1. DATA CUBE
Advanced Databases 584

2. Relational Data Extraction Few Extensions Group-by Fails CUBE ROLLUP
DATA CUBE
Motivation
Relational Data Extraction
Few Extensions
Group-by Fails
CUBE
ROLLUP
Advanced Databases 584

3. Motivation - Data Analysis
Visualization tools
Should display data trends, clusters.
N-dimensional space
Allow Dimensionality reduction
Data Summarization
Look for unusual patterns in data
Advanced Databases 584

4. Relational Data Extraction Few Extensions Group-by Fails CUBE ROLLUP
DATA CUBE
Motivation
Relational Data Extraction
Few Extensions
Group-by Fails
CUBE
ROLLUP
Advanced Databases 584

5. N-dimensional Data in 2D SQL tables
Time
Latitude
Longitude
Altitude
Temp
Pressure
Date:T1
La1
Lo1 A1 T1 P1
Date:T2
La2
Lo2 A2 T2 P2
N dimensions into N-attribute domain
For Visualization, dimensionality reduction via aggregation to include data along neglected dimensions
November 9, 2018
Advanced Databases

6. N-dimensional Data in 2D SQL tables
Time
Latitude
Longitude
Altitude
Temp
Pressure
Date:T1
La1
Lo1 A1 T1 P1
Date:T2
La2
Lo2 A2 T2 P2
Query + Extract
Each row in the above Weather table represents a weather measurement.
SQL Standard Aggregators:
COUNT()
SUM()
MIN()
MAX()
AVG()
E.g: Select AVG(Temp) FROM Weather
-> Returns a single Aggregate value for all tuples
GROUP BY:
-> Returns the aggregate value for each of the groups in the result-set, grouped by one or more columns.
E.g:
SELECT Time, Altitude, AVG(Temp)
FROM Weather
GROUP BY Time, Altitude;
Complexity?
Visualize
Advanced Databases 584

7. Relational Data Extraction Few Extensions Group-by Fails CUBE ROLLUP
DATA CUBE
Motivation
Relational Data Extraction
Few Extensions
Group-by Fails
CUBE
ROLLUP
Advanced Databases 584

8. Few Extensions Informix Illustra – Handles for User defined CallBacks
Init(&handle): Allocates the handle and initializes the aggregate computation.
Iter(&handle, value): Aggregates the next value into the current aggregate.
value = Final(&handle): Computes and returns the resulting aggregate by using data saved in the handle.
Red Brick systems
Rank(expression)
N_tile(expression, n)
Ratio_To_Total(expression)
Advanced Databases 584

9. Relational Data Extraction Few Extensions Group-by Fails CUBE ROLLUP
DATA CUBE
Motivation
Relational Data Extraction
Few Extensions
Group-by Fails
CUBE
ROLLUP
Advanced Databases 584

10. Issues with GROUP BY- Histogram
Data analysis are difficult with these SQL aggregation constructs
Issue: SQL does not allow direct construction of aggregation over computed categories
Time
Latitude
Longitude
Altitude
Temp
Pressure
Date:T1
La1
Lo1 A1 T1 P1
Date:T2
La2
Lo2 A2 T2 P2
Advanced Databases 584

11. Issues with GROUP BY- Histogram
Suppose the user wants a grouping on day, area and Max(temp) for the day
SELECT day, nation, MAX(Temp) FROM Weather GROUP BY Day(Time) AS day, Nation(Latitude, Longitude) AS nation;
Not Possible in Standard SQL
Day
Nation
Max(Temp) 1 US 67
Canada 57
Advanced Databases 584

12. Issues with GROUP BY- Histogram
Solution :
Compute indirectly from a table-valued expression which is then aggregated
SELECT day, nation, MAX(Temp) FROM
(SELECT Day(Time) AS day,
Nation(Latitude, Longitude) AS nation,
Temp FROM Weather) AS foo
GROUP BY day, nation;
Issue: Complex Nested Queries!!
Advanced Databases 584

