SLIDE 1
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Hypercubic Networks
Charles E. Leiserson 6.895 Theory of Parallel Systems
November 2, 2003
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“Ideal” Distributed-Memory Parallel Computer
P+M P+M P+M P+M P+M P+M P+M P+M
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P M 2 1 Ideal Distributed-Memory Parallel Computer P+M P+M - - PDF document
P M 2 1 Ideal Distributed-Memory Parallel Computer P+M P+M - - PDF document
Hypercubic Networks Charles E. Leiserson 6.895 Theory of Parallel Systems November 2, 2003 1 Ideal Parallel Computer P M P M P M P M 2 1 Ideal Distributed-Memory Parallel Computer P+M P+M P+M P+M P+M P+M
SLIDE 2
SLIDE 3
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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
010 011 000 001 110 111 100 101
SLIDE 4
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Cube-Connected Cycles
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Butterfly (FFT) Network
1 2 000 001 010 011 100 101 110 111 000 001 010 011 100 101 110 111
SLIDE 5
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Butterflies
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Decomposing a Butterfly
SLIDE 6
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Decomposing a Butterfly
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Decomposing a Butterfly
SLIDE 7
7
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Decomposing a Butterfly
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Decomposing a Butterfly II
SLIDE 8
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Decomposing a Butterfly II
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Decomposing a Butterfly II
SLIDE 9
9
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Decomposing a Butterfly II
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Decomposing a Butterfly II
SLIDE 10
10
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Decomposing a Butterfly II
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Decomposing a Butterfly II
SLIDE 11
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Routing on a Butterfly
1 2 000 001 010 011 100 101 110 111 000 001 010 011 100 101 110 111
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Tree in Butterfly
1 2 000 001 010 011 100 101 110 111 000 001 010 011 100 101 110 111
SLIDE 12
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Tree in Butterfly
1 2 000 001 010 011 100 101 110 111 000 001 010 011 100 101 110 111
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Beneš Network
SLIDE 13
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n/2 Beneš n/2 Beneš
Decomposing a Beneš Network
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Routing on a Beneš Network
1 2 3 4 5 6 7 5 7 4 6 2 3 1
SLIDE 14
14
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Routing on a Beneš Network
1 2 3 4 5 6 7 5 7 4 6 2 3 1
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Routing on a Beneš Network
1 2 3 4 5 6 7 5 7 4 6 2 3 1
SLIDE 15
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Routing on a Beneš Network
1 2 3 4 5 6 7 5 7 4 6 2 3 1
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Routing on a Beneš Network
1 2 3 4 5 6 7 5 7 4 6 2 3 1
SLIDE 16
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Routing on a Beneš Network
1 2 3 4 5 6 7 5 7 4 6 2 3 1
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Routing on a Beneš Network
1 2 3 4 5 6 7 5 7 4 6 2 3 1
SLIDE 17
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Routing on a Beneš Network
1 2 3 4 5 6 7 5 7 4 6 2 3 1
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Routing on a Beneš Network
1 2 3 4 5 6 7 5 7 4 6 2 3 1
SLIDE 18
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