Chapter2.ppt Algorithms Query processing and Optimization

Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe
Chapter 2
Algorithms for Query Processing
and Optimization

Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 15- 2
Chapter Outline (1)
0. Introduction to Query Processing
1. Translating SQL Queries into Relational Algebra
2. Algorithms for External Sorting
3. Algorithms for SELECT and JOIN Operations
4. Algorithms for PROJECT and SET Operations
5. Implementing Aggregate Operations and Outer Joins
6. Combining Operations using Pipelining
7. Using Heuristics in Query Optimization
8. Using Selectivity and Cost Estimates in Query
Optimization
9. Overview of Query Optimization in Oracle
10. Semantic Query Optimization

0. Introduction to Query Processing (1)
 Query optimization:
 The process of choosing a suitable execution
strategy for processing a query.
 Two internal representations of a query:
 Query Tree
 Query Graph

Introduction to Query Processing (2)

1. Translating SQL Queries into Relational
Algebra (1)
 Query block:
 The basic unit that can be translated into the
algebraic operators and optimized.
 A query block contains a single SELECT-FROM-
WHERE expression, as well as GROUP BY and
HAVING clause if these are part of the block.
 Nested queries within a query are identified as
separate query blocks.
 Aggregate operators in SQL must be included in
the extended algebra.

Translating SQL Queries into Relational
Algebra (2)
SELECT LNAME, FNAME
FROM EMPLOYEE
WHERE SALARY > ( SELECT MAX (SALARY)
FROM EMPLOYEE
WHERE DNO = 5);
SELECT MAX (SALARY)
FROM EMPLOYEE
WHERE DNO = 5
SELECT LNAME, FNAME
FROM EMPLOYEE
WHERE SALARY > C
πLNAME, FNAME (σSALARY>C(EMPLOYEE)) ℱMAX SALARY (σDNO=5 (EMPLOYEE))

2. Algorithms for External Sorting (1)
 External sorting:

Refers to sorting algorithms that are suitable for large files
of records stored on disk that do not fit entirely in main
memory, such as most database files.
 Sort-Merge strategy:

Starts by sorting small subfiles (runs) of the main file and
then merges the sorted runs, creating larger sorted subfiles
that are merged in turn.

Sorting phase: nR = (b/nB)

Merging phase: dM = Min (nB-1, nR); nP = (logdM(nR))

nR: number of initial runs; b: number of file blocks;

nB: available buffer space; dM: degree of merging;

nP: number of passes.

Algorithms for External Sorting (2)

3. Algorithms for SELECT and JOIN
Operations (1)
 Implementing the SELECT Operation
 Examples:
 (OP1):  SSN='123456789' (EMPLOYEE)
 (OP2):  DNUMBER>5(DEPARTMENT)
 (OP3):  DNO=5(EMPLOYEE)
 (OP4):  DNO=5 AND SALARY>30000 AND SEX=F(EMPLOYEE)
 (OP5):  ESSN=123456789 AND PNO=10(WORKS_ON)

Algorithms for SELECT and JOIN
Operations (2)
 Implementing the SELECT Operation (contd.):
 Search Methods for Simple Selection:

S1 Linear search (brute force):

Retrieve every record in the file, and test whether its attribute
values satisfy the selection condition.
 S2 Binary search:

If the selection condition involves an equality comparison on a
key attribute on which the file is ordered, binary search (which
is more efficient than linear search) can be used. (See OP1).

S3 Using a primary index or hash key to retrieve a
single record:

If the selection condition involves an equality comparison on a
key attribute with a primary index (or a hash key), use the
primary index (or the hash key) to retrieve the record.

Operations (3)
 S4 Using a primary index to retrieve multiple records:

If the comparison condition is >, ≥, <, or ≤ on a key field with a
primary index, use the index to find the record satisfying the
corresponding equality condition, then retrieve all subsequent records
in the (ordered) file.

S5 Using a clustering index to retrieve multiple records:

If the selection condition involves an equality comparison on a non-
key attribute with a clustering index, use the clustering index to
retrieve all the records satisfying the selection condition.

