Interconnection Networks

# Interconnection Networks

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## Interconnection Networks

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1. Interconnection Networks Charles E. Leiserson 6.896 Theory of Parallel Systems March 29, 2004

2. “Ideal” Parallel Computer P+M P+M P+M P+M P+M P+M P+M P+M

3. P M P M P M … … P M “Ideal” Parallel Computer

4. “Ideal” Parallel Computer

5. “Ideal” Parallel Computer

6. “Ideal” Parallel Computer

7. Mesh of Trees

8. Mesh of Trees

9. Hypercube d = 0 N = 1 d = 1 N = 2 d = 2 N = 4 d = 3 N = 8 d = 4 N = 16

10. Hypercube 110 111 010 011 100 101 000 001

11. Cube-Connected Cycles

12. 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 Butterfly (FFT) Network 0 1 2 0

13. Butterflies

14. Decomposing a Butterfly

15. Decomposing a Butterfly

16. Decomposing a Butterfly

17. Decomposing a Butterfly

18. Decomposing a Butterfly II

19. Decomposing a Butterfly II

20. Decomposing a Butterfly II

21. Decomposing a Butterfly II

22. Decomposing a Butterfly II

23. Decomposing a Butterfly II

24. Decomposing a Butterfly II

25. Routing on a Butterfly 0 1 2 0 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111

26. 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 Tree in Butterfly 0 1 2 0

27. 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 Tree in Butterfly 0 1 2 0

28. Beneš Network

29. Decomposing a Beneš Network n/2 Beneš n/2 Beneš

30. 0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

31. 0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

32. 0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

33. 0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

34. 0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

35. 0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

36. 0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

37. 0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

38. 0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

39. 5 0 0 1 7 2 4 3 4 6 2 5 3 6 1 7 Routing on a Beneš Network

40. Bitonic Sorting Network Hypercube connections!

41. Bitonic Sort on Butterfly

42. Bitonic Sort on Butterfly

43. Bitonic Sort on Butterfly

44. Bitonic Sort on Butterfly

45. Bitonic Sort on Butterfly

46. Bitonic Sort on Butterfly

47. Bitonic Sort on Butterfly

48. Bitonic Sort on Butterfly

49. Bitonic Sort on Butterfly

50. Bitonic Sort on Butterfly