Additional notes on Hashing

1
Additional notes on Hashing

• And notes on HW4

2
Selected Answers to the Last Assignment

• The records will hash to the following buckets
• K h(K) (bucket number)
• 2369 1
• 3760 0
• 4692 4
• 4871 7
• 5659 3
• 1821 5
• 1074 2
• 7115 3
• 1620 4
• 2428 4 overflow
• 3943 7
• 4750 6
• 6975 7 overflow
• 4981 5
• 9208 0
• Two records out of 15 are in overflow, which will
  require an additional block access. The
• other records require only one block access.
  Hence, the average time to retrieve a

3
Now if you were asked to do this with extendible
hashing

• record1 2369 1 00001
• record2 3760 16 10000
• record3 4692 20 10100
• record4 4871 7 00111
• record5 5659 27 11011
• record6 1821 29 11101
• record7 1074 18 10010
• record8 7115 11 01011
• record9 1620 20 10100
• record10 2428 28 11100
• record11 3943 7 00111
• record12 4750 14 01110
• record13 6975 31 11111
• record14 4981 21 10101
• record15 9208 24 11000

4
Lets go through the first few steps

• K mod 2 (2369 and 4871) in bucket 1, (3760 and
  4692) in bucket 0.
• Now the next record is going to cause a split to
  K mod 4
• The key in extendible hashing is only the bucket
  that overflow needs to be split for the other
  buckets you just use pointer de-referencing
• record 5659 will leave bucket 0 unchanged but
  the pointer derferences will need to be fixed
• Hash element 00 will both point to bucket 0
• Hash element 11 will point to the bucket
  containing records 4871 and 5659 (both ending in
  11) and Hash element 01 will point to record
  containing 2369.
• Then 1821 will get added to the bucket containing
  2369.
• Now adding 1074 the hash entry 10 will point to
  the new block containing this element
• Now adding record 8 (01011) will cause a split
  and we will need to go to K Mod 8.
• And so on.

5
Now if you were to do extendible hashing by
remapping (linear hash)

• This one simply remaps all the data from scratch
  while using the next hash function
• K mod 2, K mod 4, K mod 8
• The tradeoff is access cost is fixed constant
  no dereferencing
• The disadvantage is remapping frequently.