When collision occur, how do we resolve the
problem????
Rehashing Techniques
Prepared by Perla P. Cosme
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Topic Outline
1. Addressing Techniques
b. Direct Mapping
a.1 Absolute Addressing
a.2 Relative Addressing
c. Directory Look-up
b.1 Directory Structure as a Table
b.2 Directory Structure as a Tree
c. Address Calculation or Hashing
2. Address Calculation
3. Rehashing Strategies
Prepared by: Perla P. Cosme
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Rehashing Techniques
1.
2.
3.
4.
5.
6.
7.
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
Prepared by: Perla P. Cosme
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Preliminaries
To illustrate how each of the different rehashing
techniques
work, we shall apply these
rehashing techniques to a group of words (the
words the primary keys).
Note:
Primary keys need not, be an integer at all
times; it may also of character data type.
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Preliminaries
These words were subjected to a hashing function to get
their relative positions. The hash(ing) function is
described as follows:
1. Take the ASCII value of each letter in the word. The
ASCII table maybe found in almost any Computer
Science or IT book; usually found in the appendix. Or,
simply download one from the internet.
2. If not available in the ASCII table, convert the decimal
equivalent of the letter into its binary form. Consider
only the first 5 significant bits (b4b3b2b1b0) (Why?)
3. Apply XOR operation to binary numbers of the word.
4. The result is converted into its decimal equivalent.
The decimal number is the relative position.
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An Example
Let the word to be hashed is THE. Then,
relative position of the primary key, THE is 25.
hash(THE) = ASCII(T) xor ASCII(H) xor ASCII(E)
= 101002 xor 010002 xor 001012
= 110012
= 2510
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Let’s try this …
Question:
Using the same hash function, what would
be the relative position of the word OF?
Answer:
9
(How did we get the answer?)
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Hash Function Description
If we do the same process (or hashing all
the words) to some common words such as
those on Table 1, then, we can complete their
relative positions, too. (see Table 1 – next slide,
please).
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Table 1. Relative addresses of the Hashed word
WORD
Hash(WORD)
WORD
Hash(WORD)
WORD
Hash(WORD)
THE
25
IT
29
NOT
21
OF
9*
WITH
2
NO
1
AND
11
AS
18
TON
21
TO
27
HIS
18
SAYS
24
A
1
ON
1
ARE
22
IN
7
BE
7
BUT
3
THAT
9*
AT
21
FROM
22
IS
26
BY
27
OR
29
WAS
5
I
9
HAVE
26
HE
13
THIS
6
AN
15
FOR
27
HAD
13
THEY
0
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Some Notes About Table 1
1. The relative positions generated from the
hash function ranges from 0..29 only. (why?)
2. The results or the relative positions creates a
lot of collisions – best example to handle
collision.
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From this time thereon, we shall refer to
Table 1 to illustrate how the different rehashing
techniques work.
Advise: Keep a copy of the table close to
you as we illustrate the rehashing technique.
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Rehashing Techniques
1.
2.
3.
4.
5.
6.
7.
Linear Probing
Two-Pass File
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
Prepared by: Perla P. Cosme
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Question
How do we handle collisions given the
values in Table 1 using Linear Probing
Technique?
Answer:
(Please refer to the board on how the
collisions are handled.)
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Rehashing Techniques
1.
2.
3.
4.
5.
6.
7.
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
Prepared by: Perla P. Cosme
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Rehashing Techniques
1.
2.
3.
4.
5.
6.
7.
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
Prepared by: Perla P. Cosme
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Rehashing Techniques
1.
2.
3.
4.
5.
6.
7.
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
Prepared by: Perla P. Cosme
16
Rehashing Techniques
1.
2.
3.
4.
5.
6.
7.
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
Prepared by: Perla P. Cosme
17
Rehashing Techniques
1.
2.
3.
4.
5.
6.
7.
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
Prepared by: Perla P. Cosme
18
Rehashing Techniques
1.
2.
3.
4.
5.
6.
7.
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
Prepared by: Perla P. Cosme
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