Chapter 14: Query Optimization: Chapter 14: Query Optimization
Chapter 14: Query Optimization: Chapter 14: Query Optimization Introduction
Transformation of Relational Expressions
Catalog Information for Cost Estimation
Statistical Information for Cost Estimation
Cost-based optimization
Dynamic Programming for Choosing Evaluation Plans
Materialized views
Introduction: Introduction Alternative ways of evaluating a given query
Equivalent expressions
Different algorithms for each operation
Introduction (Cont.): Introduction (Cont.) An evaluation plan defines exactly what algorithm is used for each operation, and how the execution of the operations is coordinated.
Introduction (Cont.): Introduction (Cont.) Cost difference between evaluation plans for a query can be enormous
E.g. seconds vs. days in some cases
Steps in cost-based query optimization
Generate logically equivalent expressions using equivalence rules
Annotate resultant expressions to get alternative query plans
Choose the cheapest plan based on estimated cost
Estimation of plan cost based on:
Statistical information about relations. Examples:
number of tuples, number of distinct values for an attribute
Statistics estimation for intermediate results
to compute cost of complex expressions
Cost formulae for algorithms, computed using statistics
Generating Equivalent Expressions: Generating Equivalent Expressions
Transformation of Relational Expressions: Transformation of Relational Expressions Two relational algebra expressions are said to be equivalent if the two expressions generate the same set of tuples on every legal database instance
Note: order of tuples is irrelevant
In SQL, inputs and outputs are multisets of tuples
Two expressions in the multiset version of the relational algebra are said to be equivalent if the two expressions generate the same multiset of tuples on every legal database instance.
An equivalence rule says that expressions of two forms are equivalent
Can replace expression of first form by second, or vice versa
Equivalence Rules: Equivalence Rules 1. Conjunctive selection operations can be deconstructed into a sequence of individual selections.
2. Selection operations are commutative.
3. Only the last in a sequence of projection operations is needed, the others can be omitted.
Selections can be combined with Cartesian products and theta joins.
(E1 X E2) = E1 E2
1(E1 2 E2) = E1 1 2 E2
Equivalence Rules (Cont.): Equivalence Rules (Cont.) 5. Theta-join operations (and natural joins) are commutative. E1 E2 = E2 E1
6. (a) Natural join operations are associative:
(E1 E2) E3 = E1 (E2 E3) (b) Theta joins are associative in the following manner: (E1 1 E2) 2 3 E3 = E1 1 3 (E2 2 E3) where 2 involves attributes from only E2 and E3.
Pictorial Depiction of Equivalence Rules: Pictorial Depiction of Equivalence Rules
Equivalence Rules (Cont.): Equivalence Rules (Cont.) 7. The selection operation distributes over the theta join operation under the following two conditions: (a) When all the attributes in 0 involve only the attributes of one of the expressions (E1) being joined. 0E1 E2) = (0(E1)) E2
(b) When 1 involves only the attributes of E1 and 2 involves only the attributes of E2.
1 E1 E2) = (1(E1)) ( (E2))
Equivalence Rules (Cont.): Equivalence Rules (Cont.) 8. The projection operation distributes over the theta join operation as follows:
(a) if involves only attributes from L1 L2:
(b) Consider a join E1 E2.
Let L1 and L2 be sets of attributes from E1 and E2, respectively.
Let L3 be attributes of E1 that are involved in join condition , but are not in L1 L2, and
let L4 be attributes of E2 that are involved in join condition , but are not in L1 L2. ))) ( ( )) ( (( ) ( 2 1 2 1 4 2 3 1 2 1 2 1 E E E E L L L L L L L L È È È È Õ Õ Õ = Õ q q
Equivalence Rules (Cont.): Equivalence Rules (Cont.) The set operations union and intersection are commutative E1 E2 = E2 E1 E1 E2 = E2 E1
(set difference is not commutative).
Set union and intersection are associative.
(E1 E2) E3 = E1 (E2 E3) (E1 E2) E3 = E1 (E2 E3)
The selection operation distributes over , and –. (E1 – E2) = (E1) – (E2) and similarly for and in place of – Also: (E1 – E2) = (E1) – E2 and similarly for in place of –, but not for
12. The projection operation distributes over union
L(E1 E2) = (L(E1)) (L(E2))
Transformation Example: Pushing Selections: Transformation Example: Pushing Selections Query: Find the names of all customers who have an account at some branch located in Brooklyn. customer_name(branch_city = “Brooklyn” (branch (account depositor)))
Transformation using rule 7a. customer_name ((branch_city =“Brooklyn” (branch)) (account depositor))
Performing the selection as early as possible reduces the size of the relation to be joined.
