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

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

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

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

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

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

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 ?

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 ?

Page Formats Free space Slot directory Variable-length records

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

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

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

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

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

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

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)

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

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

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

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 / …

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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

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

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 = 1 page = 8 Kbytes Level 2 = 133 pages = 1 Mbyte Level 3 = 17,689 pages = 133 MBytes

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

Insertion in a B+ Tree Insert K=19 80 20 60 100 120 140 10 15 18 20 30 50 60 65 80 85 90 10 15 18 20 30 40 50 60 65 80 85 90

Insertion in a B+ Tree After insertion 80 20 60 100 120 140 10 15 18 19 20 30 40 50 60 65 80 85 90 10 15 18 19 20 30 40 50 60 65 80 85 90

Insertion in a B+ Tree Now insert 25 80 20 60 100 120 140 10 15 18 19 30 40 50 60 65 80 85 90 10 15 18 19 20 30 40 50 60 65 80 85 90

Insertion in a B+ Tree After insertion 80 20 60 100 120 140 10 15 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

Insertion in a B+ Tree But now have to split ! 80 20 60 100 120 140 10 15 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

Insertion in a B+ Tree After the split 80 20 30 60 100 120 140 10 15 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

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

Deletion from a B+ Tree After deleting 30 May change to 40, or not 80 20 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

Deletion from a B+ Tree Now delete 25 80 20 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

Deletion from a B+ Tree After deleting 25 Need to rebalance Rotate 80 20 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

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

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

Deletion from a B+ Tree Final tree 80 19 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

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