5. indexing

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IndexingIndexing

Hệ quản trị CSDL @ BM HTTT2

Outline

Introduce Types of Indexes

– Single-level Ordered Indexes– Multilevel Indexes– Dynamic Multilevel Indexes Using B-Trees and B+-Trees

Using indexes on MySQL

Reading: [1]chap. 5+6(13+14)

http://dev.mysql.com/doc/refman/5.5/en/optimization-indexes.html


Problem

Relation: Employee (ID, Name, Dept, …) 10 M tuples (Filter) Query:

SELECT * FROM Employee WHERE Name = “Bob”


Solution #1: Full Table Scan

Storage:– Employee relation stored in contiguous blocks

Query plan:– Scan the entire relation, output tuples with

Name = “Bob” Cost:

– Size of each record = 100 bytes– Size of relation = 10 M x 100 = 1 GB– Time @ 20 MB/s ≈ 1 Minute


Solution #2

Storage:– Employee relation sorted on Name attribute

Query plan:– Binary search


Solution #2

Cost:– Size of a block: 1024 bytes– Number of records per block: 1024 / 100 = 10– Total number of blocks: 10 M / 10 = 1 M– Blocks accessed by binary search: 20– Total time: 20 ms x 20 = 400 ms


Solution #2: Issues

Filters on different attributes:

SELECT * FROM EmployeeWHERE Dept = “Sales”

Inserts and Deletes


Indexes Definition: a database index is an auxiliary data structure

which allows for faster retrieval of data stored in the database

(Usually) independent of physical storage of relation:– Multiple indexes per relation

Disk resident– Large to fit in memory– Persistent

Updated when indexed relation updated– Relation updates costlier– Query cheaper


Indexes as Access Paths One form of an index: file of entries <field value, pointer to

record>, which is ordered by field value A single-level index is an auxiliary file that makes it more

efficient to search for a record in the data file. The index is called an access path on the field. The index file usually occupies considerably less disk blocks

than the data file because its entries are much smaller A binary search on the index yields a pointer to the file

record Indexes can also be characterized as dense or sparse

– A dense index has an index entry for every search key value (and hence every record) in the data file.

– A sparse (or nondense) index, on the other hand, has index entries for only some of the search values


Ví dụ Xét quan hệ EMPLOYEE(NAME, SSN, ADDRESS, JOB, SAL, ... ) Biết rằng:

– record size R=150 bytes block size B=512 bytes r=30000 records

Như vậy:– blocking factor Bfr= B div R= 512 div 150= 3 records/block– số lượng block b= (r/Bfr)= (30000/3)= 10000 blocks

Để index trên cột SSN với kích thước VSSN=9 bytes, giả thiết kích thước con trỏ dữ liệu là PR=7 bytes, ta có:– k.thước index entry RI=(VSSN+ PR)=(9+7)=16 bytes– index blocking factor BfrI= B div RI= 512 div 16= 32 entries/block– số lượng index block bl= (r/ BfrI)= (30000/32)= 938 blocks– số lần truy cập index block sử dụng binary search log2bI= log2938=

10 lần– So sánh:

• chi phí trung bình của việc tìm kiếm tuyến tính:(b/2)= 10000/2= 5000 block accesses

• Nếu file dữ liệu được sắp xếp thì chi phí binary search là:

log2r= log230000= 15 block accesses


b1

2b

ib

nb

a1

2a

ia

na

A B

a1

2a

ia

na

A = val

A > lowA < high

Single Attribute Index: General Single Attribute Index: General ConstructionConstruction


Types of Single-Level Indexes

Primary Index– Defined on an ordered data file– The data file is ordered on a key field– Includes one index entry for each block in the data file;

the index entry has the key field value for the first record in the block, which is called the block anchor

– A similar scheme can use the last record in a block.– A primary index is a nondense (sparse) index, since it

includes an entry for each disk block of the data file and the keys of its anchor record rather than for every search value.


Primary index on the ordering key field


Types of Single-Level Indexes…

Clustering Index– Defined on an ordered data file– The data file is ordered on a non-key field unlike primary

index, which requires that the ordering field of the data file have a distinct value for each record.

– Includes one index entry for each distinct value of the field; the index entry points to the first data block that contains records with that field value.

