Hypercubic%20Networks

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Hypercubic Networks

• Charles E. Leiserson
• 6.895 Theory of Parallel Systems
• November 2, 2003

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Ideal Parallel Computer
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Ideal Distributed-Memory Parallel Computer
PM
PM
PM
PM
PM
PM
PM
PM
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Interconnection Networks
linear array
binary tree
2D mesh
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Hypercube
d 0 N 1
d 1 N 2
d 2 N 4
d 3 N 8
d 4 N 16
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Hypercube
110
111
010
011
100
101
000
001
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Cube-Connected Cycles
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Butterfly (FFT) Network
0
1
2
0
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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 Butterfly
0
1
2
0
000
000
001
001
010
010
011
011
100
100
101
101
110
110
111
111
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Tree in Butterfly
0
1
2
0
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Tree in Butterfly
0
1
2
0
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Beneš Network
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Decomposing a Beneš Network
n/2 Beneš
n/2 Beneš
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Routing on a Beneš Network
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Routing on a Beneš Network
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Routing on a Beneš Network
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Routing on a Beneš Network
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Routing on a Beneš Network
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Routing on a Beneš Network
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Routing on a Beneš Network
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Routing on a Beneš Network
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Routing on a Beneš Network
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Routing on a Beneš Network