Mapping Publishing and Mapping Adaptation in the Middleware of Railway Information Grid System

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1 Mappig Publishig ad Mappig Adaptatio i the Middleware of Railway Iformatio Grid ystem You Gamei, Liao Huamig, u Yuzhog Istitute of Computig Techology, Chiese Academy of cieces, Beijig gameiu@ict.ac.c Abstract. Whe adoptig the mediator architecture to itegrate distributed, autoomous, relatioal model based database sources, mappigs from the source schema to the global schema may become icosistet whe the relatioal source schema or the global schema evolves. Without mappig adaptatio, users may access o data or wrog data. I the paper, we propose a ovel approach the global attribute as view with costraits (GAAVC) to publish mappigs, which is adaptive for the schema evolutio. Also published mappigs satisfy both source schema costraits ad global schema costraits, which eable users to get valid data. We also put forward the GAAVC based mappig publishig algorithm ad mappig adaptatio algorithms. Whe we compare our approach with others i fuctioality, it outperforms. Fially the mappig adaptatio tool GMPMA is itroduced, which has bee implemeted i the middleware of railway iformatio grid system. Itroductio A serious issue i itegratig distributed, autoomous, relatioal model based databases is the evolutio of schemas. As for mediator architecture, mappigs from source schemas to the global schema are used to create source views that query data from sources. Whe schemas chage, users will get ivalid data without modifyig mappigs. However it is time-waste ad heavy work to revise mappigs maually. I this paper we propose a GAAVC based mappig publishig algorithm ad correspodig mappig adaptatio algorithms to automatically adjust mappigs. Our mai cotributios are as follows. () We put forward the ested schema decompositio model accordig to which we propose the approach the global attribute as view to costruct mappigs. (2) We develop the GAAVC based mappig publishig approach ad the correspodig algorithm. The approach is adaptive to the evolutio of the source schema ad the global schema. Also source views created by the mappigs guaratees that data from sources is valid. (3) We develop algorithms to adjust ivalid mappigs automatically as schemas evolve. (4) We implemet the GMPMA tool that implemets the algorithms. ectio 2 itroduces related work. ectio 3 defies valid mappigs. ectio 4 gives the GAAVC approach ad the mappig publishig algorithm. ectio 5 itroduces mappig adaptatio algorithms. ectio 6 compares the GAAVC approach with

2 2 You Gamei, Liao Huamig, u Yuzhog other approaches. ectio 7 describes the architecture of GMPMA tool before sectio 8 cocludes. 2 Related Works The approach adapts to the schema evolutio if oly local attributes that have o ivalid mappigs ca still be accessed as schemas evolve. The local as view (LAV) method [] defies the local schema as the view over the global schema. Whe schemas evolve, all the local attributes that are i the same schema caot be accessed. o LAV is ot adaptive to schema chages. Because source schemas match the global schema, source schema costraits are satisfied whe global costraits are satisfied by views. The global as view (GAV) approach [2] defies the global schema as the view over the source schema. Whe schemas chage, all the local attributes that are i the same view caot be accessed. o GAV has problems whe schemas chage. Because the global schema matches source schemas, global schema costraits are satisfied whe source costraits are satisfied by views. The global-local as view (GLAV) [3] approach is a variatio of LAV. The approach has the same problem with the LAV approach. The both as view (BAV) [4] approach defies the global attribute with the view of the local schema ad the local attribute with the view of the global schema. The approach is adaptive for the schema evolutio. However, the view is defied maually. The approach has cosidered costraits of the global schema ad source schemas. The correspodece view (CV) [5] approach sets up the mappig of view, other attributes of the same view caot be accessed whe schemas chage. o the approach is ot adaptive to the schema evolutio. What is more, the approach cosiders foreig key costraits but ot key costraits of the global schema. 3 Valid Mappigs We study relatioal based XML ad relatioal schemas with key costraits ad foreig key costraits i this paper. We suppose that there is at most oe view for a set of elemets i XML schema or tables i relatioal schemas. Defiitio 3. A attribute is of the form <ID, label, type>. We use Greek alphabets,α,β,,to represet a set of attributes. Defiitio 3.2 A schema is of the form (< ID, label>, {attribute}, {schema}). Defiitio3.3 A mappig of global attributes is a expressio of source views: Mappig ( α g ): α g=g( V ( α ), V ( α ),..., ( )) (,,..., ). V α 2 = F α α α 2 α are g global attributes. V is a fuctio of attributes of oe source ad the V ( α ) is the i view of the source (i =, 2,, ). G is a fuctio of views of differet sources. i F is a composite fuctio of G ad V ad F is a fuctio of attributes of differet sources. The expressio is made up of uio, itersectio ad set differece operators.