– It is another example of nondense index where Insertion and Deletion is relatively straightforward with a clustering index.


A Clustering Index Example

A clustering index on the DEPTNUMBER ordering non-key field of an EMPLOYEE file.


Another Clustering Index Example


Types of Single-Level Indexes Secondary Index

– A secondary index provides a secondary means of accessing a file for which some primary access already exists.

– The secondary index may be on a field which is a candidate key and has a unique value in every record, or a non-key with duplicate values.

– The index is an ordered file with two fields.• The first field is of the same data type as some non-ordering

field of the data file that is an indexing field. • The second field is either a block pointer or a record pointer.• There can be many secondary indexes (and hence, indexing

fields) for the same file.– Includes one entry for each record in the data file; hence,

it is a dense index


Example of a Dense Secondary Index


An Example of a Secondary Index


Properties of Index Types


Multi-Level Indexes

Because a single-level index is an ordered file, we can create a primary index to the index itself;– In this case, the original index file is called the first-level index and the

index to the index is called the second-level index.

We can repeat the process, creating a third, fourth, ..., top level until all entries of the top level fit in one disk block

A multi-level index can be created for any type of first-level index (primary, secondary, clustering) as long as the first-level index consists of more than one disk block


A Two-level Primary Index


Multi-Level Indexes

Such a multi-level index is a form of search tree– However, insertion and deletion of new index entries is a

severe problem because every level of the index is an ordered file.

A node in a Search Tree with pointers to subtrees below it


A search tree of order p = 3.


Dynamic Multilevel Indexes Using B-Trees and B+-Trees

Most multi-level indexes use B-tree or B+-tree data structures

These data structures are variations of search trees that allow efficient insertion and deletion of new search values.

In B-Tree and B+-Tree data structures, each node corresponds to a disk block

Each node is kept between half-full and completely full


Dynamic Multilevel Indexes Using B-Trees and B+-Trees (contd.)

An insertion into a node that is not full is quite efficient– If a node is full the insertion causes a split into two nodes

Splitting may propagate to other tree levels A deletion is quite efficient if a node does not

become less than half full If a deletion causes a node to become less than half

full, it must be merged with neighboring nodes


Difference between B-tree and B+-tree In a B-tree, pointers to data records exist at all

levels of the tree

In a B+-tree, all pointers to data records exists at the leaf-level nodes

A B+-tree can have less levels (or higher capacity of search values) than the corresponding B-tree


B-tree Structures


The Nodes of a B+-tree The nodes of a B+-tree

– (a) Internal node of a B+-tree with q –1 search values.– (b) Leaf node of a B+-tree with q – 1 search values and q – 1 data pointers.


Insert: các bước thực hiện

Chèn vào nút lá Chia tách nút lá Chia tách nút con Chia tách nút gốc


Chèn vào nút lá

54 57 60 62

58


54 57 60 62

58

Chèn vào nút lá


Chèn vào nút lá

54 57 60 62

58

58


61

54 57 60 6258

54 66

Chia tách nút lá


61

54 57 61 6258

54 66

60

Chia tách nút lá


61

54 57 61 6258

54 66

60

59

Chia tách nút lá


59

54 6640

[ 59, 66)[54, 59)

74 84

9921 ……

[66,74)

Chia tách nút con


59

54 6640 74 84

9921 ……

[ 59, 66)[54, 59) [66,74)

Chia tách nút con


5954

66

40 74 84

9921 ……

[66, 99)

[ 59, 66)[54, 59)

[21,66)

[66,74)

Chia tách nút con


54 6640 74 84

59

[ 59, 66)[54, 59) [66,74)

Chia tách nút gốc


54 6640 74 84

59

[ 59, 66)[54, 59) [66,74)



54

66

40 74 8459

[ 59, 66)[54, 59) [66,74)



Delete: Các bước thực hiện

Xoá key trong nút lá

Phân bố lại key giữa các lá liền kề

Gộp các lá liền kề

Phân bố lại các key giữa hai nút con anh em

Gộp các nút con anh em



54 58 64 68 72 75

67 85…72



54 58 64 68 75

67…72 85



54 58 64 68 75

…72 85


Gộp các nút anh em

41 48 52 63 74

59

[52, 59) [59,63)

……


Gộp các nút anh em

41 48 52 63

59

[52, 59) [59,63)

59

……


Exercise

Insert a data entry with key 9 Insert a data entry with key 3 Delete a data entry with key 8, assuming that the left

sibling is checked for possible redistribution Delete a data entry with key 8, assuming that the

right sibling is checked for possible redistribution

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Using indexes in MySQLUsing indexes in MySQL


How MySQL using indexes

Most MySQL indexes (PRIMARY KEY, UNIQUE, INDEX, and FULLTEXT) are stored in B-trees.