S6 Using a secondary (B+-tree) index:

On an equality comparison, this search method can be used to
retrieve a single record if the indexing field has unique values (is a
key) or to retrieve multiple records if the indexing field is not a key.

In addition, it can be used to retrieve records on conditions involving
>,>=, <, or <=. (FOR RANGE QUERIES)

Operations (4)
 S7 Conjunctive selection:

If an attribute involved in any single simple condition in the
conjunctive condition has an access path that permits the use
of one of the methods S2 to S6, use that condition to retrieve
the records and then check whether each retrieved record
satisfies the remaining simple conditions in the conjunctive
condition.
 S8 Conjunctive selection using a composite index

If two or more attributes are involved in equality conditions in
the conjunctive condition and a composite index (or hash
structure) exists on the combined field, we can use the index
directly.

Operations (5)
 Search Methods for Complex Selection:

S9 Conjunctive selection by intersection of record
pointers:

This method is possible if secondary indexes are available on
all (or some of) the fields involved in equality comparison
conditions in the conjunctive condition and if the indexes
include record pointers (rather than block pointers).

Each index can be used to retrieve the record pointers that
satisfy the individual condition.

The intersection of these sets of record pointers gives the
record pointers that satisfy the conjunctive condition, which
are then used to retrieve those records directly.

If only some of the conditions have secondary indexes, each
retrieved record is further tested to determine whether it
satisfies the remaining conditions.

Operations (7)
 Whenever a single condition specifies the selection, we
can only check whether an access path exists on the
attribute involved in that condition.

If an access path exists, the method corresponding to that
access path is used; otherwise, the “brute force” linear search
approach of method S1 is used. (See OP1, OP2 and OP3)
 For conjunctive selection conditions, whenever more
than one of the attributes involved in the conditions have an
access path, query optimization should be done to choose
the access path that retrieves the fewest records in the
most efficient way.
 Disjunctive selection conditions

Operations (8)
 Implementing the JOIN Operation:
 Join (EQUIJOIN, NATURAL JOIN)

two–way join: a join on two files
 e.g. R A=B S

multi-way joins: joins involving more than two files.
 e.g. R A=B S C=D T
 Examples
 (OP6): EMPLOYEE DNO=DNUMBER DEPARTMENT
 (OP7): DEPARTMENT MGRSSN=SSN EMPLOYEE

Operations (9)
 Implementing the JOIN Operation (contd.):
 Methods for implementing joins:
 J1 Nested-loop join (brute force):

For each record t in R (outer loop), retrieve every record s
from S (inner loop) and test whether the two records satisfy
the join condition t[A] = s[B].
 J2 Single-loop join (Using an access structure to retrieve
the matching records):

If an index (or hash key) exists for one of the two join
attributes — say, B of S — retrieve each record t in R, one at a
time, and then use the access structure to retrieve directly all
matching records s from S that satisfy s[B] = t[A].

Operations (10)
 J3 Sort-merge join:

If the records of R and S are physically sorted (ordered) by
value of the join attributes A and B, respectively, we can
implement the join in the most efficient way possible.

Both files are scanned in order of the join attributes, matching
the records that have the same values for A and B.

In this method, the records of each file are scanned only once
each for matching with the other file—unless both A and B are
non-key attributes, in which case the method needs to be
modified slightly.

Operations (11)
 J4 Hash-join:

The records of files R and S are both hashed to the
same hash file, using the same hashing function on
the join attributes A of R and B of S as hash keys.

A single pass through the file with fewer records
(say, R) hashes its records to the hash file buckets.

A single pass through the other file (S) then hashes
each of its records to the appropriate bucket, where
the record is combined with all matching records
from R.

