1. ICS 421 Spring 2010 Indexing (1) Asst. Prof. Lipyeow Lim Information & Computer Science Department University of Hawaii at Manoa 02/18/20101Lipyeow Lim -- University of Hawaii at Manoa

2. How to speed up queries? 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa2 SELECT * FROM Sailors WHERE age>40 File of Record for Sailors Array of Sailor Tuples/Records

3. Binary Search Trees Given search value – if value < node.value, then follow left pointer – Else follow right pointer How do generalize each index node to an index page ? How do we generalize this to search pages of records ? 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa3 28 21 182021 262728303134374145 34 20263041

4. Indexes What do we store in the index nodes ? Let k be the key value for an index entry: 1.Data record with key value k 2. 3. What kind of queries does the index support? – Range – Point (or equality) 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa4

5. Indexed Sequential Access Method (ISAM) Static (m+1)-way Search Tree 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa5 P 0 K 1 P 1 K 2 P 2 K m P m index entry Non-leaf Pages Overflow page Primary pages Leaf

6. ISAM: Example Store data record at the leaf pages Do we still need the file of record ? 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa6 sid sname rating age 4020335163 10152027333740465155639798 Insert new record with age 98

7. ISAM Facts File creation: Leaf (data) pages allocated sequentially, sorted by search key; then index pages allocated, then space for overflow pages. Index entries: ; they `direct’ search for data entries, which are in leaf pages. Search: Start at root; use key comparisons to go to leaf. Cost=O(log F N) ; F = # entries/index pg, N = # leaf pgs Insert: Find leaf data entry belongs to, and put it there. If full, allocate and put in overflow page Delete: Find and remove from leaf; if empty overflow page, de-allocate. Static tree structure: inserts/deletes affect only leaf pages. 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa7

8. B+ Tree Index Insert/delete at log F N cost; keep tree height-balanced. (F = fanout, N = # leaf pages) Minimum 50% occupancy (except for root). Each node contains d <= m <= 2d entries. The parameter d is called the order of the tree. Supports equality and range- searches efficiently. 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa8 B+ Tree Index Data Entries/Leaf Pages (“Sequence Set”) Index Entries

9. B+ Tree: Search Example Leaf entries store pairs What is the order ? Search for: age=5, age=15, age>=24 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa9 13172430 2357141619202224272933343839

10. Inserting a new data entry Find correct leaf L. Put data entry onto L. – If L has enough space, done! – Else, must split L (into L and a new node L2) Redistribute entries evenly, copy up middle key. Insert index entry pointing to L2 into parent of L. This can happen recursively – To split index node, redistribute entries evenly, but push up middle key. (Contrast with leaf splits.) Splits “grow” tree; root split increases height. – Tree growth: gets wider or one level taller at top. 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa10

11. Example: Insert 8* 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa11 23578 13172430 2357141619202224272933343839 5 5 copied up to parent node 5132430 17 pushed up into parent node 17

12. Deleting a data entry Start at root, find leaf L where entry belongs. Remove the entry. – If L is at least half-full, done! – If L has only d-1 entries, Try to re-distribute, borrowing from sibling (adjacent node with same parent as L). If re-distribution fails, merge L and sibling. If merge occurred, must delete entry (pointing to L or sibling) from parent of L. Merge could propagate to root, decreasing height. 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa12

13. Miscellaneous How do we handle data with duplicates ? – Overflow buckets – Make rid part of the key – Each data entry stores Clustered vs Unclustered indexes 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa13

14. Bulk Loading a B+ Tree If we have a large collection of records, and we want to create a B+ tree on some field, doing so by repeatedly inserting records is very slow. Bulk Loading can be done much more efficiently. Initialization: Sort all data entries, insert pointer to first (leaf) page in a new (root) page. 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa14 3* 4* 6*9*10*11*12*13* 20*22* 23*31* 35* 36*38*41*44* Sorted pages of data entries; not yet in B+ tree Root

15. Bulk Loading (cont.) Index entries for leaf pages always entered into right-most index page just above leaf level. When this fills up, it splits. (Split may go up right-most path to the root.) Much faster than repeated inserts, especially when one considers locking! 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa15

16. Creating Indexes Most DBMS (eg. DB2) supports only B+ tree indexes: CREATE INDEX myIdx ON mytable(col1, col3) CREATE UNIQUE INDEX myUniqIdx ON mytable(col2, col5) CREATE INDEX myIdx ON mytable(col1, col3) CLUSTER If a primary key is specified in the CREATE TABLE statement, an (unclustered) index is automatically created for the PK. To create a clustered PK index: – Create table without PK constraint – Create index on PK with cluster option – Alter table to add PK constraint To get rid of unused indexes: DROP INDEX myIdx; 02/18/2010Lipyeow Lim -- University of Hawaii at Manoa16