Example with Multiple Transformations: Example with Multiple Transformations Query: Find the names of all customers with an account at a Brooklyn branch whose account balance is over $1000. customer_name((branch_city = “Brooklyn” balance > 1000 (branch (account depositor)))
Transformation using join associatively (Rule 6a): customer_name((branch_city = “Brooklyn” balance > 1000 (branch account)) depositor)
Second form provides an opportunity to apply the “perform selections early” rule, resulting in the subexpression
branch_city = “Brooklyn” (branch) balance > 1000 (account)
Thus a sequence of transformations can be useful
Multiple Transformations (Cont.): Multiple Transformations (Cont.)
Transformation Example: Pushing Projections: Transformation Example: Pushing Projections When we compute
(branch_city = “Brooklyn” (branch) account )
we obtain a relation whose schema is: (branch_name, branch_city, assets, account_number, balance)
Push projections using equivalence rules 8a and 8b; eliminate unneeded attributes from intermediate results to get: customer_name (( account_number ( (branch_city = “Brooklyn” (branch) account )) depositor )
Performing the projection as early as possible reduces the size of the relation to be joined.
customer_name((branch_city = “Brooklyn” (branch) account) depositor)
Join Ordering Example: Join Ordering Example For all relations r1, r2, and r3,
(r1 r2) r3 = r1 (r2 r3 )
(Join Associativity)
If r2 r3 is quite large and r1 r2 is small, we choose
(r1 r2) r3
so that we compute and store a smaller temporary relation.
Join Ordering Example (Cont.): Join Ordering Example (Cont.) Consider the expression
customer_name ((branch_city = “Brooklyn” (branch)) (account depositor))
Could compute account depositor first, and join result with branch_city = “Brooklyn” (branch) but account depositor is likely to be a large relation.
Only a small fraction of the bank’s customers are likely to have accounts in branches located in Brooklyn
it is better to compute
branch_city = “Brooklyn” (branch) account
first.
Enumeration of Equivalent Expressions: Enumeration of Equivalent Expressions Query optimizers use equivalence rules to systematically generate expressions equivalent to the given expression
Can generate all equivalent expressions as follows:
Repeat
apply all applicable equivalence rules on every equivalent expression found so far
add newly generated expressions to the set of equivalent expressions
Until no new equivalent expressions are generated above
The above approach is very expensive in space and time
Two approaches
Optimized plan generation based on transformation rules
Special case approach for queries with only selections, projections and joins
Implementing Transformation Based Optimization: Implementing Transformation Based Optimization Space requirements reduced by sharing common sub-expressions:
when E1 is generated from E2 by an equivalence rule, usually only the top level of the two are different, subtrees below are the same and can be shared using pointers
E.g. when applying join commutativity
Same sub-expression may get generated multiple times
Detect duplicate sub-expressions and share one copy
Time requirements are reduced by not generating all expressions
Dynamic programming
We will study only the special case of dynamic programming for join order optimization E1 E2
Cost Estimation: Cost Estimation Cost of each operator computer as described in Chapter 13
Need statistics of input relations
E.g. number of tuples, sizes of tuples
Inputs can be results of sub-expressions
Need to estimate statistics of expression results
To do so, we require additional statistics
E.g. number of distinct values for an attribute
More on cost estimation later
Choice of Evaluation Plans: Choice of Evaluation Plans Must consider the interaction of evaluation techniques when choosing evaluation plans
choosing the cheapest algorithm for each operation independently may not yield best overall algorithm. E.g.
merge-join may be costlier than hash-join, but may provide a sorted output which reduces the cost for an outer level aggregation.
nested-loop join may provide opportunity for pipelining
Practical query optimizers incorporate elements of the following two broad approaches:
1. Search all the plans and choose the best plan in a cost-based fashion.
2. Uses heuristics to choose a plan.
Cost-Based Optimization: Cost-Based Optimization Consider finding the best join-order for r1 r2 . . . rn.
