Improve Run Generation

1
Improve Run Generation

• Overlap input,output, and internal CPU work.
• Reduce the number of runs (equivalently, increase
  average run length).

2
Internal Quick Sort
Use 6 as the pivot (median of 3). Input first,
middle, and last blocks first. In-place
partitioning.
Input blocks from the ends toward the
middle. Sort left and right groups
recursively. Can begin output as soon as left
most block is ready.
3
Alternative Internal Sort Scheme
Partition into 3 areas, each may be more than 1
block in size.
DISK
DISK
4
Steady State Operation

• Synchronization is done when the current internal
  sort terminates.

5
New Strategy

• Use 2 input and 2 output buffers.
• Rest of memory is used for a min loser tree.

• Actually, 3 buffers adequate.

6
Steady State Operation

• Synchronization is done when the active input
  buffer gets empty (the active output buffer will
  be full at this time).

7
Initialize
3
4
8
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3
6
8
1
5
7
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6
9
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5
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5
8
Fill From Disk
8
Initialize
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6
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8
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7
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9
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8
Fill From Disk
9
Initialize
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Fill From Disk
10
Initialize
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Fill From Disk
11
Initialize
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Fill From Disk
12
Initialize
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8
Fill From Disk
13
Generate Run 1
Fill From Tree
3 5 4
Fill From Disk
14
Generate Run 1
Fill From Tree
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6
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9
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3 5 4
Fill From Disk
15
Generate Run 1
Fill From Tree
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3 5 4
Fill From Disk
16
Generate Run 1
Fill From Tree
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6
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8
3 5 4
Interchange Role Of Buffers
Fill From Disk
17
Interchange Role Of Buffers
Write To Disk
Fill From Tree
1
2
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3
2
6
3
5
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8
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9
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8
1 9 2
Fill From Disk
18
Continue With Run 1
Write To Disk
Fill From Tree
1
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6
3
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9
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8
1 9 2
Fill From Disk
19
Continue With Run 1
Write To Disk
Fill From Tree
3
1
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6
3
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8
1
1 9 2
Fill From Disk
20
Continue With Run 1
Write To Disk
Fill From Tree
3
1
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6
3
5
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8
1
1 9 2
Fill From Disk
21
Continue With Run 1
Write To Disk
Fill From Tree
3
1
2
3
4
3
2
3
4
6
3
5
4
4
8
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9
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2
4
6
8
5
7
6
9
4
5
5
8
1
1 9 2
Interchange Role Of Buffers
Fill From Disk
22
Write To Disk
Fill From Tree
Interchange Role Of Buffers
3
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1
6 1 3
Fill From Disk
23
Continue With Run 1
Write To Disk
Fill From Tree
3
3
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3
3
4
6
3
5
4
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8
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1
6 1 3
Fill From Disk
24
Continue With Run 1
Write To Disk
Fill From Tree
3
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3
3
4
6
3
5
4
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8
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8
1
6 1 3
Fill From Disk
25
Continue With Run 1
Write To Disk
Fill From Tree
3
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3
6
3
5
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8
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1
6 1 3
Fill From Disk
26
RUN SIZE

• Let k be number of external nodes in loser tree.
• Run size gt k.
• Sorted input gt 1 run.
• Reverse of sorted input gt n/k runs.
• Average run size is 2k.

27
Comparison

• Memory capacity m records.
• Run size using fill memory, sort, and output run
  scheme m.
• Use loser tree scheme.
• Assume block size is b records.
• Need memory for 4 buffers (4b records).
• Loser tree k m 4b.
• Average run size 2k 2(m 4b).
• 2k gt m when m gt 8b.

28
Comparison

• Assume b 100.

29
Comparison

• Total internal processing time using fill memory,
  sort, and output run scheme O((n/m) m
  log m) O(n log m).
• Total internal processing time using loser tree
  O(n log k).
• Loser tree scheme generates runs that differ in
  their lengths.

30
Merging Runs Of Different Length
22
22
13
7
15
7
Cost 42
Cost 44
Best merge sequence?