File Organization

1
File Organization

• File Sequence of records
• Fixed-length vs. Variable-length records
• Records are stored to Disk blocks
• Spanned vs. Unspanned Organization
• How to Allocate Disk blocks to disk?
• Contiguous vs. Linked Allocation
• File Organization
• Unordered vs. Ordered
• Hashing

2
Hashing

• Map field values to addresses
• H(field value) ? address of record
• H(k) k mod M
• ASCII codes for ASCII
• Pick random digits of hash field value

3
External Hashing for Disk Files

• Bucket One disk block or cluster of contiguous
  blocks (like fixed-size chaining)
• Hashing maps a key to a bucket number (which is
  then mapped to a physical block)

Bucket
10
40
50
20
80
30
0 1 9
41
Collision? Less problem. (many records in a
bucket)
39
19
69
4
External Hashing

• M buckets
• m max of records in a bucket
• What is best M,m?
• If of records
• If of records mM ? Collisions
• Solution 1 Reorganize with a larger/smaller M,
  and a new hash function
• Solution 2 Dynamic Hashing

5
Dynamic Hashing

• Static hashing hash address space is fixed.
• Dynamic hashing Expand and shrink the file
  dynamically.
• Extendible Hashing
• Linear Hashing

6
Extendible Hashing

• Hash values binary numbers (result of hashing is
  a non-negative integer)
• Change the number of bits used in hashing
• Start with only the leading (final) bit
• Double if overflows ? two leading bits
• Split only one bucket
• Multiple cells may point to a single bucket

7
Extendible Hashing Example h(k) is 4 bits 2
keys/bucket
Global depth (gd)
1
Local Depth

• i

0001
1

• Apply gd of bits as the hash function

1001
1100
Insert 1010
8
Example h(k) is 4 bits 2 keys/bucket
1

• i

0001
1
1001
1100
Insert 1010
9
Example h(k) is 4 bits 2 keys/bucket
1

• i

0001
1
1001
1100
Insert 1010
10
Example continued
i
2
00 01 10 11
1
0001
1001
1010
Insert 0111 0000
1100
11
Example continued
i
2
00 01 10 11
1
0001
0111
1001
1010
Insert 0111 0000
1100
12
Example continued
2
0000
0001
i
2
00 01 10 11
2
0111
Insert 1001
13
Example continued
2
0000
0001
i
2
00 01 10 11
2
0111
Insert 1001
14
Example continued
2
0000
0001
i
2
00 01 10 11
2
0111
Insert 1001
15
Extendible hashing deletion

• Reverse insert procedure
• Merge blocks and cut directory if possible
• No merging of blocks

16
Deletion example

• Run thru insert example in reverse!

17
Example 2 Least Significant Bits
GLOBAL DEPTH
Insert 20
18
Insert h(20)2010100 ? Bucket pointed to by 00
(A), full! Split A, double directory.
2
LOCAL DEPTH
Bucket A
4 12 32 16
GLOBAL DEPTH
2
2
Bucket B
1
5
21
13
00
01
2
10
Bucket C
10
11
2
DIRECTORY
Bucket D
15
7
19
DIRECTORY (doubled in size By simply copying)
19
Extendible Hashing - Question

• File size 100 records
• Bucket size 5 records
• The best-case (smallest possible) size of the
  directory?
• The worst-case?

20
Points to Note

• Does the order of insertion matter?
• Bucket split ? directory doubling
• If local depth becomes global depth
• Worst case
• Skewed hashing Multiple entries with same hash
  values.
• Directory grows very fast (exponentially).
• What about a smoother (linear) growth?
• ? Linear Hashing

21
Linear Hashing

• Another dynamic hashing scheme, an alternative to
  Extendible Hashing.
• Motivation Ext. Hashing uses a directory that
  grows by doubling Can we do better? (smoother
  growth)
• LH split buckets from left to right, regardless
  of which one overflowed (simple, but it works!)
• LH uses overflow pages (chaining approach)

22
Linear Hashing Example

• Initially h(x) x mod N (N4 here)
• Assume 3 records/bucket
• Insert 17 17 mod 4 1
• Bucket id 0 1 2
  3
• 4 8 5 9
  6 7 11

13
23
Linear Hashing Example

• Initially h(x) x mod N (N4 here)
• Assume 3 records/bucket
• Insert 17 17 mod 4 1
• Bucket id 0 1 2
  3
• 4 8 5 9 6
  7 11

Overflow for Bucket 1
13
Split bucket 0, anyway!!
24
Linear Hashing Example

• To split bucket 0, use another function h1(x)
• h0(x) x mod N , h1(x) x mod (2N)
• 0 1 2
  3
• 4 8 5 9 6
  7 11

Split
13
17
25
Linear Hashing Example

• To split bucket 0, use another function h1(x)
• h0(x) x mod N , h1(x) x mod (2N)
• Bucket id 0 1 2 3
  4
• 8 5 9 6 7
  11 4

13
17
26
Linear Hashing Example

• h0(x) x mod N , h1(x) x mod (2N)
• Insert 15 and 3 (to cell 3 - overflows)
• Bucket id 0 1 2
  3 4
• 8 5 9 6
  7 11 4

13
17
27
Linear Hashing Example

• h0(x) x mod N , h1(x) x mod (2N)
• 0 1 2 3 4
  5
• 8 9 6 7
  11 4 13 5

15
17
3
28
Linear Hashing Deletion

• Run thru insert example in reverse!