Operations (12)

Operations (13)

Operations (14)
 Factors affecting JOIN performance
 Available buffer space
 Join selection factor
 Choice of inner VS outer relation

Operations (15)
 Other types of JOIN algorithms
 Partition hash join
 Partitioning phase:

Each file (R and S) is first partitioned into M partitions using a
partitioning hash function on the join attributes:

R1 , R2 , R3 , ...... Rm and S1 , S2 , S3 , ...... Sm

Minimum number of in-memory buffers needed for the
partitioning phase: M+1.

A disk sub-file is created per partition to store the tuples for
that partition.

Joining or probing phase:

Involves M iterations, one per partitioned file.

Iteration i involves joining partitions Ri and Si.

Operations (16)
 Partitioned Hash Join Procedure:
 Assume Ri is smaller than Si.
1. Copy records from Ri into memory buffers.
2. Read all blocks from Si, one at a time and each
record from Si is used to probe for a matching
record(s) from partition Si.
3. Write matching record from Ri after joining to the
record from Si into the result file.

Operations (17)
 Cost analysis of partition hash join:
1. Reading and writing each record from R and S during the
partitioning phase:
(bR + bS), (bR + bS)
2. Reading each record during the joining phase:
(bR + bS)
3. Writing the result of join:
bRES
 Total Cost:
 3* (bR + bS) + bRES

Operations (18)
 Hybrid hash join:

Same as partitioned hash join except:

Joining phase of one of the partitions is included during the
partitioning phase.
 Partitioning phase:

Allocate buffers for smaller relation- one block for each of the
M-1 partitions, remaining blocks to partition 1.

Repeat for the larger relation in the pass through S.)
 Joining phase:

M-1 iterations are needed for the partitions R2 , R3 ,
R4 , ......Rm and S2 , S3 , S4 , ......Sm. R1 and S1 are joined
during the partitioning of S1, and results of joining R1 and S1
are already written to the disk by the end of partitioning phase.

4. Algorithms for PROJECT and SET
Operations (1)
 Algorithm for PROJECT operations (Figure 15.3b)
 <attribute list>(R)
1. If <attribute list> has a key of relation R, extract all tuples
from R with only the values for the attributes in <attribute
list>.
2. If <attribute list> does NOT include a key of relation R,
duplicated tuples must be removed from the results.
 Methods to remove duplicate tuples
1. Sorting
2. Hashing

Algorithms for PROJECT and SET
Operations (2)
 Algorithm for SET operations
 Set operations:

UNION, INTERSECTION, SET DIFFERENCE and
CARTESIAN PRODUCT
 CARTESIAN PRODUCT of relations R and S include all
possible combinations of records from R and S. The
attribute of the result include all attributes of R and S.
 Cost analysis of CARTESIAN PRODUCT

If R has n records and j attributes and S has m records and
k attributes, the result relation will have n*m records and j+k
attributes.
 CARTESIAN PRODUCT operation is very expensive and
should be avoided if possible.

Algorithms for PROJECT and SET
Operations (3)
 Algorithm for SET operations (contd.)
 UNION (See Figure 15.3c)

Sort the two relations on the same attributes.

Scan and merge both sorted files concurrently, whenever
the same tuple exists in both relations, only one is kept in
the merged results.
 INTERSECTION (See Figure 15.3d)

Sort the two relations on the same attributes.

Scan and merge both sorted files concurrently, keep in the
merged results only those tuples that appear in both
relations.
 SET DIFFERENCE R-S (See Figure 15.3e)

Keep in the merged results only those tuples that appear in
relation R but not in relation S.

5. Implementing Aggregate Operations
and Outer Joins (1)
 Implementing Aggregate Operations:
 Aggregate operators:
 MIN, MAX, SUM, COUNT and AVG
 Options to implement aggregate operators:
 Table Scan
 Index
 Example
 SELECT MAX (SALARY)
 FROM EMPLOYEE;
 If an (ascending) index on SALARY exists for the employee relation,
then the optimizer could decide on traversing the index for the largest
value, which would entail following the right most pointer in each
index node from the root to a leaf.

