Slideshow:
Extensible Hashing: Example 1
Initial state
Insert the search key X that has a hash value h(X) = 1011
Extensible Hashing: Example 1
Find the (physical) hash bucket to insert:
Insertion will cause bucket (disk block) to overflow
Extensible Hashing: Example 1
Because i' = i, we must double the logical hash table size (i++):
We must also map the new logical bucket to their physical buckets
Extensible Hashing: Example 1
We split the physical bucket (to free space for insertion)
Update the physical bucket i' parameter to 2
Extensible Hashing: Example 1
Adjust the logical → physical mapping
After the split, we try the insertion again...
Extensible Hashing: Example 1
Hash - now we use i = 2 bits:
We find bucket 11 (binary)....
Extensible Hashing: Example 1
Insert is now successful:
Done !
Extensible Hashing: Example 1
Redrawn:
Extensible Hashing: Example 2
Initial state:
Insert the search key X that has a hash value h(X) = 0010
Extensible Hashing: Example 2
Find the hash bucket to insert:
Insert the search key X that has a hash value h(X) = 0010
Extensible Hashing: Example 2
Insertion is successful !!!
Notice that we only need 1 bit to obtain the hash value !!
Extensible Hashing: Example 2
This figure clearly shows that 00 and 01 are mapped to physical bucket 00:
Extensible Hashing: Example 3
Initial state
Insert the search key X that has a hash value h(X) = 0000
Extensible Hashing: Example 3
Find the (physical) hash bucket to insert:
Insertion will cause bucket (disk block) to overflow
Extensible Hashing: Example 3
Find the (physical) hash bucket to insert:
Because bucket i' < i, we do not increase i !!!
Extensible Hashing: Example 3
We split the physical bucket (to free space for insertion)
Update the physical bucket i' parameter to 2
Extensible Hashing: Example 3
Adjust the logical → physical mapping
After the split, we try the insertion again....
Extensible Hashing: Example 3
Hash again - still using 2 bits
We find bucket 00 (binary)....
Extensible Hashing: Example 3
Insertion is successul
Done !!!
- Examples:
Extensible Hashing
- Initial State:
- Insert a record
X such that:
h(X) = 0101:
Bucket 1 is full !!!
- Because
i == i' :
- Double the logical hash table
Result:
- Re-hash
all keys in
the full bucket "1" into
buckets "01" and "11"
using 2 bits (because i' = 1) in
RandomNum:
- Adjust
the Bucket[01]
and Bucket[11]:
- Insert the
key
again ---
now using
i = 2:
Result:
- Initial State:
- Example continued:
Insert a record
X
such that:
h(X) = 0010:
- Initial State:
- Inserting a record
X
such that:
h(X) = 0010:
Result:
Note:
- Hash values
ending in
xxxxxxx00 xxxxxxx10will both hash into the same physical hash bucket !!!
- That's because
both logical hash buckets
bucket[00] and
bucket[01] are
mapped to the
same physical hash bucket
!!!
- Initial State:
- Example continued:
Insert a record
X
such that:
h(X) = 0000:
- Initial State:
- Inserting a record
X
such that:
h(X) = 0000:
- Because:
i > i'
- We do not need to double the logical hash table !!!
-
Re-hash
all keys in
the full bucket "0" into
buckets "00" and "01"
using 2 bits (because i' = 1) in
RandomNum:
Adjust the Bucket[ ]:
- Insert again using the
new configuration:
Result:
- Initial State: