1. Implementing Operations to Navigate Semantic Star Schemas Alberto Abelló, José Samos and Fèlix Saltor U. Politècnica de Catalunya & U. de Granada November 7th, 2003 DOLAP

2. November 7th, 2003Alberto Abelló2 Contents n Related Work n Multidimensional Algebra n Translation to SQL n New Drill-across possibilities n Conclusions Contents

3. November 7th, 2003Alberto Abelló3 Example of Multi-star Schema Related work

4. November 7th, 2003Alberto Abelló4 Multi-star Schemas n Kimball: Share Dimensions n Giovinazzo: Galaxy sharing Dimensions n Pedersen and Jensen: Multidimensional Object Family sharing subdimensions n Gopalkrishnan, Li, and Karlapalem: Multi-star Schemas normalizing fact tables n Moody and Kortink: –Constellation (hierarchically linked fact tables) –Galaxy (share Dimensions) –Star Cluster (sharing subDimensions) Related work

5. November 7th, 2003Alberto Abelló5 Semantic Relationships n Tryfona, Busborg, and Christiansen: EER n Trujillo, Palomar, Gómez and Song: UML (Generalization and Association inside a Star) n Abelló, Samos and Saltor: UML (Generalization, Association, Derivation and Flow between Stars) Related work

6. November 7th, 2003Alberto Abelló6 Cube Multidimensional Algebra A Cube is and injective function from an n-dimensional finite space (defined by the cartesian product of n functionally independent Levels {L 1,..,L n }), to the set of instances of a Cell (C c ). c:L 1 x.. x L n  C c injective

7. November 7th, 2003Alberto Abelló7 Composition of functions Multidimensional Algebra

8. November 7th, 2003Alberto Abelló8 Primitive Operations Multidimensional Algebra n Drill-across n Change Base n Roll-up n Union n Dice n Projection

9. November 7th, 2003Alberto Abelló9 Operations (I) Multidimensional Algebra n Change Base  :L o 1 x.. x L o n  L i 1 x.. x L i m injective  :C i c  C o c injective n Drill-across c o (x) =   (c i ) =  (c i (x)) c o (x) =   (c i ) = c i (  (x))

10. November 7th, 2003Alberto Abelló10 Operations (II) Multidimensional Algebra n Union n Roll-up c o (x) = c 1  c 2 =  :L i j  L o k exhaustive c o (x) =   (c i ) =  c i (y)  (y) = x { c 1 (x)if x  Dom(c 1 ) c 2 (x)if x  Dom(c 2 )

11. November 7th, 2003Alberto Abelló11 Operations (III) n Dice c o (x) =  m1,..,mk (c i ) = c i (x)[m 1,..,m k ] n Projection c o (x) =  P (c i ) = { c i (x)if P(x) undefif ¬P(x) Multidimensional Algebra

12. November 7th, 2003Alberto Abelló12 Derived Operations: Slice c o (x) = slice L i =k (c i ) =  L 1 x..xL i-1 xL i+1 x..xL n (  L i=k (c i )) Multidimensional Algebra

13. November 7th, 2003Alberto Abelló13 Basic query Translation to SQL

14. November 7th, 2003Alberto Abelló14 Dice Translation to SQL

15. November 7th, 2003Alberto Abelló15 Roll-up Translation to SQL

16. November 7th, 2003Alberto Abelló16 Change Base Translation to SQL

17. November 7th, 2003Alberto Abelló17 Drill-across Translation to SQL

18. November 7th, 2003Alberto Abelló18 Projection Translation to SQL

19. November 7th, 2003Alberto Abelló19 Union Translation to SQL

20. November 7th, 2003Alberto Abelló20 Effects of operations Translation to SQL

21. November 7th, 2003Alberto Abelló21 UML Relationships New Drill-across Possibilities

22. November 7th, 2003Alberto Abelló22 Derivation New Drill-across Possibilities n Implementation: Updatable views n ChangeBase –View to table -> OK –Table to view -> Iff view subsumes WHERE n Drill-across –View to table -> OK –Table to view -> Outer join

23. November 7th, 2003Alberto Abelló23 Generalization New Drill-across Possibilities n Implementation: One table for superclass and another one for each subclass n ChangeBase –Sub to super -> OK –Super to sub -> Iff criterion subsumes WHERE n Drill-across –Sub to super -> OK –Super to sub -> Outer join

24. November 7th, 2003Alberto Abelló24 Association New Drill-across Possibilities n Implementation: Foreign keys n ChangeBase –1:1 -> OK –1:N and N:1 -> Depends on the bases n Drill-across –1:1 -> OK –1:N -> Do it to an upper detail level being 1:1 –N:1 -> Double counting –Zeros -> Outer join

25. November 7th, 2003Alberto Abelló25 Flow New Drill-across Possibilities n Implementation: Foreign keys n ChangeBase –#old=#new -> OK –#old<>#new -> Weighting factors for facts –Appear or disappear -> Dice apropriately n Drill-across –#old=#new -> OK –#old<>#new -> ChangeBase –Appear or disappear -> Outer join

26. November 7th, 2003Alberto Abelló26 Conclusions n Navigational (algebraic) queries n Smoothly implemented on SQL n Multistar semantic queries Conclusions

27. November 7th, 2003Alberto Abelló27 Questions