Implementing Aggregate Operations and
Outer Joins (2)
 Implementing Aggregate Operations (contd.):
 SUM, COUNT and AVG
 For a dense index (each record has one index entry):
 Apply the associated computation to the values in the index.
 For a non-dense index:
 Actual number of records associated with each index entry must
be accounted for
 With GROUP BY: the aggregate operator must be applied separately
to each group of tuples.
 Use sorting or hashing on the group attributes to partition the file
into the appropriate groups;
 Computes the aggregate function for the tuples in each group.
 What if we have Clustering index on the grouping attributes?

Outer Joins (3)
 Implementing Outer Join:
 Outer Join Operators:
 LEFT OUTER JOIN

RIGHT OUTER JOIN

FULL OUTER JOIN.
 The full outer join produces a result which is equivalent to the union of the
results of the left and right outer joins.
 Example:
SELECT FNAME, DNAME
FROM (EMPLOYEE LEFT OUTER JOIN DEPARTMENT
ON DNO = DNUMBER);
 Note: The result of this query is a table of employee names and their
associated departments. It is similar to a regular join result, with the exception
that if an employee does not have an associated department, the employee's
name will still appear in the resulting table, although the department name
would be indicated as null.

Outer Joins (4)
 Implementing Outer Join (contd.):
 Modifying Join Algorithms:
 Nested Loop or Sort-Merge joins can be modified to
implement outer join. E.g.,

For left outer join, use the left relation as outer relation and
construct result from every tuple in the left relation.

If there is a match, the concatenated tuple is saved in the
result.

However, if an outer tuple does not match, then the tuple is
still included in the result but is padded with a null value(s).

Outer Joins (5)
 Implementing Outer Join (contd.):
 Executing a combination of relational algebra operators.
 Implement the previous left outer join example

{Compute the JOIN of the EMPLOYEE and DEPARTMENT
tables}

TEMP1FNAME,DNAME(EMPLOYEE DNO=DNUMBER DEPARTMENT)
 {Find the EMPLOYEEs that do not appear in the JOIN}

TEMP2   FNAME (EMPLOYEE) - FNAME (Temp1)

{Pad each tuple in TEMP2 with a null DNAME field}

TEMP2  TEMP2 x 'null'

{UNION the temporary tables to produce the LEFT OUTER JOIN}

RESULT  TEMP1 υ TEMP2
 The cost of the outer join, as computed above, would include the cost
of the associated steps (i.e., join, projections and union).

(1)
 Motivation
 A query is mapped into a sequence of operations.
 Each execution of an operation produces a temporary
result.
 Generating and saving temporary files on disk is time
consuming and expensive.
 Alternative:
 Avoid constructing temporary results as much as possible.
 Pipeline the data through multiple operations - pass the
result of a previous operator to the next without waiting to
complete the previous operation.

Combining Operations using Pipelining (2)
 Example:
 For a 2-way join, combine the 2 selections on the
input and one projection on the output with the
Join.
 Dynamic generation of code to allow for multiple
operations to be pipelined.
 Results of a select operation are fed in a
"Pipeline" to the join algorithm.
 Also known as stream-based processing.

7. Using Heuristics in Query
Optimization(1)
 Process for heuristics optimization
1. The parser of a high-level query generates an initial
internal representation;
2. Apply heuristics rules to optimize the internal
representation.
3. A query execution plan is generated to execute groups of
operations based on the access paths available on the files
involved in the query.
 The main heuristic is to apply first the operations that
reduce the size of intermediate results.
 E.g., Apply SELECT and PROJECT operations before
applying the JOIN or other binary operations.

Using Heuristics in Query Optimization (2)
 Query tree:

A tree data structure that corresponds to a relational
algebra expression. It represents the input relations of the
query as leaf nodes of the tree, and represents the
relational algebra operations as internal nodes.
 An execution of the query tree consists of executing an
internal node operation whenever its operands are
available and then replacing that internal node by the
relation that results from executing the operation.
 Query graph:
 A graph data structure that corresponds to a relational
calculus expression. It does not indicate an order on which
operations to perform first. There is only a single graph
corresponding to each query.

 Example:

For every project located in ‘Stafford’, retrieve the project number,
the controlling department number and the department manager’s
last name, address and birthdate.
 Relation algebra:
PNUMBER, DNUM, LNAME, ADDRESS, BDATE (((PLOCATION=‘STAFFORD’(PROJECT))
DNUM=DNUMBER (DEPARTMENT)) MGRSSN=SSN (EMPLOYEE))
 SQL query:
Q2: SELECT P.NUMBER,P.DNUM,E.LNAME,
E.ADDRESS, E.BDATE
FROM PROJECT AS P,DEPARTMENT AS D, EMPLOYEE AS E
WHERE P.DNUM=D.DNUMBER AND
D.MGRSSN=E.SSN AND
P.PLOCATION=‘STAFFORD’;

 Heuristic Optimization of Query Trees:
 The same query could correspond to many different
relational algebra expressions — and hence many different
query trees.
 The task of heuristic optimization of query trees is to find a
final query tree that is efficient to execute.
 Example:
Q: SELECT LNAME
FROM EMPLOYEE, WORKS_ON,
PROJECT
WHERE PNAME = ‘AQUARIUS’ AND
PNMUBER=PNO AND ESSN=SSN
AND BDATE > ‘1957-12-31’;

 General Transformation Rules for Relational Algebra Operations:
1. Cascade of : A conjunctive selection condition can be broken up into
a cascade (sequence) of individual  operations:

 c1 AND c2 AND ... AND cn(R) = c1 (c2 (...(cn(R))...) )
2. Commutativity of : The  operation is commutative:

c1 (c2(R)) = c2 (c1(R))
3. Cascade of : In a cascade (sequence) of  operations, all but the
last one can be ignored:

List1 (List2 (...(Listn(R))...) ) = List1(R)
4. Commuting  with : If the selection condition c involves only the
attributes A1, ..., An in the projection list, the two operations can be
commuted:

A1, A2, ..., An (c (R)) = c (A1, A2, ..., An (R))

Using Heuristics in Query Optimization
(10)
 General Transformation Rules for Relational Algebra Operations
(contd.):
5. Commutativity of ( and x ): The operation is commutative as is
the x operation:

R C S = S C R; R x S = S x R
6. Commuting  with (or x ): If all the attributes in the selection
condition c involve only the attributes of one of the relations being
joined—say, R—the two operations can be commuted as follows:

c ( R S ) = (c (R)) S
 Alternatively, if the selection condition c can be written as (c1 and c2),
where condition c1 involves only the attributes of R and condition c2
involves only the attributes of S, the operations commute as follows:

c ( R S ) = (c1 (R)) (c2 (S))

(11)
 General Transformation Rules for Relational Algebra
Operations (contd.):
7. Commuting  with (or x): Suppose that the projection list
is L = {A1, ..., An, B1, ..., Bm}, where A1, ..., An are
attributes of R and B1, ..., Bm are attributes of S. If the
join condition c involves only attributes in L, the two
operations can be commuted as follows:
 L ( R C S ) = (A1, ..., An (R)) C ( B1, ..., Bm (S))
 If the join condition C contains additional attributes not in
L, these must be added to the projection list, and a final 
operation is needed.

(12)
8. Commutativity of set operations: The set operations υ and
∩ are commutative but “–” is not.
9. Associativity of , x, υ, and ∩ : These four operations are
individually associative; that is, if  stands for any one of
these four operations (throughout the expression), we
have
 ( R  S )  T = R  ( S  T )
10. Commuting  with set operations: The  operation
commutes with υ , ∩ , and –. If  stands for any one of
these three operations, we have

c ( R  S ) = (c (R))  (c (S))

(13)
 The  operation commutes with υ. L ( R υ S ) = (L
(R)) υ (L (S))
 Converting a (, x) sequence into : If the condition c of a 
that follows a x Corresponds to a join condition, convert the
(, x) sequence into a as follows: (C (R x S)) = (R
C S)
 Other transformations

