1. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 1 Chapter 3 Conventional Data Warehouses

2. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 2 Fig. 3.1. Notation of the MultiDim model (a) Level (b) Hierarchy (c) Cardinalities (f) Analysis criterion (g) Distributing factor (e) Types of measures (d) Fact relationship with measures and associated levels (h) Exclusive relationships

3. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 3 Fig. 3.2. A conceptual multidimensional schema of a sales data warehouse

4. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 4 Fig. 3.3. Hierarchy classification

5. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 5 Fig. 3.4. A balanced hierarchy (a) Schema (b) Examples of instances

6. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 6 Fig. 3.5. An unbalanced hierarchy (a) Schema (b) Examples of instances

7. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 7 Fig. 3.6. Examples of recursive hierarchies (a)(b)

8. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 8 Fig. 3.7. Entity-relationship representation of customer types

9. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 9 Fig. 3.8. A generalized hierarchy (a) Schema (b) Examples of instances

10. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 10 Fig. 3.9. A generalized hierarchy without a joining level

11. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 11 Fig. 3.10. A noncovering hierarchy (a) Schema (b) Examples of instances

12. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 12 Fig. 3.11. A balanced nonstrict hierarchy (a) Schema (b) Examples of instances

13. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 13 Fig. 3.12. Example of aggregation for a sales amount measure (a) Strict hierarchy(b) Nonstrict hierarchy

14. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 14 Fig. 3.13. A nonstrict hierarchy with a distributing factor

15. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 15 Fig. 3.14. Transforming a nonstrict hierarchy into a strict hierarchy with an additional dimension

16. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 16 Fig. 3.15. Double-counting problem for a nonstrict hierarchy (a)(b)

17. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 17 Fig. 3.16. Alternative hierarchies (a) Schema (b) Examples of instances

18. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 18 Fig. 3.17. Parallel independent hierarchies, composed of a balanced and a noncovering hierarchy

19. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 19 Fig. 3.18. Parallel dependent hierarchies, composed of two balanced hierarchies

20. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 20 Fig. 3.19. Parallel dependent hierarchies leading to different parent members of the shared level

21. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 21 Fig. 3.20. A multidimensional schema containing several kinds of hierarchies

22. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 22 Fig. 3.21. A generalized hierarchy with different root levels (a) Schema (b) Examples of instances

23. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 23 Fig. 3.22. A generalized hierarchy with three aggregation paths and different root levels

24. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 24 Fig. 3.23. Example of a role-playing dimension

25. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 25 Fig. 3.24. A schema containing a fact dimension

26. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 26 Fig. 3.25. Multidimensional schema for analysis of bank accounts

27. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 27 Fig. 3.26. Example of double-counting problem for a multivalued dimension

28. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 28 Fig. 3.27. Decomposition of the fact relationship in Fig. 3.25 (a) Creating two fact relationships

29. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 29 Fig. 3.27. Decomposition of the fact relationship in Fig. 3.25 (b) Including a nonstrict hierarchy

30. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 30 Fig. 3.28. Alternative representation of the schema shown in Fig. 3.25

31. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 31 Fig. 3.29. Metamodel of the MultiDim model

32. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 32 Fig. 3.30. Relational representation of the example in Fig. 3.2

33. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 33 Fig. 3.31. Relations for a balanced hierarchy (a) Snowflake structure(b) Flat table

34. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 34 Fig. 3.32. Transformation of the unbalanced hierarchy shown in Fig. 3.5b into a balanced one using placeholders

35. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 35 Fig. 3.33. Relational implementation of the recursive hierarchies shown in Fig. 3.6 (a)(b)

36. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 36 Fig. 3.34. A schema with a recursive hierarchy in the Employee dimension

37. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 37 Fig. 3.35. Parent-child relational schema of an unbalanced hierarchy with instances from Fig. 3.5b

38. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 38 Fig. 3.36. Relations for the generalized hierarchy shown in Fig. 3.8

39. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 39 Fig. 3.37. Improved relational representation for the generalized hierarchy shown in Fig. 3.8

40. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 40 Fig. 3.38. Relational tables for the nonstrict hierarchy of Fig. 3.11

41. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 41 Fig. 3.39. Object-relational representation of the nonstrict hierarchy of Fig. 3.13

42. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 42 Fig. 3.40. Relations for the alternative hierarchies in Fig. 3.16

43. Copyright © 2008 Elzbieta Malinowski & Esteban Zimányi 43 Fig. 3.41. Relational schema of a set of parallel dependent hierarchies composed of two balanced hierarchies