1. File Processing : Index and Hash
2018, Spring
Pusan National University
Ki-Joune Li

2. What is index ? Index in a book Index for a file or database
Index : Keyword  Pages
Without Index
Exhaustive search : Too Expensive
Index for a file or database
A function or mechanism
FIndex : SPredicate  B (block numbers on hard disk)
e.g. find student records where student.GPA > 4.0

3. Data Retrieval Time Data retrieval on disk : Two phases
1st phase : Search with a condition (Predicate)
2nd phase : Data access
Data Access Time - File Structure - Disk Placement - Clustering, etc..
2nd Phase
Search Block Number
Search Condition
{ Block# }
Database on Disk
1st Phase

4. By maximizing blocking factor, we reduce the number of disk accesses
Blocking Factor Bf
Blocking Factor
Number of Records in a Block
Blocking Number and Number of Disk Accesses
ND = Nrecord / Bf
By maximizing blocking factor, we reduce the number of disk accesses

5. How to Accelerate Phase 1 ?
Of course, we could accelerate the phase 1
by index or by hash
Index vs. Hash
Index : a type of data structures
Needs additional data structures
Hash : a type of mechanism
May not need any additional data structure (not exactly true)

6. A Simple Idea on Index Mapping Table from keywords to block numbers
Inverted File
Why inverted file is better than nothing ?
If the table is too large (to fit in main memory)
It has to be stored on disk
Disk Access for Index Access
Keyword
Block#
Juliet
Romeo
B26
Hamlet
B22 … …
Carmen
B212

7. Searching Algorithms and Index
A good way to accelerate searching
Tree : O( logn )
Reorganize Inverted File to Tree
Binary Search Tree : Branching Factor = 2
Tree in memory space vs. in disk space
Memory space : Number of Comparisons
Disk space : Number of Block Accesses
30, b27
14, b17
40, b26
34, b17
55, b26

8. Paged Tree : m-way search tree
How to determine m ?
One Node : One Disk Page
e.g. When 1 disk page is 4 K bytes
4+4m+8(m-1) = 4096  m = 341
Very fat tree
Number of delimiters
Delimiter
57, b27 34
103, b28 …
343, b14
Block number
1, b29 44 …
54, b21
58, b17 32 …
96, b127

9. Problem of m-Way search tree
Search Performance : determined by the height
Not balanced
Average : O(log n)
Worst case : n / Bf  O(n)
Height : determined by insertion order
e.g : insertion by ascending order
How to make it balanced ?
Balanced m-Way search tree : B-tree

10. B-tree B-tree : Balanced m-way search Tree
Root Node : no child node or more than one child nodes
Internal Node : m/2 ~ m child nodes (block number)
External Node : data block number instead of child node
Balanced
Upward split
instead of downward split : Binary Tree

11. Downward Split Suppose m=3 Insert 10, 20 10 20 20 Insert 30 10 20 30
Upward Split
overflow 10 20 30 40
Insert 40

12. Downward Split 10 20 30 40 50 10 20 40 Insert 50 30 50 60 Insert 60 1070 10 20 30 40 60 50 70 40 50 10 20 30 60 70

13. Meaning of Downward Split
Always Balanced
Not so much influenced by the order of insertions
Internal Nodes : m/2 ~ m child nodes (block number)
Root Node 40 50 10 20 30 60 70
Internal Node
External Node

14. Search by B-tree
? 45 45 40 45 20 60 45 10 30 50 70
Not Found

15. Performance of B-tree Number of Comparison within a node : Trivial
Number of Nodes to visit : Depth

16. Problem of B-tree Types of Search B-tree Exact Match Search
Range Search
E.g. find students where 25<student.GPA<50
B-tree
Good for Exact match search
Bad for range search 40 50 10 20 30 60 70

17. B+-tree A Variant of B-tree Performance
Duplicate all elements at leaf nodes (external nodes)
Linked List of Leaf Nodes
Performance
Exact Match Search and Insertion
A small fraction of performance sacrifice
Range Search : much more powerful than B-tree

18. B+-tree : Example Duplication 40 10 20 30 10 20 30 40 10 20 30
overflow
Linked List 40 10 20 30 50 40 10 20 30 50 60 40 10 20 30 50 60

19. Range Search with B+-tree
Find students where GPA>3.5 35 40 10 20 30 50 60 40 10 20 30 50 60 35 40 10 20 30 50 60 35 40 10 20 30 50 60 35

20. Performance of B+-tree
Determined by the Depth
Exact Match Search and Insertion (without split)
d node (page) accesses
Range Search
node accesses ( nq : number of records to retrieve)