Permutation representation through matrix, Computer Networking

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Q. Permutation representation through Matrix?

949_Permutation representation through Matrix.png

2417_Permutation representation through Matrix1.png

Figure: Clos Network

The functioning of this above permutation is displayed in Figure. This permutation is able to be represented by subsequent matrix too,

700_Permutation representation through Matrix2.png

Figure: Permutation representation through Matrix

The upper input of all first stage switches will be connected with respective inputs of 1st middle stage switch and lower input of every first stage switches will be connected with respective inputs of 2nd switch. Likewise, all outputs of 1st switch of middle stage will be connected as upper input of switches at third stage. In Benz network to reduce the complexity the middle stage switches can recursively be broken into N/4 × N/4 (then N/8 × M/8), till switch size becomes 2×2.

The connection in a 2×2 switch will either be straight, exchange, lower broadcast or upper broadcast as shown in the below Figure.

2114_Permutation representation through Matrix3.png

The 8×8 Benz network with all switches replaced by a 2×2 is shown in below Figure:

1134_Permutation representation through Matrix4.png

Figure: Benz Network

1427_Permutation representation through Matrix5.png

The Bens network connection for permutation

would be in this manner:-

1901_Permutation representation through Matrix6.png

Figure: 8X8 BENZ NETWORK OF 4 STAGES

The permutation for P = 480_Permutation representation through Matrix7.png  would be following manner:

94_Permutation representation through Matrix8.png

Figure: Line number for n


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