CS CS4432: Database Systems II

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

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

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

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

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

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

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

CS 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

CS Many alternate methods for indexing

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

CS 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

CS  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

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

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

CS EXAMPLE 2 records/bucket INSERT: h(a) = 1 h(b) = 2 h(c) = 1 h(d) = d a c b h(e) = 1 e

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

CS 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

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

CS 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 !

CS (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

CS Example: h(k) is 4 bits; 2 keys/bucket i = Insert New directory i =

CS Insert: i = Example continued

CS i = Insert: 1001 Example continued i = 3 3

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

CS 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) - - +

CS Use what when : Indexing : Tree-Structures vs Hashing

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

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

CS Reading Chapter 14 Read – and

CS 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