There are (2(n – 1))!/(n – 1)! different join orders for above expression. With n = 7, the number is 665280, with n = 10, the number is greater than 176 billion!
No need to generate all the join orders. Using dynamic programming, the least-cost join order for any subset of {r1, r2, . . . rn} is computed only once and stored for future use.
Dynamic Programming in Optimization: Dynamic Programming in Optimization To find best join tree for a set of n relations:
To find best plan for a set S of n relations, consider all possible plans of the form: S1 (S – S1) where S1 is any non-empty subset of S.
Recursively compute costs for joining subsets of S to find the cost of each plan. Choose the cheapest of the 2n – 1 alternatives.
Base case for recursion: single relation access plan
Apply all selections on Ri using best choice of indices on Ri
When plan for any subset is computed, store it and reuse it when it is required again, instead of recomputing it
Dynamic programming
Join Order Optimization Algorithm: Join Order Optimization Algorithm procedure findbestplan(S) if (bestplan[S].cost ) return bestplan[S] // else bestplan[S] has not been computed earlier, compute it now if (S contains only 1 relation) set bestplan[S].plan and bestplan[S].cost based on the best way of accessing S /* Using selections on S and indices on S */
else for each non-empty subset S1 of S such that S1 S P1= findbestplan(S1) P2= findbestplan(S - S1) A = best algorithm for joining results of P1 and P2 cost = P1.cost + P2.cost + cost of A if cost < bestplan[S].cost bestplan[S].cost = cost bestplan[S].plan = “execute P1.plan; execute P2.plan; join results of P1 and P2 using A” return bestplan[S]
Left Deep Join Trees: Left Deep Join Trees In left-deep join trees, the right-hand-side input for each join is a relation, not the result of an intermediate join.
Cost of Optimization: Cost of Optimization With dynamic programming time complexity of optimization with bushy trees is O(3n).
With n = 10, this number is 59000 instead of 176 billion!
Space complexity is O(2n)
To find best left-deep join tree for a set of n relations:
Consider n alternatives with one relation as right-hand side input and the other relations as left-hand side input.
Modify optimization algorithm:
Replace “for each non-empty subset S1 of S such that S1 S”
By: for each relation r in S let S1 = S – r .
If only left-deep trees are considered, time complexity of finding best join order is O(n 2n)
Space complexity remains at O(2n)
Cost-based optimization is expensive, but worthwhile for queries on large datasets (typical queries have small n, generally < 10)
Interesting Sort Orders: Interesting Sort Orders Consider the expression (r1 r2) r3 (with A as common attribute)
An interesting sort order is a particular sort order of tuples that could be useful for a later operation
Using merge-join to compute r1 r2 may be costlier than hash join but generates result sorted on A
Which in turn may make merge-join with r3 cheaper, which may reduce cost of join with r3 and minimizing overall cost
Sort order may also be useful for order by and for grouping
Not sufficient to find the best join order for each subset of the set of n given relations
must find the best join order for each subset, for each interesting sort order
Simple extension of earlier dynamic programming algorithms
Usually, number of interesting orders is quite small and doesn’t affect time/space complexity significantly
Heuristic Optimization: Heuristic Optimization Cost-based optimization is expensive, even with dynamic programming.
Systems may use heuristics to reduce the number of choices that must be made in a cost-based fashion.
Heuristic optimization transforms the query-tree by using a set of rules that typically (but not in all cases) improve execution performance:
Perform selection early (reduces the number of tuples)
Perform projection early (reduces the number of attributes)
Perform most restrictive selection and join operations (i.e. with smallest result size) before other similar operations.
Some systems use only heuristics, others combine heuristics with partial cost-based optimization.
Structure of Query Optimizers: Structure of Query Optimizers Many optimizers considers only left-deep join orders.
Plus heuristics to push selections and projections down the query tree
Reduces optimization complexity and generates plans amenable to pipelined evaluation.
Heuristic optimization used in some versions of Oracle:
Repeatedly pick “best” relation to join next
Starting from each of n starting points. Pick best among these
Intricacies of SQL complicate query optimization
E.g. nested subqueries
Structure of Query Optimizers (Cont.): Structure of Query Optimizers (Cont.) Some query optimizers integrate heuristic selection and the generation of alternative access plans.
