1. Query Sampling in DB2

2. Motivation Many algorithms do not scale up with data volume
Data volume is growing fast
Many algorithms do not scale up with data volume
For exploratory analysis users often want just approximate answers

3. Solution: Sampling
Processing less data => huge performance improvement
Approximate answers often suffice
Can you tell the difference between the two pie charts? It's pretty difficult, yet the pie chart based on the sample can be computed in about 1/100th of the time.

4. Current Support of Sampling in DB2:
The Rand() Function
RAND() returns a uniform random number between 0 and 1
SELECT *
FROM original query
WHERE rand() < 0.01
Advantage: User can easily specify the size of sample he wants
Disadvantage: The RAND() operator does not provide any optimization as it is applied to the query result
Note that we need to scale up the answer for aggregates like SUM and COUNT, but not for AVERAGE

5. Current Support of Sampling in DB2: The TABLESAMPLE operator
Can place sampling clause after any SQL table reference
SELECT …
FROM T TABLESAMPLE BERNOULLI(10.0)
WHERE …
General form of sampling clause
TABLESAMPLE samplingMethod(p)
samplingMethod is one of the two:
BERNOULLI: row-level Bernoulli sampling
SYSTEM: page-level (efficient) sampling method
p = inclusion probability for each row (%) = (expected) sampling fraction

6. Current Support of Sampling in DB2: The TABLESAMPLE operator (cont.)
Advantage: By pushing sampling to the bottom of a query tree, can provide huge performance improvements
Disadvantage: How to extrapolate the sampling rate at the base table to the query result?
Joins
Group by
Count (DISTINCT)
Subqueries

7. Extrapolation Problem
Let R be a base relation referenced in query Q. Then:
uniform random sample of Q ≠
Q evaluated over a uniform random sample of R (and possibly other tables)
Example (CMN99): Let Q = R S, where:
R(A,B) = {(a1, b0), (a2, b1), (a2, b2), (a2, b3),…, (a2, bk)}
S(A,C) = {(a2, c0), (a1, c1), (a1, c2), (a1, c3),…, (a1, ck)}
sample(R, rate1) sample(S, rate2) cannot generate sample(R S, rate3) for any reasonable values of rate1 and rate2

8. Solution
Push sampling to the bottom of the query tree – effectively replacing RAND() with TABLESAMPLE - whenever possible
Selections
Projections without duplicate removal
Foreign key joins
Some types of group by (using materialized views)

9. Foreign Key Joins
A two-way join r1 r2 is a foreign key join if a join attribute is the foreign key in r1 (this definition can be easily extended to n-way join).
The relation r1 is called a source relation.
A random sample of r r2 can be produced by joining a random sample of r1 (the source relation) with r2.

10. FK-Join Query Transformation
select *
from ( select *
from F, D
where F.foreignkey = D.primarykey)
where RAND()<0.1
select *
from F TABLESAMPLE bernoulli (10), D
where F.foreignkey = D.primarykey)

11. Sampling group by queries using materialized views
select * from
(select (exp1, exp2,…)
from F, D1, D2
where F.y1=D1.x1 and
F.y2=D2.x2 and
pred1, pred2,…
group by x1, x2)
where RAND()<0.1
create view MQT as (
select DISTINCT D1.x1, D2.x2
from F, D1, D2
where F.y1=D1.x1 and F.y2=D2.x2)
select (exp1, exp2,…)
from F, MQT TABLESAMPLE bernoulli (10.0)
where F.y1=MQT.x1 and F.y2=MQT.x2
and pred1, pred2,…
group by x1, x2

12. Experiments Modified 12 queries from TPCH
62% performance improvement for 10% sample
76% improvement for 1% sample
Defined several MQTs and queries in TPCH schema
95% improvement for 1% sample