1. When collision occur, how do we resolve the problem????
Rehashing Techniques
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Topic Outline
Addressing Techniques
Direct Mapping
a.1 Absolute Addressing
a.2 Relative Addressing
Directory Look-up
b.1 Directory Structure as a Table
b.2 Directory Structure as a Tree
Address Calculation or Hashing
Address Calculation
Rehashing Strategies
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Rehashing Techniques
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
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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:
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.
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?)
Apply XOR operation to binary numbers of the word.
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) = xor xor = = 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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8. 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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9. Table 1. Relative addresses of the Hashed word
Hash(WORD)
THE 25 IT 29
NOT 21 OF 9*
WITH 2 NO 1
AND 11 AS 18
TON TO 27
HIS
SAYS 24 A ON
ARE 22 IN 7 BE
BUT 3
THAT AT
FROM IS 26 BY OR
WAS 5 I 9
HAVE HE 13
THIS 6 AN 15
FOR
HAD
THEY
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Some Notes About Table 1
The relative positions generated from the hash function ranges from only. (why?)
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
Linear Probing
Two-Pass File
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
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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
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
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Rehashing Techniques
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
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
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Rehashing Techniques
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
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
Linear Probing
Two-Pass File Creation
Separate Overflow Area
Double Hashing
Synonym Chaining
Bucket Addressing
Bucket Chaining
Prepared by: Perla P. Cosme