3 Mappig Publishig ad Mappig Adaptatio i the Middleware of Railway Iformatio Grid ystem 3 Defiitio 3.4 The mappig of the global schema R is the set of the mappigs of all the attributes of the schema: Mappig R = { α g = F ( α, α,..., ) R} α 2 α g. The expressio α KEY β deotes that α is the key of the schema of β ad α FK βdeotes that β is the foreig key of α. Mappig ( α ) deotes the mappig of α i source. Lemma 3. (Null value costraits for foreig key, briefly α FK_NULL β) uppose α FK β,if α=ull the β=ull. Defiitio 3.5 Valid data are data that satisfy key costraits ad ull value costraits for foreig key of the global schema. Defiitio 3.6 A valid source view is a source view that satisfies key costraits ad ull value costraits for foreig key of the global schema. Defiitio 3.7 Valid mappigs of a global schema are mappigs that produce valid source views. By valid mappigs of a global schema, users ca get valid data from databases. 4 The Global attribute as view with costraits (GAAVC) based Mappig Publishig Approach 4. The ested schema decompositio model R (κ, A, R (κ,a, ),,A m ) = R (κ) R 2 (κ,a ) R 3 (κ, κ ) R 4 (κ, κ,a ) R (κ, A m ), R is a est relatioal schema or XML schema. R is the sub-schema of R. κ is the key of R ad κ is the key of R. κ = (k, k 2,, k ). κ = (k, k 2,, k ). Atom schemas, R,, R, iherit foreig key costraits of R. Lemma 4. I the ested schema decompositio model, the decompositio is a lossless joi decompositio. The lemma 4. idicates that o iformatio will be lost after the decompositio. 4.2 The global attribute as view with costraits (GAAVC) approach Defiitio 4. A view key set is the keys uio of all the schemas of the view: key(r,r 2,,R ) = key(r ) key(r 2 ) key(r ) Lemma 4.2 The view key set is the key of the view. Defiitio 4.2 Key costraits o mappig are the global schema key costraits o mappig: If β g KEY α g, β g =F(β s ), α g =F(α s ), β s =( β s, β,..., s β ), α 2 s s = ( α ', α ',..., α ), the for ay α α ' ' s (i =,2,, m), there is a view key set s s 2 s s i β ( j ), s j β s KEY j α, s ' i β β s, i =. j s j

