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# 5. indexing

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### 5. indexing

1. 1. Hệ quản trị cơ sở dữ liệu Indexing Dư Phương Hạnh Bộ môn Hệ thống thông tin Khoa CNTT, trường Đại học Công nghệ Đại học Quốc gia Hanoi hanhdp@vnu.edu.vn
2. 2. 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/optimizatio 2 Hệ quản trị CSDL @ BM HTTT
3. 3. Problem  Relation: Employee (ID, Name, Dept, …)  10 M tuples  (Filter) Query: SELECT * FROM Employee WHERE Name = “Bob” 3 Hệ quản trị CSDL @ BM HTTT
4. 4. 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 4 Hệ quản trị CSDL @ BM HTTT
5. 5. Solution #2  Storage: – Employee relation sorted on Name attribute  Query plan: – Binary search 5 Hệ quản trị CSDL @ BM HTTT
6. 6. Solution #2  Cost: – – – – – 6 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 Hệ quản trị CSDL @ BM HTTT
7. 7. Solution #2: Issues  Filters on different attributes: SELECT * FROM Employee WHERE Dept = “Sales”  Inserts and Deletes 7 Hệ quản trị CSDL @ BM HTTT
8. 8. 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 8 Hệ quản trị CSDL @ BM HTTT
9. 9. 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 9 Hệ quản trị CSDL @ BM HTTT
10. 10. 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 • 10 Hệ quản trị CSDL @ BM HTTT
11. 11. Single Attribute Index: General Construction A B a1 a1 b1 a2 a2 b2 ai ai bi an an bn A = val A > low A < high 11 Hệ quản trị CSDL @ BM HTTT
12. 12. 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. 12 Hệ quản trị CSDL @ BM HTTT
13. 13. Primary index on the ordering key field 13 Hệ quản trị CSDL @ BM HTTT
14. 14. 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. 14 Hệ quản trị CSDL @ BM HTTT
15. 15. A Clustering Index Example  A clustering index on the DEPTNUMBER ordering non-key field of an EMPLOYEE file. 15 Hệ quản trị CSDL @ BM HTTT
16. 16. Another Clustering Index Example 16 Hệ quản trị CSDL @ BM HTTT
17. 17. 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 17 Hệ quản trị CSDL @ BM HTTT
18. 18. Example of a Dense Secondary Index 18 Hệ quản trị CSDL @ BM HTTT
19. 19. An Example of a Secondary Index 19 Hệ quản trị CSDL @ BM HTTT
20. 20. Properties of Index Types 20 Hệ quản trị CSDL @ BM HTTT
21. 21. 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 firstlevel index consists of more than one disk block 21 Hệ quản trị CSDL @ BM HTTT
22. 22. A Two-level Primary Index 22 Hệ quản trị CSDL @ BM HTTT
23. 23. 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 23 Hệ quản trị CSDL @ BM HTTT
24. 24. A search tree of order p = 3. 24 Hệ quản trị CSDL @ BM HTTT
25. 25. Dynamic Multilevel Indexes Using BTrees 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 25 Hệ quản trị CSDL @ BM HTTT
26. 26. Dynamic Multilevel Indexes Using BTrees 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 26 Hệ quản trị CSDL @ BM HTTT
27. 27. 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 27 Hệ quản trị CSDL @ BM HTTT
28. 28. B-tree Structures 28 Hệ quản trị CSDL @ BM HTTT
29. 29. 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. 29 Hệ quản trị CSDL @ BM HTTT
30. 30. Insert: các bước thực hiện     30 Chèn vào nút lá Chia tách nút lá Chia tách nút con Chia tách nút gốc Hệ quản trị CSDL @ BM HTTT
31. 31. Chèn vào nút lá 58 54 31 57 60 62 Hệ quản trị CSDL @ BM HTTT