Frequently used approach
heuristic rewriting of nested block structure and aggregation
followed by cost-based join-order optimization for each block
Some optimizers (e.g. SQL Server) apply transformations to entire query and do not depend on block structure
Even with the use of heuristics, cost-based query optimization imposes a substantial overhead.
But is worth it for expensive queries
Optimizers often use simple heuristics for very cheap queries, and perform exhaustive enumeration for more expensive queries
Statistics for Cost Estimation: Statistics for Cost Estimation
Statistical Information for Cost Estimation: Statistical Information for Cost Estimation nr: number of tuples in a relation r.
br: number of blocks containing tuples of r.
lr: size of a tuple of r.
fr: blocking factor of r — i.e., the number of tuples of r that fit into one block.
V(A, r): number of distinct values that appear in r for attribute A; same as the size of A(r).
If tuples of r are stored together physically in a file, then:
Histograms: Histograms Histogram on attribute age of relation person
Equi-width histograms
Equi-depth histograms
Selection Size Estimation: Selection Size Estimation A=v(r)
nr / V(A,r) : number of records that will satisfy the selection
Equality condition on a key attribute: size estimate = 1
AV(r) (case of A V(r) is symmetric)
Let c denote the estimated number of tuples satisfying the condition.
If min(A,r) and max(A,r) are available in catalog
c = 0 if v < min(A,r)
c =
If histograms available, can refine above estimate
In absence of statistical information c is assumed to be nr / 2.
Size Estimation of Complex Selections: Size Estimation of Complex Selections The selectivity of a condition i is the probability that a tuple in the relation r satisfies i .
If si is the number of satisfying tuples in r, the selectivity of i is given by si /nr.
Conjunction: 1 2. . . n (r). Assuming indepdence, estimate of tuples in the result is:
Disjunction:1 2 . . . n (r). Estimated number of tuples:
Negation: (r). Estimated number of tuples: nr – size((r))
Join Operation: Running Example: Join Operation: Running Example Running example: depositor customer
Catalog information for join examples:
ncustomer = 10,000.
fcustomer = 25, which implies that bcustomer =10000/25 = 400.
ndepositor = 5000.
fdepositor = 50, which implies that bdepositor = 5000/50 = 100.
V(customer_name, depositor) = 2500, which implies that , on average, each customer has two accounts.
Also assume that customer_name in depositor is a foreign key on customer.
V(customer_name, customer) = 10000 (primary key!)
Estimation of the Size of Joins: Estimation of the Size of Joins The Cartesian product r x s contains nr .ns tuples; each tuple occupies sr + ss bytes.
If R S = , then r s is the same as r x s.
If R S is a key for R, then a tuple of s will join with at most one tuple from r
therefore, the number of tuples in r s is no greater than the number of tuples in s.
If R S in S is a foreign key in S referencing R, then the number of tuples in r s is exactly the same as the number of tuples in s.
The case for R S being a foreign key referencing S is symmetric.
In the example query depositor customer, customer_name in depositor is a foreign key of customer
hence, the result has exactly ndepositor tuples, which is 5000
Estimation of the Size of Joins (Cont.): Estimation of the Size of Joins (Cont.) If R S = {A} is not a key for R or S. If we assume that every tuple t in R produces tuples in R S, the number of tuples in R S is estimated to be: If the reverse is true, the estimate obtained will be: The lower of these two estimates is probably the more accurate one.
Can improve on above if histograms are available
Use formula similar to above, for each cell of histograms on the two relations
Estimation of the Size of Joins (Cont.): Estimation of the Size of Joins (Cont.) Compute the size estimates for depositor customer without using information about foreign keys:
V(customer_name, depositor) = 2500, and V(customer_name, customer) = 10000
The two estimates are 5000 * 10000/2500 - 20,000 and 5000 * 10000/10000 = 5000
We choose the lower estimate, which in this case, is the same as our earlier computation using foreign keys.
Size Estimation for Other Operations: Size Estimation for Other Operations Projection: estimated size of A(r) = V(A,r)
Aggregation : estimated size of AgF(r) = V(A,r)
Set operations
For unions/intersections of selections on the same relation: rewrite and use size estimate for selections
E.g. 1 (r) 2 (r) can be rewritten as 1 2 (r)
For operations on different relations:
estimated size of r s = size of r + size of s.
estimated size of r s = minimum size of r and size of s.
estimated size of r – s = r.
