Chapter 3.2 Basic Concepts of the MDD-Model Def.: A Dimension is a data type (almost always finite), which is used as a component of a composite (multidimensional) key. Def.: Dimension-Members are elements of a dimension. Examples: frequently enumeration types or intervals: Month =( January, February, …, December) Day = [ 1:31] Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Further examples: BMW-engines = {1600, 1800, 2000, 2300, 2800, 3000, 3500, 4000, 5000, 2500D, 3000D} BMW-bodies = {3er, 5er, 7er, 7erL, 3er Kombi, 3er Cabrio, 5er Kombi, 8er, Z3} Note : not all combinations of engines and bodies are built Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Data Cube Def.: cell-address = (d1,…, dm) cell-content = (f1,…,fk) Def: Data-Cube with m dimensions D1, D2, …, Dm and k fact –types F1, F2,…, Fk is W = {( d1, d2,…, dm) ( f1, f2,…fk)}: di  Di for i = 1, …, m  fj  Fj for j =1, …k  (d1, d2,…, dm) is key} Def.: cell-address = (d1,…, dm) cell-content = (f1,…,fk) Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Data Cube Example 35 25 30 Dimension Product Cell Facts Dimension- (Measures) Dimension Product Trekking Bike GB Region Time 35 25 Dimension- 30 Members Mountain Bike June D Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Single cube vs. Multiple cubes Note: model as 1 cube with fact (f1,…,fk) or as k cubes Wi with fact fi for i = 1, …, k and all Wi have the same dimensions Choice depends on practical considerations and performance, e.g. (sales#, sales€) Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Consequences for query formulation and execution: 1 cube : select key, sales#, sales€ from W Multiple cubes: select key, sales#, sales€ from W1, W2 where W1.key = W2.key Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Number of days per month Def.: Dimension-Attributes: additional attributes for a detailed description of the dimension members. Examples: Number of days per month dimension Month = ((January,31), (February, 29), : (April, 30),..., (December,31)) Gasoline type and number of cylinders of an engine dimension BMW-engine = {(1600, Super,4),..., (2500D, Diesel,5),..., (4000, Regular,8)…} Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Density and Sparsity Def.: Dense data-cube: all combinations of (d1, …, dm) occur. Sparse data-cube is not dense Def.: Note: logical model assumes dense cubes physical storage model deals with dense and sparse cubes. Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Example: BMW Sales BMW-engines Months BMW- bodies 26.04.2017 Example: BMW Sales BMW-engines Months BMW- bodies Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Systematic Sparsity of the MDD-Model: 3er 3erKombi 3erCabrio 5er 5erKombi 7er 7erL 850 Z3 … 1600 1800 2000 2300 2800 3000 3500 4000 5000 2500D 3000D Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Relational Modeling Dimension  finite fixed relation Dimension-Element key Dimension-Attribute other non-key attributes Cube(Würfel) relation, on E/R level a relationship between dimensions Cube-key key composed of foreign keys of dimensions Measures non-key attributes of cube Dimensionality number of foreign keys Prof. R. Bayer, DWH, Ch. 3.2, SS2002

Relational Model BMW-engines Facts Month cyl fuel B-E B-E B-B M € # € # Name days Bodies B-B … Prof. R. Bayer, DWH, Ch. 3.2, SS2002

E/R-Model: Star-Schema BMW-Engines BMW-bodies Facts Months  i.e. simple star schema Prof. R. Bayer, DWH, Ch. 3.2, SS2002

E/R-Model: Snowflake-Schema The Snowflake-Schema arises from the Star-Schema by more details plus normalization: Basic body brakes Drive-train Facts BMW-bodies engine trans-mission Months extras This can be continued arbitrarily far Prof. R. Bayer, DWH, Ch. 3.2, SS2002