1. Chapter 11. Hashing

2. Contents Introduction A Simple Hashing Algorithm
Hashing Functions and Record Distributions
How Much Extra Memory Should Be Used?
Collision Resolution by Progressive Overflow
Storing More Than One Record per Address: Buckets
Making Deletions
Other Collision Resolution Techniques
Patterns of Record Access

3. 1. Introduction O-notation O(1) O(N) : sequential searching O(log2N)
O(logkN) : B-Tree (k : 리프 노드 크기)
What is Hashing?
a = h(K)
h (hash function), K (key), a (home address)
Example
K = BASS h = (first char * second char) mod 1000
a = h(K) = (66 * 65) mod 1000 = 4,290 mod 1000 = 290

4. Introduction Collision
Example key : LOWELL => a = (76 * 79) mod 1000 = 6,004 mod 1000 = OLIVIER => a = (79 * 76) mod 1000 = 6,004 mod 1000 = 4
Several ways to reduce the number of collisions
1. Spread out the records
Good hashing algorithms
2. Use extra memory
3. Put more than one record at a single address
Buckets

5. 2. A Simple Hashing Algorithm
3 Steps
1. Represent the key in numerical form
2. Fold and add
3. Divide by a prime number and use the remainder as the address
Example
Step 1. Represent the Key in Numerical Form
LOWELL =
L O W E L L
Blanks

6. A Simple Hashing Algorithm
Example (계속)
Step 2. Fold and Add
76 79 | | | | | = ( = => 2byte Maximum 값 을 초과하므로)
= => mod = = => mod = = => mod = = => mod = = => mod = 13883
Step 3. Divide by the Size of the Address Space a = s mod n (n : # of address in file) a = mod 100 = 83 a = mod 101 = 46

7. 3. Hashing Functions and Record Distributions
Distributing Records among Addresses
1 2 3 4 5 6 7 8 9 10 A B C D E F G
Record
Address
Best
(a)
1 2 3 4 5 6 7 8 9 10 A B C D E F G
Record
Address
Worst
(b)
Acceptable
Record
Address
1 2 3 4 5 6 7 8 9 10 A B C D E F G
(c)
<Figure 11.3> Different distributions. (a) Uniform distribution(Best) (b) Worst case (c) Randomly distribution (Acceptable)

8. Hashing Functions and Record Distributions
Some Other Hashing Methods
Better than random
Examine keys for a pattern
주민등록 번호
Divide the key by a prime number
Random
Square the key and take the middle =>
Radix transformation

9. 4. How Much Extra Memory Should Be Used ?
Packing Density
Example
r = 75 records
N = 100 address

10. How Much Extra Memory Should Be Used ?
Predicting Collisions for Different Packing Densities
Packing density (%)
Synonyms (%)
<Table 11.2> Effect of packing density on the proportion of records not stored at their home addresses

11. 5. Collision Resolution by Progressive Overflow
Open addressing
Linear probing
address 3
York
h(K) 1 2
Rosen
Novak’s home address 3
Jasper
York’s home address
address 2
Novak
h(K) 4
York

12. Collision Resolution by Progressive Overflow
Search Length
Key
Home Address
# of Access (Search Length)
Adams Bates Cole Dean Evans
Adams 1
Bates 2
Cole 3
Dean 4
Evans 5

13. Collision Resolution by Progressive Overflow
Search Length (계속)
Example
<Figure 11.7> Average search length versus packing density in a hashed file

14. 6. Storing More Than One Record per Address : Buckets
Key
Home Address
Green Hall Jenks King Land Marx Nutt
Green
Hall 1
Jenks 2
King
Land
Marks 3
Nutt 4

15. Storing More Than One Record per Address : Buckets
Effects of Buckets on Performance
r : # of records N : # of addresses b : # of records in a bucket
File without buckets
File with buckets
# of records # of addresses Bucket size Packing density Ratio of records to addresses
r = 750 N = b = r/N = 0.75
r = 750 N = 500 b = r/N = 1.5

16. Storing More Than One Record per Address : Buckets
<Table 11.4> Synonyms causing collisions as a percent of records for different packing densities and different bucket sizes
Packing density
Bucket size 1 2 5 10
20 %
50 %
80 %
100 %
9.4
21.3
31.2
36.8
2.2
10.4
20.4
27.1
0.1
2.5
10.3
17.6
0.0
0.4
5.3
12.5

17. 7. Making Deletions 처음상태 Key Home Address Actual address Adams Jones
Morris
Smith 1 2 3
Adams
Jones 1
Morris 2
Smith 3

18. Making Deletions (1) Tombstones for Handling Deletions
Adams
Jones 1
Morris 2
Smith 3
* Deletion of Morris
Adams
Jones 1
### 2
Smith 3
“Smith는 찾을 수 없다”
### : tombstone This mark indicates that a record once lived there but no longer does

19. Making Deletions (2) Implications of Tombstones for Insertions
Inserting “Smith”
(3) Effects of Deletions and Additions on Performance
Solution to problem of deteriorating average search length
Reorganization

20. 8. Other Collision Resolution Techniques
(1) Double Hashing
Second hashing function
Increment(c) adding
Seek time overhead

21. Other Collision Resolution Techniques
(2) Chained Progressive Overflow
Adams 1
Bates 2
Cole
Key
Home address
Actual Address
Search length(1)
Search length(2)
Adams Bates Cole Dean Evans Flint 3
Dean 4
Evans 5
Flint
Adams 2 1
Bates 3 2
Cole 5 3
Dean -1 4
Evans -1 5
Flint -1

22. Other Collision Resolution Techniques
(3) Chaining with a Separate Overflow Area
Home address
Primary data area
Overflow area
Adams
Cole 2 1
Bates 1
Dean -1 2
Flint -1 3 4
Evans -1

23. Other Collision Resolution Techniques
(4) Scatter Tables: Indexing Revisited
Adams 1 1 2 3 4
Coles 3
Bates 4
Flint -1
Deans -1
Evans -1

24. Patterns of Record Access
A small percentage of the records in a file account for a large percentage of the accesses : / 20 Rule 80% of the accesses are performed on 20% of the records