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Interconnection Networks. Charles E. Leiserson 6.896 Theory of Parallel Systems March 29, 2004. “Ideal” Parallel Computer. P+M. P+M. P+M. P+M. P+M. P+M. P+M. P+M. P. M. P. M. P. M. …. …. P. M. “Ideal” Parallel Computer. “Ideal” Parallel Computer. “Ideal” Parallel Computer. - PowerPoint PPT Presentation
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Interconnection Networks
Charles E. Leiserson
6.896 Theory of Parallel SystemsMarch 29, 2004
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“Ideal” Parallel Computer
P+MP+M P+MP+M
P+MP+M P+MP+M
P+MP+M
P+MP+M
P+MP+M
P+MP+M
3
“Ideal” Parallel Computer
…
PP
PP
PP
PP
MM
MM
MM
MM…
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“Ideal” Parallel Computer
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“Ideal” Parallel Computer
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“Ideal” Parallel Computer
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Mesh of Trees
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Mesh of Trees
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Hypercube
d = 0N = 1
d = 1N = 2
d = 2N = 4
d = 3N = 8
d = 4N = 16
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Hypercube
010010 011011
000000 001001
110110 111111
100100 101101
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Cube-Connected Cycles
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Butterfly (FFT) Network0 1 2 0
000001010011100101110111
000001010011100101110111
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Butterflies
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Decomposing a Butterfly
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Decomposing a Butterfly
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Decomposing a Butterfly
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Decomposing a Butterfly
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Decomposing a Butterfly II
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Decomposing a Butterfly II
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Decomposing a Butterfly II
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Decomposing a Butterfly II
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Decomposing a Butterfly II
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Decomposing a Butterfly II
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Decomposing a Butterfly II
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Routing on a Butterfly0 1 2 0
000001010011100101110111
000001010011100101110111
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Tree in Butterfly0 1 2 0
000001010011100101110111
000001010011100101110111
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Tree in Butterfly0 1 2 0
000001010011100101110111
000001010011100101110111
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Beneš Network
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n/2Benešn/2
Beneš
n/2Benešn/2
Beneš
Decomposing a Beneš Network
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Routing on a Beneš Network
01234567
50746231
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Routing on a Beneš Network
01234567
50746231
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Routing on a Beneš Network
01234567
50746231
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Routing on a Beneš Network
01234567
50746231
34
Routing on a Beneš Network
01234567
50746231
35
Routing on a Beneš Network
01234567
50746231
36
Routing on a Beneš Network
01234567
50746231
37
Routing on a Beneš Network
01234567
50746231
38
Routing on a Beneš Network
01234567
50746231
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Routing on a Beneš Network
50746231
01234567
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Bitonic Sorting Network
Hypercube connections!
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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Bitonic Sort on Butterfly
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