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Resizing a hash table

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Slideshow:

Motivation: the need to resize a hash index
Initially, the database has few (data ) records:

Motivation: the need to resize a hash index
Over time, the database has grown:
 
Resulting in poorer performance
Motivation: the need to resize a hash index
Over time, the database has grown:
 
Resulting in poorer performance
Solution:: increase the hash bucket size (= dynamic hashing)
How to increase the hash bucket/table size
 
How to increase the hash bucket/table size:     increase the parameter B
What happen when we change the bucket size ?

What happen when we change the bucket size ?

The old hash function will not generate bucket index in the wider range !!!
What happen when we change the bucket size ?

What happen when we change the bucket size ?

What happen when we change the bucket size ?

What happen when we change the bucket size ?
What we need to do to fix the problem when we change the bucket size of a hash table:

What happen when we change the bucket size ?
What we need to do to fix the problem when we change the bucket size of a hash table:
 
Dynamic hashing: change the bucket size without having to re-hash all keys
 

The dynamic hashing techniques that we will discuss

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• The need to grow a hash table
  • Fact:

    The performance of a hash index depends on the number of overflows

    Example:

    No overflows leads to good performance: We need only read 1 disk block to find any search key Many overflows leads to poor performance: We may need to read 3 disk blocks           to find some search keys !!!!

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• Traditional hash functions
  • Recall:

    A hash function will map a search key to a value in the range [0 .. (B−1]:

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  • A typical hash function is computed as follows:

    Hash( key ) = randomNumberGen( key ) % B

    Explanation:

    randomNumberGen(key) = computes a random integer number using the key value (as seed) The modulo operator "% B" is used to: Map the integer random number to a value in the range [0 .. (B−1)]

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• Dicdatical warning
  • Warning:

    The value of B is usually a prime number (This will spread the keys uniformly over the range [0 .. (B−1)]) However: For simplicity, in the following example, I will use: B = 10               (Because computing % 10 is easy)

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• Problem caused by changing the size of a Hash Table
  • Problem: changing the size of a hash table

    Suppose we use a hash table with size = 10 We use the following simple hash function: Hash(x) = x%10 Sample of the hash table content: Suppose we want to increase the hash table size to 20: We must use a different hash function that covers the wider range !!! For example: Hash(x) = x % 20 Result: Some search keys will be hashed into the wrong bucket !!!       Example: Consequence: We cannot find (some) the search keys stored in the hash table using the new hash function !!!

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• Naive solution to solve the problem of changing the Hash Table size
  • Naive (= simple-minded) solution to changing the Hash Table size:

    We re-map all the existing search keys using the new hash function and stored them in the new (size) hash table !!! Example:

    However:

    Re-mapping all existing search keys in a hash table is a very expensive operation !!!

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• Dynamic Hashing: Techniques to change the size of a hash table
  • We will discuss 2 "dynamic" hashing techniques where:

    The size of the hash table can increase (and decrease) When the size of hash table is changed: Only a fraction of the existing search keys need to be re-mapped !!!

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  • The dynamic hashing technqiues are:

    Extensible hashing: Extensible hashing can elminate the need/use of overflow block completely However: the size of the hash table increases exponentially.... Linear hashing: The size of the hash table increases linearly However: Linear hashing cannot elminate the need/use of overflow block