This document discusses cost optimization techniques in database management systems. It covers prerequisite concepts like relational algebra operations and set operations. It then explains how a database manages costs based on information about relations, attributes, indexes, and distinct values. Various join algorithms are described like nested-loop, block nested-loop, index nested-loop, sort-merge, and hash joins. An example of computing a join between two relations is provided. The document concludes with an assignment on the difference between nested loop and sort merge joins and learning outcomes.

1. B.Tech, CSE & IT, IV/V Sem, II/III Year
CS 502/IT405: Data Base Management System
Archana Tomar
Asst. Prof. ,Department Of Computer Science & Engineering
Unit 3
Cost optimization Technique part-2
Lecture No. 41

2. Outlines
• Prerequisite
• Cost optimization
• Join Algorithms
• Example
• Exercise
• Learning Outcomes
• References
DBMS

3. Prerequisite
• Query language
• Relational Algebra operations
• Set operation

4. Cost Based Optimization
DBMS <SELO: 5,12> <Reference No.: R1,R2> 1
Information about relations and attributes:
• NR: number of tuples
• BR: number of blocks
• SR: size of a tuple of R.
• FR: blocking factor; (FR = [NR/BR])
• V(A, R): number of distinct values
• SC(A, R): selectivity of attribute SC(A, R) = NR/V(A, R).

5. <Reference No.: R1,R2>
DBMS <SELO: 5,12> 2
Information about indexes:
• HTI: number of levels in index I (B+-tree).
• LBI: number of blocks occupied by leaf nodes in index I (first-level blocks).
• ValI: number of distinct values for the search key

6. Selection Operation
<Reference No.: R1,R2>
DBMS <SELO: 5,12> 3
σA=a(R)
where a is a constant value,
A an attribute of R
• File Scan
• S1 – Linear search cost(S1)= BR

7. Continue.
<Reference No.: R1,R2>
DBMS <SELO: 5,12> 4
• S2 – Binary search,
the file ordered based on attribute A (primary index)
cost(S2) = [log2 (BR)] +[SC(A, R)/ FR ] − 1
• If A is primary key, then SC(A, R) = 1, hence cost(S2) = [log2 (BR)].

8. Join Operations
– Nested-Loop Join
– Block Nested-Loop Join
– Index Nested-Loop Join
– Sort-Merge Join
– Hash-Join
<Reference No.: R1,R2>
DBMS <SELO: 5,12> 5

9. Nested-Loop Join
Evaluate the condition join R ✶ S
• for each tuple tR in R do begin
for each tuple tS in S do begin
check whether pair (tR, tS) satisfies join condition
if they do, add tR ◦ tS to the result
end
End
<Reference No.: R1,R2>
DBMS <SELO: 5,12> 6

10. An Improvement: Block Nested-Loop Join
for each block BR of R do begin
for each block BS of S do begin
for each tuple tR in BR do
for each tuple tS in BS do check whether pair (tR, tS) satisfies join
condition if they do, add tR ◦ tS to the result
end end end end
<Reference No.: R1,R2>
DBMS <SELO: 5,12> 7

11. • Example: –
• Compute CUSTOMERS ✶ ORDERS, with CUSTOMERS as the outer relation
<Reference No.: R1,R2>
DBMS <SELO: 5,12> 8

12. Sort-Merge Join
• first sort both relations on join attribute
• Join steps are similar to the merge stage
<Reference No.: R1,R2>
DBMS <SELO: 5,12> 9

13. Cost of computing for all joins

14. Assignment/Exercise
Difference between Nested Loop join and Sort Merge Join
13
DBMS

15. Learning Outcomes
• Understand about cost based optimization technique.
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16. References
1. Korth, Silbertz,Sudarshan, “Fundamental of Database System”, McGraw Hill
2. https://www.cs.ucdavis.edu/~green/courses/ecs165a-w11/8-query.pdf
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