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. “Ideal” Parallel Computer… P M

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. Butterfly (FFT) Network1 2
000
001
010
011
100
101
110
111
000
001
010
011
100
101
110
111

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 1 2
000
000
001
001
010
010
011
011
100
100
101
101
110
110
111
111

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

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

28. Beneš Network

29. Decomposing a Beneš Network

30. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

31. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

32. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

33. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

34. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

35. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

36. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

37. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

38. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

39. Routing on a Beneš Network5 7 4 6 2 3 1 1 2 3 4 5 6 7

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

51. Bitonic Sort on Butterfly

52. Bitonic Sort on Butterfly

53. Bitonic Sort on Butterfly