(14)
 Outline of a Heuristic Algebraic Optimization Algorithm:
1. Using rule 1, break up any select operations with conjunctive conditions into
a cascade of select operations.
2. Using rules 2, 4, 6, and 10 concerning the commutativity of select with other
operations, move each select operation as far down the query tree as is
permitted by the attributes involved in the select condition.
3. Using rule 9 concerning associativity of binary operations, rearrange the leaf
nodes of the tree so that the leaf node relations with the most restrictive
select operations are executed first in the query tree representation.
4. Using Rule 12, combine a Cartesian product operation with a subsequent
select operation in the tree into a join operation.
5. Using rules 3, 4, 7, and 11 concerning the cascading of project and the
commuting of project with other operations, break down and move lists of
projection attributes down the tree as far as possible by creating new project
operations as needed.
6. Identify subtrees that represent groups of operations that can be executed by
a single algorithm.

(15)
 Summary of Heuristics for Algebraic Optimization:
1. The main heuristic is to apply first the operations that
reduce the size of intermediate results.
2. Perform select operations as early as possible to reduce
the number of tuples and perform project operations as
early as possible to reduce the number of attributes. (This
is done by moving select and project operations as far
down the tree as possible.)
3. The select and join operations that are most restrictive
should be executed before other similar operations. (This
is done by reordering the leaf nodes of the tree among
themselves and adjusting the rest of the tree
appropriately.)

(16)
 Query Execution Plans
 An execution plan for a relational algebra query consists of
a combination of the relational algebra query tree and
information about the access methods to be used for each
relation as well as the methods to be used in computing the
relational operators stored in the tree.
 Materialized evaluation: the result of an operation is stored
as a temporary relation.
 Pipelined evaluation: as the result of an operator is
produced, it is forwarded to the next operator in sequence.

8. Using Selectivity and Cost Estimates in
Query Optimization (1)
 Cost-based query optimization:
 Estimate and compare the costs of executing a
query using different execution strategies and
choose the strategy with the lowest cost estimate.
 (Compare to heuristic query optimization)
 Issues
 Cost function
 Number of execution strategies to be considered

Using Selectivity and Cost Estimates in
 Cost Components for Query Execution
1. Access cost to secondary storage
2. Storage cost
3. Computation cost
4. Memory usage cost
5. Communication cost
 Note: Different database systems may focus on
different cost components.

 Catalog Information Used in Cost Functions
 Information about the size of a file

number of records (tuples) (r),

record size (R),

number of blocks (b)

blocking factor (bfr)
 Information about indexes and indexing attributes of a file

Number of levels (x) of each multilevel index

Number of first-level index blocks (bI1)

Number of distinct values (d) of an attribute

Selectivity (sl) of an attribute

Selection cardinality (s) of an attribute. (s = sl * r)

 Examples of Cost Functions for SELECT
 S1. Linear search (brute force) approach

CS1a = b;

For an equality condition on a key, CS1a = (b/2) if the record is
found; otherwise CS1a = b.
 S2. Binary search:

CS2 = log2b + (s/bfr) –1

For an equality condition on a unique (key) attribute, CS2
=log2b
 S3. Using a primary index (S3a) or hash key (S3b) to
retrieve a single record

CS3a = x + 1; CS3b = 1 for static or linear hashing;

CS3b = 1 for extendible hashing;

 Examples of Cost Functions for SELECT (contd.)
 S4. Using an ordering index to retrieve multiple records:
 For the comparison condition on a key field with an ordering
index, CS4 = x + (b/2)
 S5. Using a clustering index to retrieve multiple records:
 CS5 = x + ┌ (s/bfr) ┐
 S6. Using a secondary (B+-tree) index:
 For an equality comparison, CS6a = x + s;
 For an comparison condition such as >, <, >=, or <=,
 CS6a = x + (bI1/2) + (r/2)

 Examples of Cost Functions for SELECT (contd.)
 S7. Conjunctive selection:
 Use either S1 or one of the methods S2 to S6 to solve.
 For the latter case, use one condition to retrieve the records
and then check in the memory buffer whether each retrieved
record satisfies the remaining conditions in the conjunction.
 S8. Conjunctive selection using a composite index:
 Same as S3a, S5 or S6a, depending on the type of index.
 Examples of using the cost functions.

