Data Mining for Query Optimization
Jarek Gryz
2
Outline
•
Semantic Query Optimization
•
Soft Constraints
•
Query Optimization via Soft Constraints
•
Selectivity Estimation via Soft Constraints
3
Semantic Query Optimization
Use integrity constraints associated with a database to rewrite
a query into a form that may be evaluated more efficiently
Some Techniques:
•
Join Elimination
•
Predicate Elimination
•
Join Introduction
•
Predicate Introduction
•
Detecting an Empty Answer Set
4
Commercial implementations of SQO
Early Experiences:
•
Could not spend too much time on optimization
•
Few integrity constraints are ever defined
•
Association with deductive databases
Few (if any!)
5
Join elimination: example
select
p_name, p_retailprice, s_name, s_address
from
tpcd.lineitem, tpcd.partsupp, tpcd.part, tpcd.supplier
where
p_partkey = ps_partkey and s_suppkey = ps_suppkey and
ps_partkey = l_partkey and ps_suppkey = l_suppkey;
RI constraints:
part

partsupp (on partkey)
supplier

partsupp (on partkey)
partsupp

lineitem (on partkey and suppkey)
select
p_name, p_retailprice, s_name, s_address
from
tpcd.lineitem, tpcd.partsupp, tpcd.part, tpcd.supplier
where
p_partkey = l_partkey and s_suppkey = l_suppkey;
6
Algorithm for join elimination
1. Derive column transitivity classes from the
join predicates in the query
2. Divide the relations in the query that are
related through RI constraints into
removable and non

removable
3. Eliminate all removable relations from the
query
4. Add is not null predicate to foreign key
columns of all tables whose RI parents were
removed
7
Algorithm for join elimination: example
C.C
PS.S
O.C
S.S
PS.S
O.C
C.C
S.S
PS.S
O.C
9
Performance results for join
elimination
10
Predicate Introduction: Example
select
sum(l_extendedprice * l_discount) as revenue
from
tpcd.lineitem
where
shipdate >date('1994

01

01');
select
sum(l_extendedprice * l_discount) as revenue
from
tpcd.lineitem
where
shipdate >date('1994

01

01') and receiptdate >= date('1994

01

01');
Check constraint:
receiptdate >= shipdate
Clustered Index on
receiptdate
11
Algorithm for Predicate Introduction
N

set of predicates derivable from the query and
check constraints
•
If
N
is inconsistent, stop.
•
Else, for each predicate A op B in
N
, add it to the
query if:
•
A or B is a join column
•
B is a major column of an index
•
no other index on B’s table can be used in the plan
for the original query
13
Queries
select
100.00 * sum
(case
when p_type like 'PROMO%'
then l_extendedprice * (1

l_discount)
else 0
end)
/ sum(l_extendedprice * (1

l_discount)) as promo_revenue
from
tpcd.lineitem, tpcd.part
where
l_partkey = p_partkey and
l_shipdate >= date('1998

09

01') and
l_shipdate < date('1998

09

01') + 1 month;
Given the check constraint
l_receiptdate >= l_shipdate
we may add
a new predicate to the query:
l_receiptdate >= date(‘1998

09

01’)
14
Performance Results for Index
Introduction
15
The Culprit
New query plan uses an index, but the original table
scan is still better!
Why did this happen:
•
incorrect estimate of the filter factor
•
underestimation of the CPU cost of locking index pages
16
Soft Constraints
17
Soft Constraints
Traditional (“hard”) integrity constraints are
defined to prevent incorrect updates. A
soft
constraint
is a statement that is true about
the current state of the database, but does
not verify updates. In fact, a soft constraint
can be
invalidated
by an update.
18
Soft Constraints (cont.)
•
Absolute soft constraints
–
no violation in
the current state of the database
Absolute soft constraints can be used for optimization in exactly
the same way traditional constraints are.
•
Statistical soft constraints
–
can have some
(small) degree of violation
Statistical soft constraints can be used for improved selectivity
estimation
19
Implementation of Soft Constraints
In Oracle the standard integrity constraints are
marked with a
rely
option, so that they are
not verified on updates.
In DB2 soft constraints are called
informational constraints.
20
Informational Check Constraint
Example 1:
Create an employee table where a
minimum salary of $25,000 is guaranteed by the
application
CREATE TABLE
emp(empno
INTEGER NOT NULL
PRIMARY KEY,
name
VARCHAR
(20),
firstname
VARCHAR
(20),
salary
INTEGER CONSTRAINT minsalary
CHECK
(salary >= 25000)
NOT ENFORCED
ENABLE QUERY
OPTIMIZATION
);
21
Enforcing Validation
Example 2
: Alter the employee table to start
enforcing the minimum wage of $25,000
using DB2. DB2 will also verify existing
data right away.
ALTER TABLE
emp
ALTER
CONSTRAINT
minsalary
ENFORCED
22
Informational RI Constraint
Example 3:
Create a department table where the
application ensures the existence of departments to
which the employees belong.
CREATE TABLE
dept(deptno
INTEGER NOT NULL PRIMARY
KEY
,
deptName
VARCHAR
(20),
budget
INTEGER
);
ALTER TABLE
emp
ADD COLUMN
dept
INTEGER NOT NULL
CONSTRAINT
dept_exist
REFERENCES
dept
NOT ENFORCED
ENABLE QUERY OPTIMIZATION
);
23
Query Optimization via Empty
Joins
24
Example
select
Model
from
Tickets T, Registration R
where
T.RegNum = R.RegNum and T.date > “1990

01

01”
and R.Model LIKE “BMW Z3%”
select
Model
from
Tickets T, Registration R
where
T.RegNum = R.RegNum and T.date >
“1997

01

01”
and R.Model LIKE “BMW Z3%”
First BMW Z3 series cars were made in 1997.
25
Matrix representation of empty joins
A,B
(R
S)
26
Staircase data structure
•
Jarek Gryz:
27
Properties of the algorithm
•
Time Complexity
O
(nm)
requires a single scan of the sorted data
•
Space Complexity
O(min(n,m))
only two rows of the matrix need be kept in memory
•
Scalable with respect to:
•
number of tuples in the join result
•
number of discovered empty rectangles
•
size of the domain of one of the attributes
28
How many empty rectangles are there?
Tests done on 4 pairs of attributes with numerical domain present in
typical joins in a real

world workload of a health insurance company.
29
How big are the rectangles?
30
Query rewrite: simple case
select …
from R, S,...
where R.C=S.C and
60<R.A<80 and
20<S.B<80 and...
select …
from R, S,...
where R.C=S.C and
60<R.A<80 and
20<S.B<60
and...
31
Query rewrite: complex case
select
…
from
R, S,...
where
R.C=S.C and
60<R.A<80 and
20<S.B<80 and...
select
…
from
R, S,...
where
R.C=S.C and
(… and …) or
(… and …) or
(… and …) or
...
32
Experiment I: Size of the Overlap
33
Experiment 2: Type of Overlap
34
Experiment 3: Number of Empty
Joins Used in Rewrite
35
How much do the rectangles
overlap with queries?
36
Query optimization experiments
•
real

world workload of 26 queries
•
5 of the queries “qualified” for the rewrite
•
only simple rewrites were considered
•
all rewrites led to improved performance
37
Query Cardinality Estimate via
Empty Joins
38
Query Cardinality Estimate via
Empty Joins (SIEQE)
•
Cardinality estimates crucial for designing
good query evaluation plans
•
Uniform data distribution (UDA): standard
assumption in database systems
•
Histograms effective in single dimensions:
too expensive to build and maintain
otherwise
39
The Strategy
Q1
Q2
•
With UDA, the “density”: 1 tuple/sq unit
•
Empty joins cover 20% of the area
•
Adjusted density: 1.25 tuples/sq unit
Cardinality
UDA
SIEQE
Q1
100
62
Q2
100
125
40
Experiments
Number of queries for which the error is less than a given limit
42
Discovery of Check Constraints
and Their Application in DB2
We discover two types of (rules) check constraints:
•
correlations between attributes over ordered domains
•
partitioning of attributes
43
Correlations between attributes
over ordered domains
Rules have the form:
Y = bX + a + [emin, emax]
Algorithm
for all tables in the database
for all comparable variable pairs (X and Y) in the table
apply OLS estimation to get the function of the
form: Y = a + bX
calculate the max and min error (or residual)
emax and emin
endfor
endfor
44
Partitioning
Rules have the form
:
If X = a, then Y
[emin, emax]
Algorithm
for
all
tables
in
the
database
for
any
qualifying
variable
pair
(X
and
Y)
in
the
table
calculate
partitions
by
using
GROUP
BY
X
statements
find
the
max
and
min
value
of
Y
for
each
partition
endfor
endfor
45
Experiments in TPC

