Lecture 8 Objectives Physical Database Design

Ordered Files
Find
Say we wanted to find record with ordering key value K then we require
a binary search
The binary search starts by reading the middle block, M, calculated as:
M = (1 + B) div 2 where B is the number of blocks
Suppose:
the smallest value in block M is called S and
the largest value in block M is called L
There are 3 possibilities:
1. K < S – this means record K is somewhere in blocks 1 to M-1
2. K < L – this means record K is somewhere in blocks M+1 to B
3. Neither 1 or 2 in which case record K is in the current block, M
In cases 1 and 2 the search continues at the next mid block
For Ordered Files on average we will require ⎡log 2 B ⎤ block access
Hash Files
• Here one or more fields in a record is used to
calculate the location of record for storage and
retrieval
• Unit of storage is a bucket
– these contain blocks which store up to bfr records
• e.g if bfr = 4 then you can store 4 records max per block
• A hash function is used to calculate location of
bucket
– Enter record into next free space in block
– If all the blocks are used up then create an overflow
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Find cont.
Ordered Files
Given the following blocks, find record with key value, K=300
block 1 block 2 block 3 block 4 block 5 block 6
1 2 3 4 5 7 8 11 12 14 16 18 20 30 40 50 100 150 200 300 400
B = 6 so read mid-block number i.e (1 +6) div 2 = block 3
300 not in block 3 and K>18 so look between blocks 4 to 6
block 4 block 5 block 6
20 30 40 50 100 150 200 300 400
Read new mid-block number (4+6) div 2 = block 5
300 not in block 5 and K>200 so look at block 6 - found
Correct block found with 3 block accesses i.e ⎡log2 6 ⎤ =3
- quicker than a linear search which requires 6 file block access
Hash Files
Insert
Assume we have 2 blocks per bucket with bfr = 4
Also assume we have a hash function on K mod 5 – so could have:
Bucket 1 Bucket 2
1 6 11 16 21 26 31 36 22
2 7 12 17
Use overflow buckets when there is no room (collisions)
e.g insert 41 and 46
Bucket 1 Bucket 2
1 6 11 16 21 26 31 36 22
2 7 12 17
Overflow Bucket
bucket and place record in there 41 46
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