 Examples of Cost Functions for JOIN
 Join selectivity (js)
 js = | (R C S) | / | R x S | = | (R C S) | / (|R| * |S |)

If condition C does not exist, js = 1;

If no tuples from the relations satisfy condition C, js =
0;

Usually, 0 <= js <= 1;
 Size of the result file after join operation
 | (R C S) | = js * |R| * |S |

 Examples of Cost Functions for JOIN (contd.)
 J1. Nested-loop join:
 CJ1 = bR + (bR*bS) + ((js* |R|* |S|)/bfrRS)
 (Use R for outer loop)
 J2. Single-loop join (using an access structure to retrieve
the matching record(s))
 If an index exists for the join attribute B of S with index
levels xB, we can retrieve each record s in R and then use
the index to retrieve all the matching records t from S that
satisfy t[B] = s[A].
 The cost depends on the type of index.

 Examples of Cost Functions for JOIN (contd.)
 J2. Single-loop join (contd.)

For a secondary index,

CJ2a = bR + (|R| * (xB + sB)) + ((js* |R|* |S|)/bfrRS);

For a clustering index,

CJ2b = bR + (|R| * (xB + (sB/bfrB))) + ((js* |R|* |S|)/bfrRS);

For a primary index,

CJ2c = bR + (|R| * (xB + 1)) + ((js* |R|* |S|)/bfrRS);

If a hash key exists for one of the two join attributes — B of S

CJ2d = bR + (|R| * h) + ((js* |R|* |S|)/bfrRS);
 J3. Sort-merge join:

CJ3a = CS + bR + bS + ((js* |R|* |S|)/bfrRS);

(CS: Cost for sorting files)

 Multiple Relation Queries and Join Ordering
 A query joining n relations will have n-1 join operations, and
hence can have a large number of different join orders when
we apply the algebraic transformation rules.
 Current query optimizers typically limit the structure of a
(join) query tree to that of left-deep (or right-deep) trees.
 Left-deep tree:
 A binary tree where the right child of each non-leaf node is
always a base relation.

Amenable to pipelining

Could utilize any access paths on the base relation (the right
child) when executing the join.

9. Overview of Query Optimization in
Oracle
 Oracle DBMS V8
 Rule-based query optimization: the optimizer chooses
execution plans based on heuristically ranked operations.

(Currently it is being phased out)
 Cost-based query optimization: the optimizer examines
alternative access paths and operator algorithms and
chooses the execution plan with lowest estimate cost.

The query cost is calculated based on the estimated usage of
resources such as I/O, CPU and memory needed.
 Application developers could specify hints to the ORACLE
query optimizer.
 The idea is that an application developer might know more
information about the data.

 Semantic Query Optimization:

Uses constraints specified on the database schema in order to
modify one query into another query that is more efficient to
execute.
 Consider the following SQL query,
SELECT E.LNAME, M.LNAME
FROM EMPLOYEE E M
WHERE E.SUPERSSN=M.SSN AND E.SALARY>M.SALARY
 Explanation:

Suppose that we had a constraint on the database schema that
stated that no employee can earn more than his or her direct
supervisor. If the semantic query optimizer checks for the
existence of this constraint, it need not execute the query at all
because it knows that the result of the query will be empty.
Techniques known as theorem proving can be used for this
purpose.

Summary
0. Introduction to Query Processing
1. Translating SQL Queries into Relational Algebra
2. Algorithms for External Sorting
3. Algorithms for SELECT and JOIN Operations
4. Algorithms for PROJECT and SET Operations
5. Implementing Aggregate Operations and Outer Joins
7. Using Heuristics in Query Optimization
8. Using Selectivity and Cost Estimates in Query
Optimization
9. Overview of Query Optimization in Oracle

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