Sorting Networks

1. Sorting Networks

2. Sorting 4 10 9 9 3 8 1 7 4 2 3 10 2 8 1 7

3. Sorting Network (Bitonic Sorting Network)

4. Sorting Network (Bitonic Sorting Network)

5. Comparator max(x,y) x min(x,y) y

6. Comparator max 1 9 9 1 min

7. Comparator max 100 100 4 4 min

9. Levels 1 2 3 Width = 4 Depth = 3

10. 1 8 2 5

11. 8 1 5 2 Level 1

12. 8 5 1 2 Level 2

13. 8 5 2 1 Level 3

14. Input Output 1 8 8 5 2 2 5 1

15. Input Output 4 10 9 9 3 8 1 7 2 4 10 3 8 2 7 1

16. levels 2 1 3 4 5 6 4 10 9 9 3 8 1 7 2 4 10 3 8 2 7 1

17. Recursive construction of Bitonic Sorting Network Sort(n) Sort(n/2) In Merge(n) Out Sort(n/2) depth

18. Recursive construction of merging network Merge(n) Merge(n/2) Merge(n/2) depth

19. Induction Basis Sort(2) Merge(2)

20. Width Sorting network depth: Merger width Total depth

21. Counting Networks

22. The Counting Problem 0 Shared variable

23. Token = Increment request 0 Shared variable

24. Increment request 0 1 Shared variable

25. 1 Shared variable

26. Increment request 1 Shared variable

27. Increment request 1 2 Shared variable

28. 2 Shared variable

29. Increment request 2 Shared variable

30. Increment request 2 3 Shared variable

31. Sequential Bottleneck 2 3 1 4 0 5 6 Shared variable The requests have to be serialized

32. Counting Network Outputs Inputs

33. Counting Network

34. Balancer Token Outputs Inputs

35. Balancer Outputs Inputs

36. Balancer

37. Balancer

38. Balancer

39. Balancer

40. Balancer

41. Balancer

42. Balancer All tokens together

43. Balancer Step property

44. Balancer Step property Another example

45. Balancer Step property Another example

46. Balancer Step property Another example

47. Counting Network (Bitonic Counting Network)

48. Counting Network

49. Counting Network

50. Counting Network