All the three estimates may be quite inaccurate, but provide upper bounds on the sizes.
Size Estimation (Cont.): Size Estimation (Cont.) Outer join:
Estimated size of r s = size of r s + size of r
Case of right outer join is symmetric
Estimated size of r s = size of r s + size of r + size of s
Estimation of Number of Distinct Values: Estimation of Number of Distinct Values Selections: (r)
If forces A to take a specified value: V(A, (r)) = 1.
e.g., A = 3
If forces A to take on one of a specified set of values: V(A, (r)) = number of specified values.
(e.g., (A = 1 V A = 3 V A = 4 )),
If the selection condition is of the form A op r estimated V(A, (r)) = V(A.r) * s
where s is the selectivity of the selection.
In all the other cases: use approximate estimate of min(V(A,r), n (r) )
More accurate estimate can be got using probability theory, but this one works fine generally
Estimation of Distinct Values (Cont.): Estimation of Distinct Values (Cont.) Joins: r s
If all attributes in A are from r estimated V(A, r s) = min (V(A,r), n r s)
If A contains attributes A1 from r and A2 from s, then estimated V(A,r s) =
min(V(A1,r)*V(A2 – A1,s), V(A1 – A2,r)*V(A2,s), nr s)
More accurate estimate can be got using probability theory, but this one works fine generally
Estimation of Distinct Values (Cont.): Estimation of Distinct Values (Cont.) Estimation of distinct values are straightforward for projections.
They are the same in A (r) as in r.
The same holds for grouping attributes of aggregation.
For aggregated values
For min(A) and max(A), the number of distinct values can be estimated as min(V(A,r), V(G,r)) where G denotes grouping attributes
For other aggregates, assume all values are distinct, and use V(G,r)
Additional Optimization Techniques: Additional Optimization Techniques Nested Subqueries
Materialized Views
Optimizing Nested Subqueries**: Optimizing Nested Subqueries** Nested query example: select customer_name from borrower where exists (select * from depositor where depositor.customer_name = borrower.customer_name)
SQL conceptually treats nested subqueries in the where clause as functions that take parameters and return a single value or set of values
Parameters are variables from outer level query that are used in the nested subquery; such variables are called correlation variables
Conceptually, nested subquery is executed once for each tuple in the cross-product generated by the outer level from clause
Such evaluation is called correlated evaluation
Note: other conditions in where clause may be used to compute a join (instead of a cross-product) before executing the nested subquery
Optimizing Nested Subqueries (Cont.): Optimizing Nested Subqueries (Cont.) Correlated evaluation may be quite inefficient since
a large number of calls may be made to the nested query
there may be unnecessary random I/O as a result
SQL optimizers attempt to transform nested subqueries to joins where possible, enabling use of efficient join techniques
E.g.: earlier nested query can be rewritten as select customer_name from borrower, depositor where depositor.customer_name = borrower.customer_name
Note: the two queries generate different numbers of duplicates (why?)
Borrower can have duplicate customer-names
Can be modified to handle duplicates correctly as we will see
In general, it is not possible/straightforward to move the entire nested subquery from clause into the outer level query from clause
A temporary relation is created instead, and used in body of outer level query
Optimizing Nested Subqueries (Cont.): Optimizing Nested Subqueries (Cont.) In general, SQL queries of the form below can be rewritten as shown
Rewrite: select … from L1 where P1 and exists (select * from L2 where P2)
To: create table t1 as select distinct V from L2 where P21 select … from L1, t1 where P1 and P22
P21 contains predicates in P2 that do not involve any correlation variables
P22 reintroduces predicates involving correlation variables, with relations renamed appropriately
V contains all attributes used in predicates with correlation variables
Optimizing Nested Subqueries (Cont.): Optimizing Nested Subqueries (Cont.) In our example, the original nested query would be transformed to create table t1 as select distinct customer_name from depositor select customer_name from borrower, t1 where t1.customer_name = borrower.customer_name
The process of replacing a nested query by a query with a join (possibly with a temporary relation) is called decorrelation.
Decorrelation is more complicated when
the nested subquery uses aggregation, or
when the result of the nested subquery is used to test for equality, or
when the condition linking the nested subquery to the other query is not exists,
and so on.
