrn lotion 8: GED(p, P E) gt th grph it istn 9: Dist(p, P E) φ GED(p, P E)+ϕ Lo p(p, P E)+ ψ (mx n(p, P E) S n(p, P E)) # Dfinition 8 : if CNS is not mpty n is sm with ((p, ) T,Dist(p,P E) D) thn : Conf(, P E) Conf(p, )+Conf(p, ) : if Dist(p, P E) Dist(p,P E) thn 3: Dist(p,P E) Dist(p, P E) 4: n if 5: ls 6: CNS (,Dist(p, P E)) 7: n if 8: n if 9: n if : n for : sort th lmnts in CNS y th vlu of istn : rturn first svrl nit no sts of CNS. trou in Stion 3 is triggr y th signr. Th xution pth within th rfrn mol is foun n us to mth ginst th pttrns isovr in th lst moul (lin ). Th son stp is just lulting th istn (Dfinition 8) twn pttrns n th xution pth (lin 5-9). Sin th omputtion omplxity of GED is high, it tks th most of tim for istn lultion. Bsis, w opt itionl msurs to inrs th ffiiny n ury, for xmpl, filtring th pttrns through I/O onstrints for istn lultion (lin 4) n summing th onfin vlus for sm nit no sts (lin - 7). Th nit no st is rommn to molrs on th istn twn its orrsponing pttrn (i.., influning upstrm sugrph) n th xution pth is suffiintly smll (lin -). As shown in Fig. 4, on th whol moling work is finish, th nwly omplt usinss pross n rhiv to th workflow rpository n srv s th provnn for futur rommntion. Sugrph Mining Pross -moling Workflow pository Prprossing Sugrph Domposition frn Mol Arhiving Dsignr Pttrn Extrtion Pttrn Disovry ommntion Triggring Cnit no st Workflow ommntion Pttrn Tl Exution Pth Distn Clultion Figur 4: Th frmwork of grph-s workflow rommntion 5. EXPEIMENTAL EVALUATION Bs on synthti tst, w fous on stuying th ffiiny n fftivnss of our grph-s workflow rommntion. In orr to mk omprison, w lso implmnt our vrsion of Flowommnr whih hivs similr prformn s tht rport in [6]. Aoring to [6], Flowommnr is ttr thn othr thniqus oth in fftivnss n ffiiny. Howvr, sin Flowommnr osn t support omplx workflow struturs ontining rnhs whih support y ours, th omprtiv 53

5 stuy hs n only onut on simpl tst whih is similr to th tst us in [6]. By simulting th rl usinss prosss, th omplx tst ontins vritis of struturs (i.., AND-join, O-join, AND-split, t.). Th systms r oth vlop in Jv (Jk.6) n ll xprimnts r on on.53ghz Intl Cor Duo E7 PC with 3.4GB min mmory, running Winows XP. In ition, th onfin for pttrn isovry of th whol prour is fix to.5. Efftivnss Stuy. Th fftivnss is msur y th ury for th tivitis or tsks for whih rommntion must givn. W st th wight vlus to: for GED, 6 for pttrn lotion, for ommon nos numr. Bs on this wights omintion, w stuy th fftivnss y iviing oth simpl n omplx tsts to iffrnt tst sts, of whih th sizs rng from to. In Fig. 5(), w rnomly hoos tst st n it is foun tht oth mthos prsnts th trns tht th ury inrss s th numr of top rommntions inrs. Howvr, from Fig. 5() w n s tht th Grph-s mtho hivs ttr ury thn tht of Flowommnr whn th top rommntion numr rh to 3. This is us thr is no strutur similrity msur involv in Flowommnr. Sin th usinss pross in omplx tst ontins iffrnt omplx struturs, Flowommnr fils on it. As shown in Fig. 5(), our mtho not only works wll on iffrnt tst sts ut lso prsnts sty ury of 8% rroun whn it msur y top rommntions. Effiiny Stuy. Th ffiiny is vlut y th vrg rommntion tim for tst nos. Gnrlly, th ffiiny is trmin y th numr of pttrns. To stuy th ffiiny, w lso ivi th simpl n omplx tsts into 5 tst sts with rng of -. Th isovr pttrn numrs r shown in Tl. Not tht, vn in sm tst st, th pttrn numrs of Flowommnr (not y F in th tl) n grph-s r iffrnt sin thir wy for isovring r iffrnt. Th tst rsults r shown in Fig. 6. From Fig. 6() w n s, Flowommnr spnt lss tim thn ours whih oul minly xplin y th rson tht th istn mtri of grph-s is mor omplit n involv mor msurs thn tht of Flowommnr. As for th tsts on omplx tst shown in Fig. 6(), th vrg rommntion tim for h no inrss s th numr of usinss prosss inrs. This is us th numr of pttrns grows with th inrs of usinss pross numr. Nvrthlss, th tim is ontroll within ms vn whn th pttrn numr xs 4. Th ov Aury Flowommnr Grph s Top ommntions (N) () simpl tst Aury S S S3 S4 S5 Tst Sts (ID) () omplx tst Figur 5: Th fftivnss stuy Top Top Tl : Th numr of pttrns for mthing Numr of BPs F Simpl Grph Complx Avrg tim (ms) Flowommnr Grph s Numr of usinss prosss () simpl tst Avrg Tim (ms) Grph s Numr of usinss prosss () omplx tst Figur 6: Th ffiiny stuy tsts prov tht th grph-s mtho w propos is ffiint nough for prtil uss. 6. CONCLUSION AND FUTUE WOK In this ppr, w propos grph-s workflow rommntion thniqu whih oul us for improving th ffiiny n ury of pross moling. W rss th prolm of istn lultion twn two prosss ontining omplx struturs. Th xprimntl vlutions shown tht th grph-s workflow rommntion w propos is fsil for prtil uss. Sin fw rsrhs fous on workflow rommntion n our work is tnttiv ttmpt, muh work still hs to on n improv in th futur. For xmpl, how to fin inirt influning pttrns whih nfit for rommntion ury is hllnging. 7. EFEENCES [] W.M.P.V.D.AlstnL.Mrustr.Workflow Mining: Disovring Pross Mols from Evnt Logs. IEEE Trnstions on Knowlg n Dt Enginring, 6:8 4, 4. [] H. Bunk. On rltion twn grph it istn n mximum ommon sugrph. Pttrn ognition Lttrs, 8(8): , 997. [3]. Dijkmn, M. Dums, n L. Grí-Bñulos. Grph mthing lgorithms for usinss pross mol similrity srh. Businss Pross Mngmnt, pgs 48 63, 9. [4]. Dijkmn, M. Dums, B. Vn Dongn,. Käärik, n J. Mnling. Similrity of usinss pross mols: Mtris n vlution. Informtion Systms, 36():498 56,. [5] X. Yn n J. Hn. gspn: Grph-Bs Sustrutur Pttrn Mining. In IEEE Intrntionl Confrn on Dt Mining, pgs 7 74,. [6] J. Zhng, Q. Liu, n K. Xu. Flowrommnr: workflow rommntion thniqu for pross provnn. In Proings of th 8th Austrlsin Dt Mining Confrn (AusDM 9): Dt Mining n Anlytis 9. ACS Prss, 9. 53