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1
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
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“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
32
Routing on a Beneš Network
01234567
50746231
33
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
39
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
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