32. 32. Chèn vào nút lá 58 54 32 57 60 62 Hệ quản trị CSDL @ BM HTTT
33. 33. Chèn vào nút lá 58 54 33 57 58 60 62 Hệ quản trị CSDL @ BM HTTT
34. 34. Chia tách nút lá 61 54 54 34 57 58 60 66 62 Hệ quản trị CSDL @ BM HTTT
35. 35. Chia tách nút lá 61 54 54 35 57 58 60 66 62 Hệ quản trị CSDL @ BM HTTT
36. 36. Chia tách nút lá 61 54 54 36 57 58 66 60 61 62 Hệ quản trị CSDL @ BM HTTT
37. 37. Chia tách nút lá 59 61 54 54 37 57 58 66 60 61 62 Hệ quản trị CSDL @ BM HTTT
38. 38. Chia tách nút lá 61 54 54 38 57 58 59 66 60 61 62 Hệ quản trị CSDL @ BM HTTT
39. 39. Chia tách nút con … 21 99 … 59 40 39 54 [54, 59) 66 74 [ 59, 66) 84 [66,74) Hệ quản trị CSDL @ BM HTTT
40. 40. Chia tách nút con … 21 99 … 59 40 40 54 [54, 59) 66 74 [ 59, 66) 84 [66,74) Hệ quản trị CSDL @ BM HTTT
41. 41. Chia tách nút con 66 … 21 99 … [21,66) 40 41 54 [54, 59) [66, 99) 59 74 [ 59, 66) 84 [66,74) Hệ quản trị CSDL @ BM HTTT
42. 42. Chia tách nút gốc 59 40 42 54 [54, 59) 66 74 [ 59, 66) 84 [66,74) Hệ quản trị CSDL @ BM HTTT
43. 43. Chia tách nút gốc 59 40 43 54 [54, 59) 66 74 [ 59, 66) 84 [66,74) Hệ quản trị CSDL @ BM HTTT
44. 44. Chia tách nút gốc 66 40 44 54 [54, 59) 59 74 [ 59, 66) 84 [66,74) Hệ quản trị CSDL @ BM HTTT
45. 45. 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 45 Hệ quản trị CSDL @ BM HTTT
46. 46. Gộp các lá liền kề 72 … 54 46 58 64 67 85 68 72 75 Hệ quản trị CSDL @ BM HTTT
47. 47. Gộp các lá liền kề 72 … 54 47 58 64 67 85 68 75 Hệ quản trị CSDL @ BM HTTT
48. 48. Gộp các lá liền kề 72 … 54 48 58 64 68 67 85 75 Hệ quản trị CSDL @ BM HTTT
49. 49. Gộp các lá liền kề 72 … 54 49 58 64 68 85 75 Hệ quản trị CSDL @ BM HTTT
50. 50. Gộp các nút anh em … 41 48 … 63 52 [52, 59) 50 59 74 [59,63) Hệ quản trị CSDL @ BM HTTT
51. 51. Gộp các nút anh em … 41 48 52 59 … 63 [52, 59) 51 59 [59,63) Hệ quản trị CSDL @ BM HTTT
52. 52. 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 52 Hệ quản trị CSDL @ BM HTTT
53. 53. Hệ quản trị cơ sở dữ liệu Using indexes in MySQL Dư Phương Hạnh Bộ môn Hệ thống thông tin Khoa CNTT, trường Đại học Công nghệ Đại học Quốc gia Hanoi hanhdp@vnu.edu.vn
54. 54. 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. 54 Hệ quản trị CSDL @ BM HTTT
55. 55. How MySQL using indexes  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; 55 Hệ quản trị CSDL @ BM HTTT
56. 56. How MySQL using indexes  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: 56 Hệ quản trị CSDL @ BM HTTT
57. 57. 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. 57 Hệ quản trị CSDL @ BM HTTT
58. 58. 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). 58 Hệ quản trị CSDL @ BM HTTT
59. 59. 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). 59 Hệ quản trị CSDL @ BM HTTT
60. 60. 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 60 Hệ quản trị CSDL @ BM HTTT
61. 61. Multiple-Column Index Example  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'; – SELECT * FROM test WHERE last_name='Widenius' AND (first_name='Michael' OR first_name='Monty'); – SELECT * FROM test WHERE last_name='Widenius' AND first_name >='M' AND first_name < 'N'; 61 Hệ quản trị CSDL @ BM HTTT
62. 62. Multiple-Column Index Example  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'; 62 Hệ quản trị CSDL @ BM HTTT
63. 63. Verifying Index Usage  Next lecture: Optimizing queries. 63 Hệ quản trị CSDL @ BM HTTT