Interconnection Networks Charles E Leiserson 6 896 Theory

Interconnection Networks Charles E. Leiserson 6. 896 Theory of Parallel Systems March 29, 2004 1

“Ideal” Parallel Computer P+M P+M 2

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

“Ideal” Parallel Computer 4

“Ideal” Parallel Computer 5

“Ideal” Parallel Computer 6

Mesh of Trees 7

Mesh of Trees 8

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

Hypercube 110 010 111 011 100 000 101 001 10

Cube-Connected Cycles 11

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

Butterflies 13

Decomposing a Butterfly 14

Decomposing a Butterfly 15

Decomposing a Butterfly 16

Decomposing a Butterfly 17

Decomposing a Butterfly II 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

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

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

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

Beneš Network 28

Decomposing a Beneš Network n/2 Beneš 29

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

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

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

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

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

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

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

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

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

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

Bitonic Sorting Network Hypercube connections! 40

Bitonic Sort on Butterfly 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