1. CS 44321 CS4432: Database Systems II

2. CS 44322 Index definition in SQL Create index name on rel (attr) (Check online for index definitions in SQL) Drop INDEX name

3. CS 44323 ATTRIBUTE LIST  MULTIKEY INDEX e.g., CREATE INDEX foo ON R(A,B,C) Note

4. CS 44324 Motivation: Find records where DEPT = “Toy” AND SAL > 50k Multi-key Index

5. CS 44325 Strategy I: Use one index, say Dept. Get all Dept = “Toy” records and check their salary I1I1

6. CS 44326 Use 2 Indexes; Manipulate Pointers ToySal > 50k Strategy II:

7. CS 44327 Multiple Key Index One idea: Strategy III: I1I1 I2I2 I3I3

8. CS 44328 Example Record Dept Index Salary Index Name=Joe DEPT=Sales SAL=15k Art Sales Toy 10k 15k 17k 21k 12k 15k 19k

9. CS 44329 For which queries is this index good? Find RECs Dept = “Sales” SAL=20k Find RECs Dept = “Sales” SAL > 20k Find RECs Dept = “Sales” Find RECs SAL = 20k

10. CS 443210 Many alternate methods for indexing

11. CS 443211 key  h(key) Hashing...... Buckets (typically 1 disk block)

12. CS 443212 One example hash function Key = ‘x 1 x 2 … x n ’ n-byte character string Have b buckets Hash function : –h: add (x 1 + x 2 + ….. X n) modulo b

13. CS 443213  This may not be best function …  Read Knuth Vol. 3 if you really need to select a good function. Good hash  Expected number of function:keys/bucket is the same for all buckets

14. CS 443214 Within a bucket: Do we keep keys sorted? Yes, if CPU time critical & Inserts/Deletes not too frequent

15. CS 443215 Next: example to illustrate inserts, overflows, deletes h(K)

16. CS 443216 EXAMPLE 2 records/bucket INSERT: h(a) = 1 h(b) = 2 h(c) = 1 h(d) = 0 01230123 d a c b h(e) = 1 e

17. CS 443217 01230123 a b c e d EXAMPLE: deletion Delete: e f f g maybe move “g” up c d

18. CS 443218 Rule of thumb: Try to keep space utilization between 50% and 80% Utilization = # keys used total # keys that fit If < 50%, wasting space If > 80%, overflows significant depends on how good hash function is & on # keys/bucket

19. CS 443219 How do we cope with growth? Overflows and reorganizations Dynamic hashing Extensible hashing Others …

20. CS 443220 Extensible hashing : idea 1 (a) Use i of b bits output by hash function b h(K)  use i  grows over time…. Note: enables future doubling of space ! 00110101

21. CS 443221 (b) Hash to directory of pointers to buckets (instead of buckets directly) h(K)[i ] to bucket Note : Double space by doubling the directory !............ Extensible hashing : idea 2

22. CS 443222 Example: h(k) is 4 bits; 2 keys/bucket i = 1 1 1 0001 1001 1100 Insert 1010 1 1100 1010 New directory 2 00 01 10 11 i = 2 2 0 1

23. CS 443223 1 0001 2 1001 1010 2 1100 Insert: 0111 0000 00 01 10 11 2 i = Example continued 0111 0000 0111 0001 2 2

24. CS 443224 00 01 10 11 2 i = 2 1001 1010 2 1100 2 0111 2 0000 0001 Insert: 1001 Example continued 1001 1010 000 001 010 011 100 101 110 111 3 i = 3 3

25. CS 443225 Extensible hashing: deletion Merge blocks and cut directory if possible (Reverse insert procedure)

26. CS 443226 Extensible hashing If directory fits into main memory, then access cost is 1 IO, otherwise 2 IOs Can handle growing files - with less wasted space - with no full reorganizations Summary + Indirection (Not bad if directory in memory) Directory doubles in size (Now it fits, now it does not) - - +

27. CS 443227 Use what when : Indexing : Tree-Structures vs Hashing

28. CS 443228 Hashing good for probes given key e.g., SELECT … FROM R WHERE R.A = 5 Indexing vs Hashing

29. CS 443229 INDEXING (Including B Trees) good for Range Searches: e.g., SELECT FROM R WHERE R.A > 5 Indexing vs Hashing

30. CS 443230 Reading Chapter 14 Read –14.3.1 and 14.3.2

31. CS 443231 The BIG picture…. Chapters 11 & 12: Storage, records, blocks... Chapter 13 & 14: Access Mechanisms - Indexes - B trees - Hashing - Multi key Chapter 15 & 16: Query Processing NEXT