Interconnection Networks Charles E Leiserson 6 896 Theory
- Slides: 53
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