13. Issues with GROUP BY- Rollups
Model
Year
Color
Sales
by Year by Model by Color
by Model by Year
Sales By Model
Chevy
1994
1995
Black
White 50 40 85
115 90
200
290
Not Relational!
Rollup
N states gives rise to 2^N possible aggregation columns
Drill down
Advanced Databases 584

14. Issues with GROUP BY- Rollups
Solution 1:
Model
Year
Color
Sales
Sales by Model by Year
Sales by Model
Chevy
1994
1995
Black
White 50 40 85
115 90
200
290
Enormous Number of Domains
Increase in number of columns ∞ power set of the number of aggregated attributes
Advanced Databases 584

15. Issues with GROUP BY- Rollups
Solution 2: Pivot table in Excel
Pivot on color column
Sum sales model
Year/Color
1994
1994 total
1995
1995 total
Grand Total
Black
White
Chevy 50 40 90 85
115
200
290
Explosion in number of Columns!
->Transposes the Spreadsheet
-> Aggregate values based on their column ‘Values’
-> Increases as Pivot increases
Advanced Databases 584

16. Issues with GROUP BY- Rollups
Another Solution:
Prevents Exponential Growth by ALL
Dummy Value “ALL” added to fill in super-aggregation terms
Model
Year
Color
Units
Chevy
1994
1995
ALL
Black
White 50 40 90 85
115
200
290
Advanced Databases 584

17. Issues with GROUP BY- Rollups
SELECT `ALL', `ALL', `ALL', SUM(Sales)
FROM Sales
WHERE Model = `Chevy‘
UNION
SELECT Model, `ALL', `ALL', SUM(Sales)
WHERE Model = `Chevy'
GROUP BY Model
SELECT Model, Year, `ALL', SUM(Sales)
GROUP BY Model, Year
SELECT Model, Year, Color, SUM(Sales)
GROUP BY Model, Year, Color;
Model
Year
Color
Units
Chevy
1994
1995
ALL
Black
White 50 40 90 85
115
200
290
SQL statement to build this table from Sales Data
Advanced Databases 584

18. Issues with GROUP BY- Cross Tabulation
What is cross-tabulation??
Symmetric aggregation result table
Cross-tab is two dimensional aggregation. If more aggregation values are added then it grows in dimension
Advanced Databases 584

19. Issues with GROUP BY- Cross Tabulation
Equivalent Relational Representation in terms of ‘ALL’ values
Explosion in terms of number of cross-tabs!
Chevy Sales Cross Tab:
Chevy
1994
1995
Total(ALL)
Black
White 50 40 90 85
115
200
135
155
290
Ford Sales Cross Tab:
Ford
1994
1995
Total(ALL)
Black
White 50 10 06 85 75
160
135 20
Advanced Databases 584

20. Why CUBE instead of Group By’s
-> Group Bys solve aggregation
-> But roll-up and Cross-tab is daunting!
E.g A 6 Dimensional cross-tab requires 64-way union of 64 different GROUP BY operators!!!!!
Solution: Lets look at the CUBE!
Advanced Databases 584

21. Relational Data Extraction Few Extensions Group-by Fails CUBE ROLLUP
DATA CUBE
Motivation
Relational Data Extraction
Few Extensions
Group-by Fails
CUBE
ROLLUP
Advanced Databases 584

22. CUBE Operators Generalization of group-by, roll-up and cross-tab
N-1 lower dimensional aggregates appear as points, lines, planes, cubes, hyper-cubes
Advanced Databases 584

23. Data Cubes : What, Why, Where, How
What? Operator in OLAP for fast analysis of data
Why? Requirement to manipulate and analyze data from multiple perspectives. Traditional relational databases fit into this multi-dimensional data analysis???
Where? Used in OLAP
Advanced Databases 584

24. Data Cubes : What, When, Why, How
Advanced Databases 584

25. OLAP
On-Line Analytical Processing - A type of data processing that allows decision makers to examine data according to the dimensions of the business
Data warehousing is a type of OLAP.
OLAP systems are built upon Multidimensional Databases - i.e., they are designed from the ground up to support the definition and query of multidimensional data cubes/structures.
The core of any OLAP system is an OLAP cube a.k.a Data cube
Advanced Databases 584

