Chapter 3.2 Basic Concepts of the MDD-Model

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)

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

Data Cube

Def: Data-Cube with m dimensions D₁, D₂, …, D_m and k fact –types F₁, F₂,…, F_k is

W = {( d₁, d₂,…, d_m) ( f₁, f₂,…f_k)}:

d_i  D_i for i = 1, …, m  f_j  F_j for j =1, …k  (d₁, d₂,…, d_m) is key}

Def.: cell-address = (d

,…, d

)

cell-content = (f ,…,f )

Data Cube Example

Product

Trekking Bike

GB Region

Time

35

Cell Facts (Measures)

Dimension

June

Dimension- Members

Mountain Bike

D

30 25

Single cube vs. Multiple cubes

Note: model as 1 cube with fact (f

,…,f

)

or as k cubes W

with fact f

for i = 1, …, k and all W

have the same dimensions

Choice depends on practical considerations and

performance, e.g. (sales#, sales€)

Consequences for query formulation and execution:

1 cube : select key, sales#, sales€

from W

Multiple cubes: select key, sales#, sales€

from W

, W

where W

.key = W

.key

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)…}

Density and Sparsity

Def.: Dense data-cube: all combinations of (d₁, …, d_m) occur.

Sparse data-cube is not dense

Def.:

Note:

• logical model assumes dense cubes

• physical storage model deals with dense and sparse cubes.

cells of

number total

cells occupied

of number 1 



sparsity

Example: BMW Sales

Months

BMW- BMW-engines

Systematic Sparsity of the MDD-Model:

1600 1800 2000 2300 2800 3000 3500 4000 5000 2500D

3er 3erKombi 3erCabrio 5er 5erKombi 7er 7erL 850 Z3 …

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

Relational Model

cyl fuel B-E

BMW-engines Facts

B-E B-B M € # Name days

Bodies

B-B … Month

E/R-Model: Star-Schema

BMW-Engines Facts BMW-bodies

Months

E/R-Model: Snowflake-Schema

The Snowflake-Schema arises from the Star-Schema by more details plus normalization:

engine

Basic body brakes

Drive-train

trans- mission

Facts

Months extras

BMW-bodies