1. Based on notes by Jim Gray
Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab, and Sub-Totals
Jim Gray Microsoft
Adam Bosworth Microsoft
Andrew Layman Microsoft
Hamid Pirahesh IBM
Presented by: Changwu Li
Based on notes by Jim Gray
9/17/2018

2. The Data Analysis Cycle
Spread Sheet
Table 1 10 15 12 9 6 3
Size vs Speed
Access Time (seconds) -9 -6 -3
Cache
Main
Secondary
Disc
Nearline
Tape
Offline
Online 4 2 -2 -4
Price vs Speed
Size(B)
$/MB
visualize
Extract
analyze
User extracts data from database with query
Then visualizes, analyzes data with desktop tools
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3. Relational Aggregate Operators
SQL has several aggregate operators:
sum(), min(), max(), count(), avg()
Other systems extend this with many others:
stat functions, financial functions, ...
The basic idea is:
Combine all values in a column
into a single scalar value.
Syntax
select sum(units)
from inventory;
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4. Relational Group By Operator
Group By allows aggregates over table sub-groups
Result is a new table
Syntax:
select deptno, sum(salary)
from emp
group by deptno
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5. Problems With This Design
Users Want Histograms
Users want sub-totals and totals
drill-down & roll-up reports
Users want CrossTabs
Conventional wisdom
These are not relational operators
They are in many report writers and query engines
F() G() H()
sum
M T W T F S S
AIR
HOTEL
FOOD
MISC
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6. Table 5a: Ford Sales Cross Tab
A cross tab example
Table 5a: Ford Sales Cross Tab
Ford
1994
1995
total (ALL)
black 50 85
135
white 10 75 60
160
220
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7. How to solve this problem? Answer: cube
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8. The Idea: Think of the N-dimensional Cube Each Attribute is a Dimension
N-dimensional Aggregate (sum(), max(),...)
fits relational model exactly:
a1, a2, ...., aN, f()
Super-aggregate over N-1 Dimensional sub-cubes
ALL, a2, ...., aN , f()
a3 , ALL, a3, ...., aN , f()
...
a1, a2, ...., ALL, f()
this is the N-1 Dimensional cross-tab.
Super-aggregate over N-2 Dimensional sub-cubes
ALL, ALL, a3, ...., aN , f()
a1, a2 ,...., ALL, ALL, f()
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9. An Example
CUBE
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10. Why the ALL Value?
Need a new “Null” value (overloads the null indicator)
Value must not already be in the aggregated domain
Can’t use NULL since may aggregate on it.
Think of ALL as a token representing the set
All(color)={red, white, blue},
All(year)={1990, 1991, 1992},
All(model)={Chevy, Ford}
Follow “set of values” semantics.
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11. CUBE operator: Syntax select model, make, year, sum(sales)
Proposed syntax:
Note: Group By operator repeats aggregate list
in select list
in group by list
select model, make, year, sum(sales)
from car_sales
where model in {“chevy”, “ford”}
and year between 1990 and 1994
group by model, make, year with cube
having sum(sales) > 0;
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12. How To Compute the Cube?
If each attribute has Ni values CUBE has P (Ni+1) values
Compute N-D cube with hash if fits in RAM
Compute N-D cube with sort if overflows RAM
Same comments apply to subcubes:
compute N-D-1 subcube from N-D cube.
Aggregate on “biggest” domain first when >1 deep
Aggregate functions need hidden variables:
e.g. average needs sum and count.
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13. Example: Compute 2D core of 2 x 3 cube Then compute 1D edges
Then compute 0D point
Works for algebraic and distributive functions Saves “lots” of calls
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14. Real world implementation
Both Oracle 9i and SQL server 2000
An example in Oracle 9i:
select deptno, job, sum(sal) as salary
from emp
group by cube(deptno, job)
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15. -------- ------------------ -------------------- 10 CLERK 1300
DEPTNO JOB SALARY
10 CLERK
10 MANAGER
10 PRESIDENT
20 ANALYST
20 CLERK
20 MANAGER
30 CLERK
30 MANAGER
30 SALESMAN
ANALYST
CLERK
MANAGER
PRESIDENT
SALESMAN
2902
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16. 1999 ACM Turing Award
Jim Gray
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