4 4 You Gamei, Liao Huamig, u Yuzhog Lemma 4.3 (key costraits o ull mappig) If β g KEY α g, Mappig s (β g )= ull, ad the mappigs of β g ad α g satisfy key costraits o mappig, the Mappig s (α g )=ull. Lemma 4.4 (foreig key costraits o ull mappig,β g FK_NULL α g ) if β g FK α g, Mappig(β g )=ull, the Mappig(α g )=ull. Defiitio 4.3 (the global attribute as view approach, GAAV) the GAAV approach is usig source views to express each atom schema of the global schema. Defiitio 4.4 (the global attribute as view with costraits (GAAVC) approach) Give the ested schema R ( κ, A, R ( κ, A,...),..., Am ), the mappig expressio of R: R mappig ={ κ = F α, α,..., α ), A = F A, A,..., A ), ( s s 2 s 2 (, s, s 2, s κ = F 3 ( α s, α s 2,..., α s ), A = F 4 ( A s, A s 2,..., A s ),, A m = F k ( A m, s, A,,..., m s A 2 m, s ) }, mappigs are costructed accordig to the followig rules: ) Accordig to the ested schema decompositio model, the approach costructs mappigs betwee atom schemas ad source schemas, which are equal to mappigs betwee the origial global schema ad source schemas 2) Mappigs of atom schemas satisfy key costraits o mappig. 3) Mappigs of atom schemas satisfy foreig key costraits o ull mappig. 4) The mappig expressio of a atom schema is the expressio of the attribute i deepest schema, while operads are all the attributes of the atom schema. Theorem 4. Mappigs that created by the GAAVC approach are valid mappigs. 4.3 Mappig Expressios Mappigs of atom schemas of the global schema are expressed as follows: The key mappig expressio: <addkey, <global key>, expressio (<<source attributes>, source view costraits>)> The o-primary attribute mappig expressio: <addattribute, <global key, global o-primary attribute>, expressio (<<source attributes>, source view costraits>)>. The GAAVC approach adapts to schema evolutios because attributes that have o ivalid mappig ca still be accessed whe schemas chage. Lemma 4.5 Give к KEY A, source view costraits of R(к) ad R(к, A) are the same. 4.4 The GAAVC Based Mappig Publishig Algorithm Give a global schema, source schemas ad a set of mappigs betwee the global schema ad source schemas, we set up mappigs accordig to GAAVC approach. tep : verify if mappigs satisfy key costraits o mappig. If ot, exit. tep 2: get М the miimal cover of global fuctioal depedecies. tep 3: get ordered partitios of М so that β ad α are i the same partitio ad β is before α if β KEY α or β FK α.

5 Mappig Publishig ad Mappig Adaptatio i the Middleware of Railway Iformatio Grid ystem 5 tep 4: build mappig expressios of attributes of each ordered partitio i sequece. The mappig expressio of α is built oly if for ay attributes β, β KEY α or β FK α, Mappig(β) ull. tep 2 gets rid of redudat fuctioal depedecies of global schema ad step 3 makes partitios to decrease searchig times. 5 Mappig adaptatios Whe a schema chages, we should adjust mappigs to esure them valid. Addig attributes has o ifluece o mappigs. Whe reamig a schema or a attribute, we oly review all the mappig expressios to chage the ame. 5. Deletig a attribute or deletig the mappig of a attribute The step 2, 3, 7 ad 8 i the followig algorithm esure key costraits o mappig. The step 4, 5,, ad 2 esure foreig key costraits o ull mappig. deleteattribute(α k ){ if α k is a global attribute, that is α g for each mappig expressio E that cotais α g 2 delete E 3 for each attribute set λ, Mappig(λ) ull, κ FK λ, κ is the key of E 4 deleteattribute(λ) 5 if α k is a attribute of source, that is α s 6 for each mappig expressio E that cotais α s 7 delete E the mappig of source 8 if the global attributes βof E is key 9 if o mappig expressio cotais β 0 for each attribute set λ, Mappig(λ) ull ad β FK λ) deleteattribute(λ) } 2

6 6 You Gamei, Liao Huamig, u Yuzhog 5.2 Deletig a foreig key costrait tep 2 ad step 3 i the followig algorithm esure key costraits o mappig, while step 5 ad step 6 esure foreig key costraits o ull mappig. deleteforeigkey (α FK β){ if α ad β are attributes of source for each mappig expressio E that cotais α FK β 2 delete the mappig of E i source 3 if the global attributes βi E are the primary key ad o mappig expressio cotais β 4 for each global attribute set λ, Mappig(λ) ull ad β FK λ 5 deleteattribute(λ) } Addig a foreig key costrait Whe addig a source foreig key costrait, the existig mappigs are still valid. Whe addig a global foreig key costrait, step 3 ad step 4 i the followig algorithm esure foreig key costraits o ull mappig. addforeigkey (α FK β){ if α ad β are global attributes 2 if Mappig(β) ull ad Mappig(α)=ull 3 deleteattribute (β) } Addig a source mappig The foreig key costraits o ull mappig are esured by step, step 2 ad step 3. AddourceMappig(Mappig s (α m )= F(α s )){ for each global attributes λ, λ FK α m if Mappig(λ) = ull 2 exit 3 if the mappig of α m satisfy key costraits o mappig whe addig Mappig s (α m )= F(α s ) 4

