1. CSE 544: Lecture 11 Storing Data, Indexes
Monday, 5/1/2006

2. Outline Storing data: disks and files - 9.5-9.7
Types of Indexes - Chapter 8.3
B-trees - Chapter 10

3. Managing Free Blocks By the OS By the RDBMS (typical: why ?)
Linked list of free blocks
Bit map

4. Files of Records Types of files: Heap file - unordered Sorted file
Clustered file - sorted, plus a B-tree
Will discuss heap files only; the others are similar, only sorted by the key

5. Pages with some free space
Heap Files
Full pages
Linked list of pages:
Data page
Data page
Data page
Data page
Header page
Pages with some free space
Data page
Data page
Data page
Data page

6. Heap Files Better: directory of pages Data page Header Data page

7. Page Formats Issues to consider 1 page = fixed size (e.g. 8KB)
Records:
Fixed length
Variable length
Record id = RID
Typically RID = (PageID, SlotNumber)
Log entries refer to RIDs. Plus, foreign keys may be optimized to RID’s, but I’m not sure if this is implemented in any system
Why do we need RID’s in a relational DBMS ?

8. Page Formats Slot 1 Slot 2 Slot N Free space N
Fixed-length records: packed representation
Slot 1
Slot 2
Slot N
Free space N
Need to move records around when one is deleted
Problems ?

9. Page Formats
Free space
Slot directory
Variable-length records

10. Record Formats Field 1 Field 2 . . . Field K
Fixed-length records --> all fields have fixed length
Field 1
Field 2
. . .
Field K

11. Record Formats Field 1 Field 2 . . . Field K Variable length records
Record header
Remark: NULLS require no space at all (why ?)

12. Spanning Records Across Blocks
When records are very large
Or even medium size: saves space in blocks
Commercial RDBMS avoid this
block
header
block
header R1 R2 R3 R2

13. LOB Large objects Supported by modern database systems
Binary large object: BLOB
Character large object: CLOB
Supported by modern database systems
E.g. images, sounds, texts, etc.
Storage: attempt to cluster blocks together

14. Modifications: Insertion
File is unsorted (= heap file)
add it to the end (easy )
File is sorted:
Is there space in the right block ?
Yes: we are lucky, store it there
Is there space in a neighboring block ?
Look 1-2 blocks to the left/right, shift records
If anything else fails, create overflow block

15. Overflow Blocks
Blockn-1
Blockn
Blockn+1
Overflow
After a while the file starts being dominated by overflow blocks: time to reorganize

16. Modifications: Deletions
Free space in block, shift records
Maybe be able to eliminate an overflow block
Can never really eliminate the record, because others may point to it
Place a tombstone instead (a NULL record)

17. Modifications: Updates
If new record is shorter than previous, easy 
If it is longer, need to shift records, create overflow blocks

18. Record Formats: Fixed Length
Base address (B)
Address = B+L1+L2
Information about field types same for all records in a file; stored in system catalogs.
Finding i’th field requires scan of record.
Note the importance of schema information! 9

19. Indexes Search key = can be any set of fields
not the same as the primary key, nor a key
Index = collection of data entries
Data entry for key k can be:
The actual record with key k
(k, RID)
(k, list-of-RIDs) 7

20. Index Classification Primary/secondary Clustered/unclustered
Primary = may reorder data according to index
Secondary = cannot reorder data
Clustered/unclustered
Clustered = records close in the index are close in the data
Unclustered = records close in the index may be far in the data
Dense/sparse
Dense = every key in the data appears in the index
Sparse = the index contains only some keys
B+ tree / Hash table / …

21. 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

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

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

24. Primary Index with Duplicate Keys
Sparse index: pointer to lowest search key in each block:
Search for 20
...but need to search here too 10 10 20 30
20 is here... 10 20 20 30 40

25. Primary Index with Duplicate Keys
Better: pointer to lowest new search key in each block:
Search for 20
Search for 15 ? 35 ? 10 10 20 10 20 30 40
20 is here...
...ok to search from here 30 50 60 70 80 30 40 50

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

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

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

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

30. Applications of Secondary Indexes
Secondary indexes needed for heap files
Also for 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

31. 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

32. 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)

33. B+ Trees Basics Parameter d = the degree
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

34. B+ Tree Example
d = 2
Find the key 40 80
40  80 20 60
100
120
140
20 < 40  60 10 15 18 20 30 40 50 60 65 80 85 90
30 < 40  40 10 15 18 20 30 40 50 60 65 80 85 90

35. 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

36. 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

37. 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

38. 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
parent
parent K3 K1 K2 K3 K4 K5 P0 P1 P2 P3 P4 p5 K1 K2 P0 P1 P2 K4 K5 P3 P4 p5

39. 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

40. 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

41. 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

42. 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

43. 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

44. 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

45. Deletion from a B+ Tree Delete 30 80 20 30 60 100 120 140 10 15 18 1925 30 40 50 60 65 80 85 90 10 15 18 19 20 25 30 40 50 60 65 80 85 90

46. Deletion from a B+ Tree After deleting 30 May change to 40, or not 8020 30 60
100
120
140 10 15 18 19 20 25 40 50 60 65 80 85 90 10 15 18 19 20 25 40 50 60 65 80 85 90

47. Deletion from a B+ Tree Now delete 25 80 20 30 60 100 120 140 10 15 1819 20 25 40 50 60 65 80 85 90 10 15 18 19 20 25 40 50 60 65 80 85 90

48. Deletion from a B+ Tree After deleting 25 Need to rebalance Rotate 8020 30 60
100
120
140 10 15 18 19 20 40 50 60 65 80 85 90 10 15 18 19 20 40 50 60 65 80 85 90

49. Deletion from a B+ Tree Now delete 40 80 19 30 60 100 120 140 10 15 1850 60 65 80 85 90 10 15 18 19 20 40 50 60 65 80 85 90

50. Deletion from a B+ Tree After deleting 40 Rotation not possible
Need to merge nodes 80 19 30 60
100
120
140 10 15 18 19 20 50 60 65 80 85 90 10 15 18 19 20 50 60 65 80 85 90

51. Deletion from a B+ Tree Final tree 80 19 60 100 120 140 10 15 18 19 2050 60 65 80 85 90 10 15 18 19 20 50 60 65 80 85 90

52. In Class Suppose the B+ tree has depth 4 and degree d=200
How many records does the relation have (maximum) ?
How many index blocks do we need to read and/or write during:
A key lookup
An insertion
A deletion