1. Lecture 21: Indexes
Monday, November 13, 2000

2. Outline
Addresses (3.3)
Index Structures (4.1, 4.2, 4.3)

3. Physical Addresses
Each block and each record have a physical address that consists of:
The host
The disk
The cylinder number
The track number
The block within the track
For records: an offset in the block
sometimes this is in the block’s header

4. Logical Addresses Logical address: a string of bytes (10-16)
More flexible: can blocks/records around
But need translation table:
Logical address
Physical address L1 P1 L2 P2 L3 P3

5. Main Memory Address
When the block is read in main memory, it receives a main memory address
Need another translation table
Memory address
Logical address M1 L1 M2 L2 M3 L3

6. Optimization: Pointer Swizzling
= the process of replacing a physical/logical pointer with a main memory pointer
Still need translation table, but subsequent references are faster

7. Pointer Swizzling Block 2 Block 1 Disk read in memory swizzled Memory
unswizzled

8. Pointer Swizzling
Automatic: when block is read in main memory, swizzle all pointers in the block
On demand: swizzle only when user requests
No swizzling: always use translation table

9. Pointer Swizzling When blocks return to disk: pointers need unswizzled
Danger: someone else may point to this block
Pinned blocks: we don’t allow it to return to disk
Keep a list of references to this block

10. Indexes
An index on a file speeds up selections on the search key fields for the index.
Any subset of the fields of a relation can be the search key for an index on the relation.
Search key is not the same as key (minimal set of fields that uniquely identify a record in a relation).
An index contains a collection of data entries, and supports efficient retrieval of all data entries with a given key value k. 7

11. Index Classification Primary/secondary Clustered/unclustered
Dense/sparse
B+ tree / Hash table / …

12. Primary Index File is sorted on the index attribute
Dense index: sequence of (key,pointer) pairs 10 20 10 20 30 40 30 40 50 60 70 80 50 60 70 80

13. Primary Index Sparse index 10 20 30 40 50 60 70 80 10 30 50 90 70 110
130
150 50 60 70 80

14. Primary Index with Duplicate Keys
Dense index: 10 10 20 30 40 10 20 50 60 70 80 20 30 40

15. Primary Index with Duplicate Keys
Sparse index: pointer to lowest search key in each block:
Search for 20 10 10 20 30 10 20 20 30 40

16. Primary Index with Duplicate Keys
Better: pointer to lowest new search key in each block:
Search for 20 10 10 20 30 40 10 20 50 60 70 80 30 40 50

17. Secondary Indexes To index other attributes than primary key
Always dense (why ?) 20 30 10 20 30 20 20 30 10 20 10 30

18. Clustered/Unclustered
Primary indexes = usually clustered
Secondary indexes = usually unclustered

19. Clustered vs. Unclustered Index
Data entries
Data entries
(Index File)
(Data file)
Data Records
Data Records
CLUSTERED
UNCLUSTERED 12

20. Secondary Indexes Applications:
index other attributes than primary key
index unsorted files (heap files)
index clustered data

21. Applications of Secondary Indexes
Clustered data
Company(name, city), Product(pid, maker)
Select city
From Company, Product
Where name=maker
and pid=“p045”
Select pid
From Company, Product
Where name=maker
and city=“Seattle”
Products of company 2
Products of company 3
Products of company 1
Company 1
Company 2
Company 3

22. Composite Search Keys
Composite Search Keys: Search on a combination of fields.
Equality query: Every field value is equal to a constant value. E.g. wrt <sal,age> index:
age=20 and sal =75
Range query: Some field value is not a constant. E.g.:
age =20; or age=20 and sal > 10
Examples of composite key
indexes using lexicographic order.
11,80 11
12,10 12
name
age
sal
12,20 12
13,75
bob 12 10 13
<age, sal>
cal 11 80
<age>
joe 12 20
10,12
sue 13 75 10
20,12
Data records
sorted by name 20
75,13 75
80,11 80
<sal, age>
<sal>
Data entries in index
sorted by <sal,age>
Data entries
sorted by <sal> 13

23. B+ Trees Search trees Idea in B Trees: Idea in B+ Trees:
make 1 node = 1 block
Idea in B+ Trees:
Make leaves into a linked list (range queries are easier)

24. B+ Trees Basics Parameter d
Each node has >= d and <= 2d keys (except root)
Each leaf has >=d and <= 2d keys: 30
120
240
Keys k < 30
Keys 30<k<=120
Keys 120<k<=240
Keys 240<k 40 50 60
Next leaf 40 50 60

25. B+ Tree Example
d = 2 80 20 60
100
120
140 10 15 18 20 30 40 50 60 65 80 85 90 10 15 18 20 30 40 50 60 65 80 85 90

26. B+ Tree Design How large d ? Example: 2d x 4 + (2d+1) x 8 <= 4096
Key size = 4 bytes
Pointer size = 8 bytes
Block size = 4096 byes
2d x 4 + (2d+1) x 8 <= 4096
d = 170

27. Searching a B+ Tree Exact key values: Range queries: Start at the root
Proceed down, to the leaf
Range queries:
As above
Then sequential traversal
Select name
From people
Where age = 25
Select name
From people
Where 20 <= age
and age <= 30

28. B+ Trees in Practice Typical order: 100. Typical fill-factor: 67%.
average fanout = 133
Typical capacities:
Height 4: 1334 = 312,900,700 records
Height 3: 1333 = 2,352,637 records
Can often hold top levels in buffer pool:
Level 1 = page = Kbytes
Level 2 = pages = Mbyte
Level 3 = 17,689 pages = 133 MBytes

29. Insertion in a B+ Tree Insert (K, P) Find leaf where K belongs, insert
If no overflow (2d keys or less), halt
If overflow (2d+1 keys), split node, insert in parent:
If leaf, keep K3 too in right node
When root splits, new root has 1 key only
(K3, ) to parent K1 K2 K3 K4 K5 P0 P1 P2 P3 P4 p5 K1 K2 P0 P1 P2 K4 K5 P3 P4 p5

30. Insertion in a B+ Tree Insert K=19 80 20 60 100 120 140 10 15 18 20 3050 60 65 80 85 90 10 15 18 20 30 40 50 60 65 80 85 90

31. Insertion in a B+ Tree After insertion 80 20 60 100 120 140 10 15 1819 20 30 40 50 60 65 80 85 90 10 15 18 19 20 30 40 50 60 65 80 85 90

32. Insertion in a B+ Tree Now insert 25 80 20 60 100 120 140 10 15 18 1930 40 50 60 65 80 85 90 10 15 18 19 20 30 40 50 60 65 80 85 90

33. Insertion in a B+ Tree After insertion 80 20 60 100 120 140 10 15 1819 20 25 30 40 50 60 65 80 85 90 10 15 18 19 20 25 30 40 50 60 65 80 85 90

34. Insertion in a B+ Tree But now have to split ! 80 20 60 100 120 140 1015 18 19 20 25 30 40 50 60 65 80 85 90 10 15 18 19 20 25 30 40 50 60 65 80 85 90

35. Insertion in a B+ Tree After the split 80 20 30 60 100 120 140 10 1518 19 20 25 30 40 50 60 65 80 85 90 10 15 18 19 20 25 30 40 50 60 65 80 85 90