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Partitioned Hashing

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Slideshow:

"Traditional" hashing
 
The input of the hash function is the complete searck key K
Problem with the "traditional" hashing technique
 
Partitioned hashing
 
The search key consists of a composite value:

Partitioned hashing
 
Each part is hashed using its own hash function:

Partitioned hashing
 
The different hash values are concatenated to form the final hash value:

Partitioned hashing - Example
 
 

Advantage of Partitioned Hashing

Eample of a Partitioned Hashing Index file

Eample of a Partitioned Hashing Index file

Eample of a Partitioned Hashing Index file

Some example hash values:

Eample of a Partitioned Hashing Index file
 
The Partitioned Hash Index file:

(I wrote the hash value as x.yy to highlight the different hash components)
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• Prelude: "traditional" hashing
  • Traditional hashing:

    The hash function returns the hash value:

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  • Problem with traditional hashing:

    If the key is composite and some component of the key is not known: we cannot compute a meaningful hash value at all !!!

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• Partitioned Hashing
  • Partititioned Hashing:

    The key is a composite: Partititioned Hashing uses n hash functions, one function on one component: The hash value is the concatenation of the individual hash function values:

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  • Example:

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• Advantage of Partitioned Hashing
  • Partitioned Hashing can generate a meaningful hash value for incomplete keys:

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• A complete example
  • Data on people who buy jewelry:

    (age, salary (in $1,000)) A(25,60) D(45,60) G(50,75) J(50,100) B(50,120) E(70,110) H(85,140) K(30,260) C(25,400) F(45,350) I(50,275) L(60,260)

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  • Example hash functions: (for illustration of partitioned hashing only)

    Age: h1( age ) = age % 2 Salary: h2( salary ) = salary % 4

    Some Hash Function values:

    A(25,60) D(45,60) G(50,75) J(50,100) | | | | | | | | V V V V V V V V 100 100 011 000 <---- partitioned hash values B(50,120) E(70,110) H(85,140) K(30,260) C(25,400) F(45,350) I(50,275) L(60,260)

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  • The Partitional Hash index:

    Note:

    I write the hash values as: 0.00 0.01 0.10 0.11 1.00 1.01 1.10 1.11 so you can see the 2 parts more easily In reality, the hash values are as follows: 000 001 010 011 100 101 110 111