1. Indexing, Access and Database System Architecture
CSCI 6442
©Copyright 2019, David C. Roberts, all rights reserved

2. Agenda Database performance goals DBMS use of disk Searching B-trees
Intro to DBMS Architecture

3. Why Focus on B-Tree?
The B-tree is essential to join processing in RDBMS
Without the B-Tree, no RDBMS!
Performance characteristics of join are the most important factor in overall DBMS performance
Many of the performance problems you will see are related to B-tree performance in some way.

4. DBMS Performance Data is stored on disk
Disk is necessary for database to be reliably available
Disk is millions of times slower than anything that happens in RAM
Number of disk accesses is a good measure of DBMS cost for an operation

5. Disk vs. RAM RAM is accessible in any order
Any sort of structures can be used
Data structure courses usually cover data structures for RAM
We’ll talk about how to make efficient use of disk

6. Disk as Pages
Disk is composed of fixed-length records, rotating around
To access information, we need to move the head and wait for the disk to rotate
We wait the same time whether we use one byte or all the record
We call this fixed length record a page

7. Search Methods Linear search Binary search
Binary tree-structured search
N-ary trees
B-trees
Hashing

8. Linear Search Elements are stored in arrival order
Search starts at the beginning, continues until desired value is found
Average number of accesses for n elements is approximately n/2

9. Binary Search Elements are stored in order by value to be searched
Search starts at midpoint
With each probe, half of candidates are removed
Average number of probes is log2n

10. Disadvantages of Binary Search
Elements must be kept in order
Inserting one element may require reorganization of entire list
If stored, search jumps from bucket to bucket

11. Using Linked Structure for Binary Search
Using links we can separate physical organization from search sequence
Avoids possible need to reorganize the entire store because of a single update
Accelerates update, still allows fast search

12. Example Binary Search Tree

13. Problems with Binary Search Tree
Each node is likely to be on a different page, making inefficient use of disk accesses
Balance of the tree is also an issue
What if, instead of just one key at each node, we could store a whole page full of keys?
Then we would use disk efficiently and have a very shallow tree

14. Balance

15. Balance
A tree is said to be balanced if the length of all the paths from the root to the leaves differ by no more than one.

16. The problem—how to make efficient use of disk space and also keep the tree balanced. The answer—the b-tree, the brilliant invention of Beyer and McCreight.

17. B-tree
We allow nodes to be incompletely filled in order to maintain perfect balance of the tree
We grow the tree from the bottom; when a node is over-full we split it and put an added node one level up
Deletions are the reverse of additions

18. B-tree

19. B-tree
We understand that with each entry there is an address in storage. Having understood that, we omit them from the rest of the diagrams
Data Store

20. B-tree

21. B-tree 1

22. B-tree 1 4

23. B-tree 1 4 6

24. B-tree 1 4 6 8

25. B-tree 5 1 4 6 8

26. B-tree
When a node is full, to add a value we split the node and put the middle value in the level above. 5 1 4 6 8

27. How It Really Looks

28. B-tree questions
How large should node size be? How many values should it contain?
Are the values indexed by a b-tree properly called keys?
How full are b-tree nodes, on the average, after the system has been operating for a while?

29. B-plus tree Usually the b+-tree, a variation on the b-tree is used
B+ trees have all indexed values represented in the leaves
Other nodes do not have pointers to rows, only pointers to other nodes
B+ trees provide very high density of indexes

30. B+ tree Some values, and pointers to blocks in the sequence set
Index Set
All values, and pointers to rows in the database
Sequence Set

31. The insert algorithm for B+ Trees
B+ Tree Add Algorithm
The insert algorithm for B+ Trees
Leaf Page Full
Index Page FULL
Action NO
Place the record in sorted position in the appropriate leaf page
YES
Split the leaf page
Place Middle Key in the index page in sorted order.
Left leaf page contains records with keys below the middle key.
Right leaf page contains records with keys equal to or greater than the middle key.
Split the leaf page.
Records with keys < middle key go to the left leaf page.
Records with keys >= middle key go to the right leaf page.
Split the index page.
Keys < middle key go to the left index page.
Keys > middle key go to the right index page.
The middle key goes to the next (higher level) index. IF the next level index page is full, continue splitting the index pages.

32. B+ Tree Delete Algorithm
The delete algorithm for B+ Trees
Leaf Page Below Fill Factor
Index Page Below Fill Factor
Action NO
Delete the record from the leaf page. Arrange keys in ascending order to fill void. If the key of the deleted record appears in the index page, use the next key to replace it.
YES
Combine the leaf page and its sibling. Change the index page to reflect the change.
Combine the leaf page and its sibling.
Adjust the index page to reflect the change.
Combine the index page with its sibling. Continue combining index pages until you reach a page with the correct fill factor or you reach the root page.

33. Hashing
Develop a function that maps data values into a range of storage addresses
For each search value, use a function to compute a hash value and store the associated data at that address
To search, just compute the hash value and look at that address

34. Hashing
Instead of storing the data at the hash address, store a pointer to the data
The table of pointers is called a hash table
Using hashing for a search locates a stored value in just one access
Number of accesses to locate a value is independent of n

35. Hashing Question
Why are b-trees the most used index method for database systems and not hashing, given that hashing is faster?
Hint—think about the disadvantages of hashing

36. Introduction to Database System Architecture

37. DBMS Software Architecture
Application
Program
Buffer
System
Global
Area
Database
System
Application
Program
Buffer
Application
Program
Buffer
Application
Program
Buffer

38. Query Processing Architecture
SQL
Lexical
Analyzer
Tokens
Syntax
Analyzer
Quads
Executor
Results

39. Executor Software Architecture
SQL Executor
Table Management
Index Management
Row Management
Node Management
Page Management
Data Store

40. Next week: more about DBMS architecture and performance