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Illustrating Extensible Hashing using a decimal number example

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Slideshow:

The traditional hashing technique

Hash index identifies the hash bucket directly
The extensible hashing technique

Hash index identifies the hash bucket indirectly through a mapping table
The extensible hashing technique
The effect of changing (doubling) the hash function range:

The extensible hashing technique
The effect of changing (doubling) the hash function range:

Notice that the physical bucket array size has not changed (still 10 buckets) !!!
The extensible hashing technique
We can map the additional logical hash buckets to the physical hash buckets as follows:

Notice the mapping will preserve the outcome of the old hash function !!!
The extensible hashing technique
We can map the additional logical hash buckets to the physical hash buckets as follows:

In other words: we do not need to rehash any key when we change the hash function !!!
Gradual increase in the physical buck size
Suppose we insert a seearch key into a full hash bucket:

Traditionally, we resolve the overflow using a overflow disk block to store the new search key
Gradual increase in the physical buck size
ALternative way to resolve overflow: (1) increase the physical bucket array

We rehash the keys in the overflow bucket into 2 physical buckets using the new hash function
Gradual increase in the physical buck size
ALternative way to resolve overflow: (2) remap the logical → physical bucket array

Notice the larger hash range is correct (without having to rehash all search keys) !!
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• Illustrating Extensible Hashing using a decimal number example
  • Consider the following hash function:

    Hash(x) = x % 10

    And the following state:

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  • Extensible Hashing introduces an extra level of mapping:

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  • Suppose that we change the hash function to:

    Hash(x) = x % 20

    In Extensible Hashing, we will double the logical hahs table:

    We do not have to re-hash any search key to make the new hash function work.

    We just map the new logical hash buckets to the correct physical hash buckets:

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  • Furthermore, we can accomodate bucket overflow graduately:

    Suppose we insert the search key 39 into a full bucket: We do not need to split all buckets !!! We only have to split the overflow bucket: And then link the new (physical) hash bucket to the hash table: