8 query processing and optimization

Chapter 15
Algorithms for Query Processing
and Optimization

Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe

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


Slide 15- 2

0. Introduction to Query Processing (1)


Query processing:




Query optimization:




Is the list of activities that are perform to obtain the
required tuples that satisfy a given query.
The process of choosing a suitable execution
strategy for processing a query.

Two internal representations of a query:



Query Tree
Query Graph


Slide 15- 3

Introduction to Query Processing (2)


Slide 15- 4

Introduction to Query Processing (2)


Slide 15- 5

1. Translating SQL Queries into Relational
Algebra






Parser & Translator:
 Syntax
 Schema element
 Converts the query into R.A expression.
Optimizer
 Find all equivalent R.A expressions
 Find the R.A expression with least cost
 Cost(CPU, Block access, time spent)
 Will create query evaluation plan which tell what R.A
and what algorithm is used.
Query evaluation plan:
 Evaluate the above plan and get the result

Slide 15- 6

1. Translating SQL Queries into Relational
Algebra


Query block:








The basic unit that can be translated into the
algebraic operators and optimized.

A query block contains a single SELECT-FROMWHERE 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.


Slide 15- 7

Translating SQL Queries into Relational
Algebra
SELECT
FROM
WHERE

SELECT
FROM
WHERE

LNAME, FNAME
EMPLOYEE
SALARY > (
SELECT
FROM
WHERE

LNAME, FNAME
EMPLOYEE
SALARY > C

πLNAME, FNAME (σSALARY>C(EMPLOYEE))

SELECT
FROM
WHERE

MAX (SALARY)
EMPLOYEE
DNO = 5);

MAX (SALARY)
EMPLOYEE
DNO = 5

ℱMAX SALARY (σDNO=5 (EMPLOYEE))
Slide 15- 8

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.


Slide 15- 9

Algorithms for External Sorting (2)


Slide 15- 10

3. Algorithms for SELECT and JOIN
Operations (1)


Implementing the SELECT Operation



Examples:






(OP1): s SSN='123456789' (EMPLOYEE)
(OP2): s DNUMBER>5(DEPARTMENT)
(OP3): s DNO=5(EMPLOYEE)
(OP4): s DNO=5 AND SALARY>30000 AND SEX=F(EMPLOYEE)
(OP5): s ESSN=123456789 AND PNO=10(WORKS_ON)


Slide 15- 11

Algorithms for SELECT and JOIN
Operations (2)



Implementing the SELECT Operation (contd.):
Search Methods for Simple Selection:


S1 Linear search (brute force):




S2 Binary search:




Retrieve every record in the file, and test whether its attribute
values satisfy the selection condition.
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.


Slide 15- 12

Operations (3)



 S4 Using a primary index to retrieve multiple records:




S5 Using a clustering 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.
If the selection condition involves an equality comparison on a nonkey 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)


Slide 15- 13

Operations (4)





S7 Conjunctive selection using a individual index :




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. E.g index has been created on the composite key
(Essn, Pno) of the relational R( Works_on)


Slide 15- 14

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.


Slide 15- 15

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


Slide 15- 16

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


Slide 15- 17

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].


Slide 15- 18

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.


Slide 15- 19

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.


Slide 15- 20

Operations (14)



Factors affecting JOIN performance




Available buffer space
Join selection factor
Choice of inner VS outer relation


Slide 15- 21

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.


Slide 15- 22

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.


Slide 15- 23

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


Slide 15- 24

Operations (18)



Hybrid hash join:


Same as partitioned hash join except:




Partitioning phase:






Joining phase of one of the partitions is included during the
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.


Slide 15- 25

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


Slide 15- 26

Algorithms for PROJECT and SET
Operations (2)



Algorithm for SET operations
Set operations:






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




UNION, INTERSECTION, SET DIFFERENCE and
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.


Slide 15- 27

Algorithms for PROJECT and SET
Operations (3)



Algorithm for SET operations (contd.)
UNION (See Figure 15.3c)





INTERSECTION (See Figure 15.3d)





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.
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.

Slide 15- 28

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.


Slide 15- 29

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?


Slide 15- 30

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
FROM



FNAME, DNAME
(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.


Slide 15- 31

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).


Slide 15- 32

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}




{UNION the temporary tables to produce the LEFT OUTER JOIN}




TEMP2  TEMP2 x 'null'
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).


Slide 15- 33

8 query processing and optimization

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