Outline – Query Optimization
CSE 562
Database Systems
•  Overview
•  Relational algebra level
–  Algebraic Transformations
•  Detailed query plan level
Query Processing:
Algebraic Optimization
–  Estimate Costs
–  Estimating size of results
–  Estimating # of IOs
–  Generate and compare plans
Some slides are based or modified from originals by
Database Systems: The Complete Book,
Pearson Prentice Hall 2nd Edition
©2008 Garcia-Molina, Ullman, and Widom
UB CSE 562
2
UB CSE 562
Algebraic Rewritings:
Commutative and Associative Laws
Relational Algebra Optimization
Commutative
•  Transformation rules
(preserve equivalence)
•  What are good transformations?
Cartesian
Product
×
R
Associative
S
S
×
×
×
R
R
S
Natural
Join
R
S
S
R
T
×
×
R
T
S
T
R
S
T
R
S
•  Question 1: Do the above hold for both sets and bags?
•  Question 2: Do commutative and associative laws hold
for arbitrary Theta Joins?
UB CSE 562
3
UB CSE 562
4
1
Algebraic Rewritings:
Commutative and Associative Laws
Commutative
Union
∪
R
Associative
S
∪
∪
∪
S
R
R
S
S
T
R
R
∩
∩
∩
R
S
T
S
∩
∩
∩
∪
∪
R
S
Intersection
Algebraic Rewritings for Selection:
Decomposition of Logical Connectives
T
R
T
∪
S
Does it apply
to bags?
•  Question 1: Do the above hold for both sets and bags?
•  Question 2: Is difference commutative and associative?
5
UB CSE 562
Algebraic Rewritings for Selection:
Decomposition of Negation
Question
6
UB CSE 562
Pushing Selection Through
Binary Operators: Union and Difference
Complete
∪
Union
∪
–
–
Difference
–
•  Exercise: Do the rules for intersection
UB CSE 562
7
UB CSE 562
8
2
Pushing Selection Through
Cartesian Product and Join
Rules: π + σ combined
Let X = subset of R attributes
Z = attributes in predicate P (subset of R attributes)
The right direction
requires that cond refers to
S attributes only
The right direction
refers to
requires that cond
S attributes only
The right
direction
requires
that all th
e attribut
by cond ap
es used
pear in bo
th R and S
•  Exercise: Do the rule for theta join
9
UB CSE 562
Pushing Simple Projections Through
Binary Operators: Union
Pushing Simple Projections Through
Binary Operators: Join and Product
•  A projection is simple if it only consists of an attribute list
•  B is the list of R
attributes that
appear in A
•  Similar for C
∪
∪
Union
•  Question: What is B
and C ?
•  Question 1: Does the above hold for both bags and sets?
•  Question 2: Can projection be pushed below intersection
and difference?
•  Answer for both bags and sets
UB CSE 562
10
UB CSE 562
•  Exercise: Write the rewriting rule that pushes projection
below theta join
11
UB CSE 562
12
3
Rules: π + σ +
combined
Projection Decomposition
•  Let X = set of attributes
•
Y = set of attributes
•
XY = X U Y
•  Z’ = Z U {attributes used in cond}
UB CSE 562
13
14
UB CSE 562
Some Rewriting Rules Related to
Aggregation: SUM
Projection Decomposition
•
σcond[SUMGroupbyList;GroupedAttribute→ResultAttribute(R)]
⇔
SUMGroupbyList;GroupedAttribute→ResultAttribute[σcond(R)]
if cond involves only the GroupbyList
•  SUMGL;GA→RA(R ∪ S)
⇔
PLUSRA1,RA2:RA[(SUMGL;GA→RA1R)
(SUMGL;GA→RA2 S)]
•  SUMGL2;RA1→RA2[SUMGL1;GA→RA1(R)]
⇔
SUMGL2:GA→RA2(R)
•  Question: does the above hold for both bags and sets?
UB CSE 562
15
UB CSE 562
16
4
Derived Rules: σ +
combined
Derivation for first one
More Rules can be Derived:
σp∧q (R S) =
σp[σq (R S)] =
σp[R σq (S)] =
[σp (R)] [σq (S)]
σp∧q (R S) = [σp (R)] [σq (S)]
σp∧q∧m (R S) = σm[σp (R) σq (S)]
σpvq (R S) = [σp (R) S] U [R σq (S)]
•  p only at R
•  q only at S
•  m at both R and S
17
UB CSE 562
σp1∧p2 (R) → σp1[σp2 (R)]
•
σp (R
•
•
UB CSE 562
18
Conventional Wisdom:
Do Projects Early
Which are “good” transformations?
•
UB CSE 562
[σp (R)] S
R
S → S
R πx[σp (R)] → πx{σp[πxz (R)]}
S) →
19
UB CSE 562
20
5
But…
More Transformations in Textbook
What if we have A, B indexes?
B = “cat”
•  Eliminate common sub-expressions
•  Other operations: duplicate elimination
A=3
Intersect pointers to get
pointers to matching tuples
21
UB CSE 562
UB CSE 562
22
Bottom line
•  No transformation is always good at the logical
query plan level
•  Usually good:
–  early selections
–  elimination of Cartesian products
–  elimination of redundant sub-expressions
•  Many transformations lead to “promising” plans
–  Commuting/rearranging joins
–  In practice too “combinatorially explosive” to be
handled as rewriting of logical query plan
UB CSE 562
23
6