The document discusses Bitonic sort, a parallel sorting algorithm that is well-suited for SIMD array processors. It begins with background on sorting and parallel approaches. It then describes the characteristics of SIMD array processors, including single instruction, multiple data execution and multiple processing elements. The main part of the document outlines the Bitonic sort algorithm, which works by repeatedly merging sublists into larger Bitonic lists until the full list is sorted. It provides an example of sorting 8 elements to illustrate the algorithm's stages of building monotonic and Bitonic lists. Bitonic sort runs in O(log n) time on SIMD array processors by performing sorting operations in parallel across processing elements.

1. 1
Bitonic Sort
in
Shared SIMD Array Processor
Anukul Chandra Panda, Pankaj K Sa
{pandaa,pankajksa}@nitrkl.ac.in
Banshidhar Majhi
bmajhi@nitrkl.ac.in
Presented By :
Dilruk G.A. (148209B)
Jagoda S.D. (148214K)

2. Index …
 Background of Sorting
 SIMD Array Processor
 Bitonic Sort Algorithm
 Conclusion
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3. Background of Sorting
 Sorting of data is needed everywhere
• Data Structures, Joins in databases, Searching Algorithms
 Simple algorithms required O(n2)
• Selection Sort, Insertion Sort, Bubble Sort
 Even advanced algorithm take O(nLogn)
• Merge Sort, Heap Sort, Cube Sort
 Parallel sorting solve the problem
• Bitonic Sort, Parallel Merge Sort
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4. SIMD Array Processor
 Special purpose
processor
• Ex: multi core, GPU
 Single Instruction ,
Multiple Data
• One instruction work on multiple
data items simultaneously
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 Single Program Counter
 Multiple Processing Elements (PEs)

5. Bitonic Sorting Algorithm
 List A: (3, 4, 7, 8) monotonically increasing.
 List B: (6, 5, 2, 1) monotonically decreasing.
 List AB: (3, 4, 7, 8, 6, 5, 2, 1) Bitonic list.
 Bitonic list is two monotonic lists concatenated
together, one increasing and one decreasing.
 For n elements n/2 comparators are using.
 Repeatedly build Bitonic lists and then sort them.
 Just logn stages are required to sort the Bitonic list.
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6. Bitonic Sorting Algorithm
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7. Time Complexity
 In line 2 a shared memory access is needed.
 Line 26 need one more operation to write
data back to the array.
 Within nested loop 2 memory references are
multiplied
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8. Bitonic Sort
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15
16
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17
11
10
8x monotonic lists: 16,11,14,10,17,15,12,13
4x bitonic lists: (16,11),(14,10),(17,15),(12,13)

9. Bitonic Sort
12
15
16
14
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17
11
10
8x monotonic lists: 16,11,14,10,17,15,12,13
4x bitonic lists: (16,11),(14,10),(17,15),(12,13)

10. Bitonic Sort
12
15
16
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17
11
10
13
17
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14
12
15
16
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4x monotonic lists: (11,16),(14,10),(15,17),(13,12)
2x bitonic lists: (11,16,14,10),(15,17,13,12)

11. Bitonic Sort
12
15
16
14
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17
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10
13
17
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14
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15
16
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4x monotonic lists: (11,16),(14,10),(15,17),(13,12)
2x bitonic lists: (11,16,14,10),(15,17,13,12)

12. Bitonic Sort
12
15
16
14
13
17
11
10
13
17
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14
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16
10
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17
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14
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15
10
16
4x monotonic lists: (11,16),(14,10),(15,17),(13,12)
2x bitonic lists: (11,16,14,10),(15,17,13,12)

13. Bitonic Sort
12
15
16
14
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17
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10
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17
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17
11
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2x monotonic lists: (10,11,14,16),(17,15,13,12)
1x bitonic lists: (10,11,14,16,17,15,13,12)

14. Bitonic Sort
12
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sorting

15. Bitonic Sort
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sorting

16. Bitonic Sort
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sorting

17. Bitonic Sort
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sorting

18. Bitonic Sort
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sorting

19. Bitonic Sort
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Done
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20. Bitonic Sorting Example …
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21. Bitonic Sorting Example …
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22. Bitonic Sorting Example
Tuesday, June 16, 2015 22

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