Materialized Views**: Materialized Views** A materialized view is a view whose contents are computed and stored.
Consider the view create view branch_total_loan(branch_name, total_loan) as select branch_name, sum(amount) from loan group by branch_name
Materializing the above view would be very useful if the total loan amount is required frequently
Saves the effort of finding multiple tuples and adding up their amounts
Materialized View Maintenance: Materialized View Maintenance The task of keeping a materialized view up-to-date with the underlying data is known as materialized view maintenance
Materialized views can be maintained by recomputation on every update
A better option is to use incremental view maintenance
Changes to database relations are used to compute changes to the materialized view, which is then updated
View maintenance can be done by
Manually defining triggers on insert, delete, and update of each relation in the view definition
Manually written code to update the view whenever database relations are updated
Periodic recomputation (e.g. nightly)
Above methods are directly supported by many database systems
Avoids manual effort/correctness issues
Incremental View Maintenance: Incremental View Maintenance The changes (inserts and deletes) to a relation or expressions are referred to as its differential
Set of tuples inserted to and deleted from r are denoted ir and dr
To simplify our description, we only consider inserts and deletes
We replace updates to a tuple by deletion of the tuple followed by insertion of the update tuple
We describe how to compute the change to the result of each relational operation, given changes to its inputs
We then outline how to handle relational algebra expressions
Join Operation: Join Operation Consider the materialized view v = r s and an update to r
Let rold and rnew denote the old and new states of relation r
Consider the case of an insert to r:
We can write rnew s as (rold ir) s
And rewrite the above to (rold s) (ir s)
But (rold s) is simply the old value of the materialized view, so the incremental change to the view is just ir s
Thus, for inserts vnew = vold (ir s)
Similarly for deletes vnew = vold – (dr s) A, 1
B, 2 1, p
2, r
2, s A, 1, p
B, 2, r
B, 2, s
Selection and Projection Operations: Selection and Projection Operations Selection: Consider a view v = (r).
vnew = vold (ir)
vnew = vold - (dr)
Projection is a more difficult operation
R = (A,B), and r(R) = { (a,2), (a,3)}
A(r) has a single tuple (a).
If we delete the tuple (a,2) from r, we should not delete the tuple (a) from A(r), but if we then delete (a,3) as well, we should delete the tuple
For each tuple in a projection A(r) , we will keep a count of how many times it was derived
On insert of a tuple to r, if the resultant tuple is already in A(r) we increment its count, else we add a new tuple with count = 1
On delete of a tuple from r, we decrement the count of the corresponding tuple in A(r)
if the count becomes 0, we delete the tuple from A(r)
Aggregation Operations: Aggregation Operations count : v = Agcount(B)(r).
When a set of tuples ir is inserted
For each tuple r in ir, if the corresponding group is already present in v, we increment its count, else we add a new tuple with count = 1
When a set of tuples dr is deleted
for each tuple t in ir.we look for the group t.A in v, and subtract 1 from the count for the group.
If the count becomes 0, we delete from v the tuple for the group t.A
sum: v = Agsum (B)(r)
We maintain the sum in a manner similar to count, except we add/subtract the B value instead of adding/subtracting 1 for the count
Additionally we maintain the count in order to detect groups with no tuples. Such groups are deleted from v
Cannot simply test for sum = 0 (why?)
To handle the case of avg, we maintain the sum and count aggregate values separately, and divide at the end
Aggregate Operations (Cont.): Aggregate Operations (Cont.) min, max: v = Agmin (B) (r).
Handling insertions on r is straightforward.
Maintaining the aggregate values min and max on deletions may be more expensive. We have to look at the other tuples of r that are in the same group to find the new minimum
Other Operations: Other Operations Set intersection: v = r s
when a tuple is inserted in r we check if it is present in s, and if so we add it to v.
If the tuple is deleted from r, we delete it from the intersection if it is present.
Updates to s are symmetric
The other set operations, union and set difference are handled in a similar fashion.
Outer joins are handled in much the same way as joins but with some extra work
we leave details to you.
Handling Expressions: Handling Expressions To handle an entire expression, we derive expressions for computing the incremental change to the result of each sub-expressions, starting from the smallest sub-expressions.
