EE - EE 4720 Lecture Notes Generated from file lsli19.dvi....

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EE 4720 Lecture Notes Generated from file lsli19.dvi. This page was generated using an imperfect translator. Text may be poorly positioned and mathematics will be barely readable. Illustrations will not show at all. If possible, view the PostScript versions of these notes. 13-1 * * 13-1 Recursive Decomposition of The Clos Network Result is a much-lower-cost rearrangeable network. In contrast, the network obtained when recursive decomposition was applied to the Omega network had the same properties. For scalable Clos networks with n > 1: Center-stage cells are recursive. Other cells are atomic. 13-1 EE 7725 Lecture Transparency. Formatted 13:04, 19 November 1997 from lsli1* *9. 13-1 13-2 * * 13-2 Two Methods To Compute Cost The powerful way: write recurrence equations: Let C(n; m) be cost of network of size n using m m cells. C(1; m) = m2 xp C(n; m) = m2 mn1 xp +mC(n 1; m) + m2 mn1 xp = 2mn+1 xp +mC(n 1; m)
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Equations like this can easily (more or less) be solved in closed form. The easy? clever? way: Observation: every stage consists of mn1 cells. Number of stages: 2n 1. C(n; m) = m2 mn1 (2n 1) xp = mn+1 (2n 1) xp Substituting N = mn and n = log m N : C(N; m) = mN (2 log m N 1) xp Cost is almost twice the cost of an omega network. But, it is much less than non-recursive Clos network. And it's still a permutation network. 13-2 EE 7725 Lecture Transparency. Formatted 13:04, 19 November 1997 from lsli1* *9. 13-2 13-3 * * 13-3 The Benes Network Named after V. Benes, described in a 1962 BSTJ paper. It is a recursively decomposed Clos network. Routing:
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Use looping algorithm several times: - We're finished if network consists of a single 2 2 crossbar. - Otherwise, use looping algorithm, remembering that this is a recursive network. Result is settings for first and last stages, and permutations for two center-stage recursive cells. - Route each center-stage recursive cell using this procedure. 13-3 EE 7725 Lecture Transparency. Formatted 13:04, 19 November 1997 from lsli1* *9. 13-3 13-4 * * 13-4 Routing Example P = 05 115 213 37 43 50 68 171 89 96 1012 111 1210 132 1414 1* *54 Routing Example, Continued 13-4 EE 7725 Lecture Transparency. Formatted 13:04, 19 November 1997 from lsli1* *9. 13-4 13-5 * * 13-5
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P = 05 115 213 37 43 50 68 171 89 96 1012 111 1210 132 1414 1* *54 13-5 EE 7725 Lecture Transparency. Formatted 13:04, 19 November 1997 from lsli1* *9. 13-5 13-6 * * 13-6 Routing Example, Continued. P1 =
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EE - EE 4720 Lecture Notes Generated from file lsli19.dvi....

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