7 Mappig Publishig ad Mappig Adaptatio i the Middleware of Railway Iformatio Grid ystem 7 add the mappig Mappig s (α m )= F(α s ) } Deletig a source mappig tep 2 esures key costraits o mappig. tep 4, 5 ad 6 esure foreig key costraits o ull mappig. deleteourcemappig(mappig s (α m )= F(α s )){ for each mappig expressio E that cotais α m delete the mappig of E i source 2 if α m is a set of attributes of key κ 3 if Mappig(κ) = ull 4 for each attributes λ,mappig(λ) ull ad κ FK λ 5 deleteattribute(λ) } 6 6 Comparisos Publishig methods Comparisos Table. Mappig publishig approaches comparisos LAV GAV GLAV BAV CV GAAVC Be adaptive to schema evolutio No No No Yes No Yes Cosider key ad foreig key Yes Yes Yes Yes Oly foreig Yes costraits key costraits Adjust mappigs maually No No No Yes No No The detailed discussio is i related works. From the table, it ca be see that our GAAVC approach outperforms. 7 Architecture of the GAAVC based mappig publishig ad mappig adaptatio (GMPMA) tool We implemet the GAAVC based mappig publishig algorithm ad mappig adaptatio algorithms usig the GMPMA tool. Figure shows the architecture of the GMPMA tool. With the graphical user iterface or the moitor, schema evolutios are detected. The the mappig publishig ad mappig adaptatio egie costructs mappigs or adjusts mappigs. The architecture has bee implemeted i the middleware of the railway iformatio grid system.

8 8 You Gamei, Liao Huamig, u Yuzhog source schema source schema global schema global schema database global schema source schema cache database source schema global schema source schema Graphical User Iterface schema chages mappigs mappig publishig ad mappig adaptatio egie source schema chages source schema moitor mappigs mappigs mappigs mappigs database Fig.. The GMPMA Architecture 8 Coclusios To esure users to get valid data whe schemas evolve, we propose the GAAVC based mappig publishig algorithm ad mappig adaptatio algorithms ad implemet them i the GMPMA tool i the middleware of railway iformatio grid system. Our approach is uique i may ways: ) The GAAVC approach costructs the mappigs that adapt to the schema evolutio. 2) Our mappigs eable users to get valid data. 3) We cosider mappigs from oe computatio expressio of some source attributes to oe global attribute. How to make adaptatio to schema evolutios of object-orieted databases is our future work. Refereces. T. Kirk, A.Y. Levy, ad Y. agiv. The iformatio maifold. I: Proc of the AAAI prig ymposium o Iformatio Gatherig From Heterogeeous, Distributed Eviromets. AAAI press, 995, 85~9. 2. H. Garcia-Molia, Y. Papakostatiou, D. Quass, A. Rajarara, Y. agiv, J. Ullma, V. Vassalos, ad J. Widom. The TIMMI Approach to Mediatio: Data Models ad Laguages. Joural of Itelliget Iformatio ystems, 997,8(2): 7~ M. Friedma, A. Y. Levy, ad T. D. Millstei. Navigatioal Plas For Data Itegratio. I: Proc of the ixteeth Natioal Coferece o Artificial Itelligece ad Eleveth coferece o Iovative Applicatios of Artificial Itelligece. AAAI Press / The MIT Press, 999, 67~ P. McBrie, A. Poulovassilis. Data itegratio by Bi-directioal chema Trasformatio Rules. I: Proc of the 9th Iteratioal Coferece o Data Egieerig. Morga Kaufma, 2003, 227~ Y. Velegrakis, R. J. Miller, L. Popa. Mappig Adaptatio uder Evolvig chemas. I Iteratioal Coferece of Very Large Databases (VLDB), eptember 2003, pp