26. OLAP CUBE Company sales of a part to a customer at a store location
Advanced Databases 584

27. Advanced Databases 584 Combination Count {P1, Calgary, Vance} 2
{P2, Vancouver, Richard} 11
{P2, Calgary, Vance} 4
{P3, Vancouver, Richard} 9
{P3, Calgary, Vance} 1
{P4, Vancouver, Richard}
{P1, Toronto, Vance} 5
{P5, Vancouver, Richard}
{P3, Toronto, Vance} 8
{P1, Calgary, Richard}
{P5, Toronto, Vance}
{P2, Calgary, Richard}
{P5, Montreal, Vance}
{P3, Calgary, Richard}
{P1, Vancouver, Bob} 3
{P2, Calgary, Allison}
{P3, Vancouver, Bob}
{P3, Calgary, Allison}
{P5, Vancouver, Bob}
{P1, Toronto, Allison}
{P1, Montreal, Bob}
{P2, Toronto, Allison}
{P3, Montreal, Bob}
{P3, Toronto, Allison} 6
{P4, Montreal, Bob} 7
{P4, Toronto, Allison}
{P5, Montreal, Bob}
Advanced Databases 584

28. Create a Data CUBE
Generate the power set (set of all subsets) of the aggregation columns by overloading GROUP BY operator.
The data cube operator builds a table containing all these aggregate values. The total
aggregate using function f() is represented as the tuple:
ALL, ALL, ALL, : : :, ALL, f(*)
Advanced Databases 584

29. Create a Data CUBE
Advanced Databases 584

30. CUBE is a relational Operator
Create a Data CUBE
CUBE is a relational Operator
If C1,C2,… CN are cardinalities of N attributes
Then resulting cube relation is ∏(Ci +1)
i.e initial SALES table is 2*3*3 = 18 rows
The derived data cube
3*4*4 = 48 rows
Advanced Databases 584

31. CUBE-Syntax and Semantics
SELECT day, nation, MAX(Temp) FROM Weather GROUP BY CUBE Day(Time) AS day, Country(Latitude, Longitude) AS nation;
Semantics:
Aggregates over all the <select list> in the GROUP BY .
It then unions in each super-aggregate of the global cube- substituting ALL for aggregation columns
-> If there are N attributes in <select list> there will be 2^N - 1 super-aggregate values.
Advanced Databases 584

32. Relational Data Extraction Few Extensions Group-by Fails CUBE ROLLUP
DATA CUBE
Motivation
Relational Data Extraction
Few Extensions
Group-by Fails
CUBE
ROLLUP
Advanced Databases 584

33. ROLL-UP Operator SOLUTION: ROLLUP!
To compute only a set of aggregates like this, CUBE would be an overkill!
SOLUTION: ROLLUP!
Advanced Databases 584

34. ROLL-UP Operator Difference :
ROLLUP produces just the super-aggregates
Difference :
CUBE generates a result set that shows aggregates for all combinations of values in the selected columns.
ROLLUP generates a result set that shows aggregates for a hierarchy of values in the selected columns.
(v1 ,v2 ,...,vn, f()),
(v1 ,v2 ,...,ALL, f()),
...
(v1 ,ALL,...,ALL, f()),
(ALL,ALL,...,ALL, f()).
Advantage:
->Unlike CUBE in which the answer set is Multi-dimensional…. ROLL UP is naturally sequential
-> Operators like SUM(),AVG() work well with ROLLUP
Advanced Databases 584

35. CUBE and ROLLUP Algebra
SELECT Manufacturer, Year, Month, Day, Color, Model,
SUM(price) AS Revenue
FROM Sales
GROUP BY Manufacturer,
ROLLUP Year(Time) AS Year,
Month(Time) AS Month,
Day(Time) AS Day,
CUBE Color, Model;
GroupBy
ROLLUP
CUBE
Advanced Databases 584

36. CUBE and ROLLUP Algebra
GROUP BY <select list>
ROLLUP <select list>
CUBE <select list>
“Powerful”
Advanced Databases 584

37. CUBE and ROLLUP Algebra
A nice link illustrating the difference between ROLLUP and CUBE
Advanced Databases 584