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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