E.g. consider E1 E2 where each of E1 and E2 may be a complex expression
Suppose the set of tuples to be inserted into E1 is given by D1
Computed earlier, since smaller sub-expressions are handled first
Then the set of tuples to be inserted into E1 E2 is given by D1 E2
This is just the usual way of maintaining joins
Query Optimization and Materialized Views: Query Optimization and Materialized Views Rewriting queries to use materialized views:
A materialized view v = r s is available
A user submits a query r s t
We can rewrite the query as v t
Whether to do so depends on cost estimates for the two alternative
Replacing a use of a materialized view by the view definition:
A materialized view v = r s is available, but without any index on it
User submits a query A=10(v).
Suppose also that s has an index on the common attribute B, and r has an index on attribute A.
The best plan for this query may be to replace v by r s, which can lead to the query plan A=10(r) s
Query optimizer should be extended to consider all above alternatives and choose the best overall plan
Materialized View Selection: Materialized View Selection Materialized view selection: “What is the best set of views to materialize?”.
Index selection: “what is the best set of indices to create”
closely related, to materialized view selection
but simpler
Materialized view selection and index selection based on typical system workload (queries and updates)
Typical goal: minimize time to execute workload , subject to constraints on space and time taken for some critical queries/updates
One of the steps in database tuning
more on tuning in later chapters
Commercial database systems provide tools (called “tuning assistants” or “wizards”) to help the database administrator choose what indices and materialized views to create
Extra Slides:Additional Optimization Techniques: Extra Slides: Additional Optimization Techniques (see bibliographic notes)
Top-K Queries : Top-K Queries Top-K queries
select * from r, s where r.B = s.B order by r.A ascending limit 10
Alternative 1: Indexed nested loops join with r as outer
Alternative 2: estimate highest r.A value in result and add selection (and r.A <= H) to where clause
If < 10 results, retry with larger H
Optimization of Updates: Optimization of Updates Halloween problem
update R set A = 5 * A where A > 10
If index on A is used to find tuples satisfying A > 10, and tuples updated immediately, same tuple may be found (and updated) multiple times
Solution 1: Always defer updates
collect the updates (old and new values of tuples) and update relation and indices in second pass
Drawback: extra overhead even if e.g. update is only on R.B, not on attributes in selection condition
Solution 2: Defer only if required
Perform immediate update if update does not affect attributes in where clause, and deferred updates otherwise.
Parametric Query Optimization: Parametric Query Optimization Example select * from r natural join s where r.a < $1
value of parameter $1 not known at compile time
known only at run time
different plans may be optimal for different values of $1
Solution 1: optimize at run time, each time query is submitted
can be expensive
Solution 2: Parametric Query Optimization:
optimizer generates a set of plans, optimal for different values of $1
Set of optimal plans usually small for 1 to 3 parameters
Key issue: how to do find set of optimal plans efficiently
best one from this set is chosen at run time when $1 is known
Solution 3: Query Plan Caching
If optimizer decides that same plan is likely to be optimal for all parameter values, it caches plan and reuses it, else reoptimize each time
Implemented in many database systems
Join Minimization: Join Minimization Join minimization
select r.A, r.B from r, s where r.B = s.B
Check if join with s is redundant, drop it
E.g. join condition is on foreign key from r to s, no selection on s
Other sufficient conditions possible select r.A, s1.B from r, s as s1, s as s2 where r.B=s1.B and r.B = s2.B and s1.A < 20 and s2.A < 10
join with s2 is redundant and can be dropped (along with selection on s2)
Lots of research in this area since 70s/80s!
Multiquery Optimization: Multiquery Optimization Example
Q1: select * from (r natural join t) natural join s
Q2: select * from (r natural join u) natural join s
Both queries share common subexpression (r natural join s)
May be useful to compute (r natural join s) once and use it in both queries
But this may be more expensive in some situations
e.g. (r natural join s) may be expensive, plans as shown in queries may be cheaper
Multiquery optimization: find best overall plan for a set of queries, expoiting sharing of common subexpressions between queries where it is useful
Simple heuristic used in some database systems:
optimize each query separately
detect and exploiting common subexpressions in the individual optimal query plans
May not always give best plan, but is cheap to implement
Set of materialized views may share common subexpressions
As a result, view maintenance plans may share subexpressions
Multiquery optimization can be useful in such situations
End of Chapter: End of Chapter