H
Rules
discovered
through
partitioning
:
If
L_LINESTATUS=F,
then
L_SHIPDATE=(
01
/
04
/
1992
,
06
/
17
/
1995
),
m
=
0
.
50
If
L_LINESTATUS=O,
then
L_SHIPDATE=(
06
/
19
/
1995
,
12
/
25
/
1998
),
m
=
0
.
50
TPC

H contains the following check constraint:
L_RECEIPTDATE > L_SHIPDATE
Our algorithm discovered the following rule:
L_RECEIPTDATE = L_SHIPDATE + (1, 30), m = 0.0114.
46
Applications
•
DBA Wizard
•
Semantic Query Optimization
•
Improved Filter Factor Estimates
47
Example
ARRIVAL DATE <= ‘1999

06

15’
AND
DEPARTURE_DATE >= ‘1999

06

15’
The
filter factor estimate for the query would be:
ff = ff1 * ff2
Consider a query issued against a hotel database, that requests the number of guests
staying in the hotel on a given date.
If
‘1999

06

15’
was approximately midway in the date ranges, we would estimate a
quarter of all the guests that came in over the number of years would be in the answer
of the query!
48
Example (cont.)
Assume that the following check constraint was discovered:
DEPARTURE_DATE >= ARRIVAL_DATE + (1 DAY, 5 DAYS)
The original condition in the query predicate can then be changed to:
ARRIVAL_DATE <= ‘1999

06

15’
AND
ARRIVAL_DATE >= ‘1999

06

18’
or
ARRIVAL_DATE
BETWEEN
‘1999

06

15’
AND
‘1999

06

18’
The filter factor is now estimated to:
ff = (ff1 + ff2
–
1)
49
Other Research on the Use of Soft
Constraints in Query Optimization
50
Query

driven Approach
•
Built multidimensional histograms based on
query results (Microsoft)
•
Improve cardinality estimates by looking at
the intermediate query results (IBM)
Both techniques generate statistical soft constraints
51
Data

driven Approach
•
Lots of methods using Bayesian networks to
infer statistical soft constraint
•
Lots of methods to discover functional
dependencies in data (absolute soft
constraints)
•
Most recently, BHUNT and CORDS use
sampling to discover soft constraints (IBM)
52
References
•
Q. Cheng, J. Gryz, F. Koo, T. Y. Cliff Leung, L. Liu, X. Qian, B.
Schiefer:
Implementation of Two Semantic Query Optimization
Techniques in DB2 Universal Database
. VLDB 1999.
•
J. Edmonds, J. Gryz, D. Liang, R. Miller:
Mining for Empty Rectangles
in Large Data Sets.
ICDT 2001.
•
J. Gryz, B. Schiefer, J. Zheng, C. Zuzarte
:
Discovery and Application
of Check Constraints in DB2.
ICDE 2001.
•
P. Godfrey, J. Gryz, C. Zuzarte:
Exploiting Constraint

Like Data
Characterizations in Query Optimization
. SIGMOD 2001.
•
J. Gryz, D. Liang:
Query Optimization via Empty Joins
. DEXA 2002.
•
J. Gryz, D. Liang:
Query Cardinality Estimation via Data Mining
. IIS
2004.
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