1. CS4432: Database Systems II
Lecture #12
Professor Elke A. Rundensteiner
CS 4432
lecture #11 - indexing & hashing

2. lecture #11 - indexing & hashing
key  h(key)
<key>
Buckets
(typically 1
disk block) .
CS 4432
lecture #11 - indexing & hashing

3. One example hash function
Key = ‘x1 x2 … xn’ n-byte character string
Have b buckets
Example hash function :
h: add (x1 + x2 + ….. Xn) modulo b
CS 4432
lecture #11 - indexing & hashing

4. lecture #11 - indexing & hashing
 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 4432
lecture #11 - indexing & hashing

5. lecture #11 - indexing & hashing
Within a bucket:
Do we keep keys sorted?
Yes, but only if CPU time critical
& Inserts/Deletes not too frequent
CS 4432
lecture #11 - indexing & hashing

6. Next: example to illustrate inserts, overflows, deletes
h(K)
CS 4432
lecture #11 - indexing & hashing

7. EXAMPLE 2 records/bucket1 2 3
INSERT:
h(a) = 1
h(b) = 2
h(c) = 1
h(d) = 0 d a c b e
h(e) = 1
CS 4432
lecture #11 - indexing & hashing

8. lecture #11 - indexing & hashing
EXAMPLE: deletion
Delete: e f 1 2 3 a d b d c c e
maybe move
“g” up f g
CS 4432
lecture #11 - indexing & hashing

9. lecture #11 - indexing & hashing
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 4432
lecture #11 - indexing & hashing

10. How do we cope with growth?
Overflows and reorganizations
Dynamic hashing
Extensible hashing
Others …
CS 4432
lecture #11 - indexing & hashing

11. 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 4432
lecture #11 - indexing & hashing

12. lecture #11 - indexing & hashing
Extensible hashing : idea 2
(b) Hash to directory of pointers to buckets (instead of buckets directly)
h(K)[i ] to bucket
(c) Assume directory of pointers is contiguous
Note : Double space by doubling the directory ! . .
CS 4432
lecture #11 - indexing & hashing

13. Example: h(k) is 4 bits; 2 keys/bucket
New directory 2 00 01 10 11
i = 1
i =
0001 1 1 1
1001 1
1100
1010
1100
Insert 1010
CS 4432
lecture #11 - indexing & hashing

14. lecture #11 - indexing & hashing
Example continued 2
0000
0111
0001
i = 2 00 01 10 11 1
0001
0111 2
1001
1010
Insert:
0111
0000 2
1100
CS 4432
lecture #11 - indexing & hashing

15. lecture #11 - indexing & hashing
Example continued
000
001
010
011
100
101
110
111 3
i =
0000 2
i =
0001 2 00 01 10 11
0111 2
1001
1010 2
1001
1010
Insert:
1001 2
1100
CS 4432
lecture #11 - indexing & hashing

16. Extensible hashing: deletion
Merge blocks and cut directory if possible
(Reverse insert procedure)
CS 4432
lecture #11 - indexing & hashing

17. lecture #11 - indexing & hashing
Extensible hashing
Summary
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 + +
Indirection
(Not bad if directory in memory)
Directory doubles in size
(Now it fits, now it does not) -
CS 4432
lecture #11 - indexing & hashing

18. lecture #11 - indexing & hashing
Use what when :
Indexing : Tree-Structures vs Hashing
CS 4432
lecture #11 - indexing & hashing

19. lecture #11 - indexing & hashing
Indexing vs Hashing
Hashing good for equality probes given key:
e.g., SELECT …
FROM R
WHERE R.A = 5
CS 4432
lecture #11 - indexing & hashing

20. lecture #11 - indexing & hashing
Indexing vs Hashing
Tree indexing (Including B Trees) good for Range Searches:
e.g., SELECT
FROM R
WHERE R.A > 5
CS 4432
lecture #11 - indexing & hashing