publication . Preprint . 2005

The Linking Probability of Deep Spider-Web Networks

Pippenger, Nicholas;
Open Access English
  • Published: 14 Feb 2005
We consider crossbar switching networks with base $b$ (that is, constructed from $b\times b$ crossbar switches), scale $k$ (that is, with $b^k$ inputs, $b^k$ outputs and $b^k$ links between each consecutive pair of stages) and depth $l$ (that is, with $l$ stages). We assume that the crossbars are interconnected according to the spider-web pattern, whereby two diverging paths reconverge only after at least $k$ stages. We assume that each vertex is independently idle with probability $q$, the vacancy probability. We assume that $b\ge 2$ and the vacancy probability $q$ are fixed, and that $k$ and $l = ck$ tend to infinity with ratio a fixed constant $c>1$. We consi...
free text keywords: Mathematics - Probability, Mathematics - Combinatorics, 90B18, 60C05
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