MySQL uses indexes for these operations:– To find the rows matching a WHERE clause quickly.– To eliminate rows from consideration. If there is a choice

between multiple indexes, MySQL normally uses the index that finds the smallest number of rows.

– To retrieve rows from other tables when performing joins. MySQL can use indexes on columns more efficiently if they are declared as the same type and size.



MySQL uses indexes for these operations (cont):– To find the MIN() or MAX() value for a specific indexed

column key_col. This is optimized by a preprocessor that checks whether you are using WHERE Key_part_N = constant on all key parts that occur before key_col in the index. In this case, MySQL does a single key lookup for each MIN() or MAX() expression and replaces it with a constant. If all expressions are replaced with constants, the query returns at once:

SELECT MIN(key_part2),MAX(key_part2) FROM tbl_name WHERE key_part1=10;



MySQL uses indexes for these operations (cont):– To sort or group a table if the sorting or grouping is done

on a leftmost prefix of a usable key (for example, ORDER BY key_part1, key_part2). If all key parts are followed by DESC, the key is read in reverse order.

– In some cases, a query can be optimized to retrieve values without consulting the data rows. (An index that provides all the necessary results for a query is called a covering index.) If a query uses only columns from a table that are numeric and that form a leftmost prefix for some key, the selected values can be retrieved from the index tree for greater speed:


Column Indexes

A single column, storing copies of the values from that column in a data structure, allowing fast lookups for the rows with the corresponding column values.

The B-tree data structure lets the index quickly find a specific value, a set of values, or a range of values, corresponding to operators such as =, >, ≤, BETWEEN, IN, and so on, in a WHERE clause.

The maximum number of indexes per table and the maximum index length is defined per storage engine. All storage engines support at least 16 indexes per table and a total index length of at least 256 bytes. Most storage engines have higher limits.


Prefix Indexes

With col_name(N) syntax in an index specification, you can create an index that uses only the first N characters of a string column.

Indexing only a prefix of column values in this way can make the index file much smaller.

When you index a BLOB or TEXT column, you must specify a prefix length for the index. For example:

CREATE TABLE test (blob_col BLOB, INDEX(blob_col(10)));

Prefixes can be up to 1000 bytes long (767 bytes for InnoDB tables).


Multiple-Column Indexes

MySQL can create multiple columns index consist of up to 16 columns

MySQL can use multiple-column indexes for queries that test all the columns in the index, or queries that test just the first column, the first two columns, the first three columns, and so on.

If the table has a multiple-column index, any leftmost prefix of the index can be used by the optimizer to find rows. For example, if you have a three-column index on (col1, col2, col3), you have indexed search capabilities on(col1), (col1, col2), and (col1, col2, col3).


Multiple-Column Index Example

CREATE TABLE test

( id INT NOT NULL,

last_name CHAR(30) NOT NULL,

first_name CHAR(30) NOT NULL,

PRIMARY KEY (id),

INDEX name (last_name,first_name));

The name index can be used for lookups in queries that

specify values in a known range for combinations

of last_name and first_name values. It can also be used for

queries that specify just a last_name value because that

column is a leftmost prefix of the index



The name index is used for lookups in the following queries:

– SELECT * FROM test WHERE last_name='Widenius';

– SELECT * FROM test WHERE last_name='Widenius'

AND first_name='Michael';


AND (first_name='Michael' OR first_name='Monty');


AND first_name >='M' AND first_name < 'N';



The name index is not used for lookups in the following queries:

– SELECT * FROM test WHERE first_name='Michael';

– SELECT * FROM test WHERE last_name='Widenius' OR

first_name='Michael';


Verifying Index Usage

Next lecture: Optimizing queries.

5. indexing

Technology