Interconnection Networks

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

Mesh of Trees

Hypercube d = 0 N = 1 d = 1 N = 2 d = 2 N = 4 d = 3 N = 8 d = 4 N = 16

Hypercube 110 111 010 011 100 101 000 001

Cube-Connected Cycles

000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 Butterfly (FFT) Network 0 1 2 0

Butterflies

Decomposing a Butterfly

Decomposing a Butterfly II

Routing on a Butterfly 0 1 2 0 000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111

000 000 001 001 010 010 011 011 100 100 101 101 110 110 111 111 Tree in Butterfly 0 1 2 0

Beneš Network

Decomposing a Beneš Network n/2 Beneš n/2 Beneš

0 5 1 0 2 7 3 4 6 4 5 2 6 3 7 1 Routing on a Beneš Network

5 0 0 1 7 2 4 3 4 6 2 5 3 6 1 7 Routing on a Beneš Network

Bitonic Sorting Network Hypercube connections!

Bitonic Sort on Butterfly