This document discusses hash indexes and extendible hashing. It begins by explaining basic hash tables and how they allow direct access to records via a hash function. It then describes how hashing can be used in a database management system by storing records in disk blocks based on their hashed key value. The major challenges with static hashing are overflow blocks and coping with data growth. Extendible hashing is presented as a solution that dynamically splits buckets as they overflow and uses an indirection directory that doubles in size as needed to accommodate more data.

1. 1
CS143: Hash Index

2. 2
What is a Hash Table?
• Hash Table
– Hash function
• h(k): key ‡ integer [0…n]
• e.g., h(‘Susan’) = 7
– Array for keys: T[0…n]
– Given a key k, store it in
T[h(k)]
5
Susan4
James3
2
Neil1
0
h(Susan) = 4
h(James) = 3
h(Neil) = 1

3. 3
Why Hash Table?
• Direct access
• Saved space
– Do not reserve a space for
every possible key
• How can we use this idea for
a record search in a DBMS?

4. 4
Hashing for DBMS
(Static Hashing)
(key, record)
.
.
.
Disk blocks
(buckets)
search key Æ h(key)
0
1
2
3
4

5. 5
Issues?
• What hash function?
• Overflow?
• How to store records?

6. 6
Record storage
1. Whole record
2. Key and pointer
.
.
.
record
.
.
.
record
key 1
h(key)
h(key)

7. 7
Overflow and Chaining
• Insert
h(a) = 1
h(b) = 2
h(c) = 1
h(d) = 0
h(e) = 1
• Delete
h(b) = 2
h(c) = 1
0
1
2
3
Do we keep keys sorted inside a block?

8. 8
Questions
• Q: Do we keep keys sorted
inside a block?
• Q: How much space should
we use for “good”
performance?

9. 9
What Hash Function?
• Example
– Key = ‘x1 x2 … xn’ n byte
character string
– Have b buckets
– h: (x1 + x2 + ….. xn) mod b
• Desired property
– Uniformity: same # of keys for
every bucket
• Reference
– “The Art of Computer
Programming Vol. 3” by Knuth

10. 10
Major Problem of
Static Hashing
• How to cope with growth?
– Data tends to grow in size
– Overflow blocks unavoidable
10
20
30
40
50
60
70
80
90
39
31
35
36
32
38
34
33
overflow blocks
hash buckets

11. 11
Idea 1
• Periodic reorganization
– New hash function
– Complete reassignment of records
– Very expensive
10
20
30
40
50
…
33
10
20
30
40
50
60
70
80
90
33
40
50
60

12. 12
Idea 2
• Why don’t we split a bucket
when it overflows?
0 a
3 b
2 d
1 c
e
Insert: h(g) = 1

13. 13
(a) Use i of b bits output by
hash function
Extendible Hashing
(two ideas)
00110101h(K) Æ
b
use i Æ grows over time

14. 14
(b) Use directory that
maintains pointers to hash
buckets (indirection)
Extendible Hashing
(two ideas)
.
.
.
.
.
.
c
e
hash bucketdirectory
h(c)

15. 15
Example
• h(k) is 4 bits; 2 keys/bucket
Insert 0111, 1010
1
1
1
0001
1001
1100
0
1
i =

16. 16
Example continued
Insert 0000
1
0001
2
1001
1010
2
1100
00
01
10
11
2i =
0111

17. 17
Example continued
Insert 1011
00
01
10
11
2i =
21001
1010
21100
20111
20000
0001

18. 18
Questions on
Extendible Hashing
• Q: What will happen if we
have a lot of duplicate search
keys?

19. 19
Duplicate keys
• Insert 0001
1
1
1
0001
0
1
i =
0001

20. 20
Questions on
Extendible Hashing
• Can we provide minimum
space guarantee?

21. 21
Space Waste
2
1
40001
40000
0000
4i =
3

22. 22
Extendible Hashing:
Deletion
• Two options
a) No merging of buckets
b) Merge buckets and shrink
directory if possible

23. 23
Bucket Merge Example
Can we merge a and b? b and c?
Can we shrink the directory?
1
0001
2
1001
2
1100
00
01
10
11
2i =
a
b
c

24. 24
Bucket Merge
Condition
• Bucket merge condition
– Bucket i’s are the same
– First (i-1) bits of the hash key
are the same
• Directory shrink condition
– All bucket i’s are smaller than
the directory i

25. 25
Summary of
Extendible Hashing
• Can handle growing files
– No periodic reorganizations
• Indirection
– Up to 2 disk accesses to
access a key
• Directory doubles in size
– Not too bad if the data is not
too large

26. 26
Hashing vs. Tree
• Can an extendible-hash index
support?
SELECT
FROM R
WHERE R.A > 5
• Which one is better, B+tree
or Extendible hashing?
SELECT
FROM R
WHERE R.A = 5