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By using two types of constant-size switches, it is possible to build
butterfly fat-trees with essentially arbitrary channel capacities as
illustrated in Figure~\ref{fig:scalable-fat-tree} borrowed from
Leiserson.

\begin{figure}
 \centering
 \mbox{\psfig{figure=/homes/rig/figtest/fig-scalable-fat-tree.ps,%
bbllx=120pt,bblly=500pt,bburx=360pt,bbury=750pt}}
 \caption[A scalable fat-tree.]{A scalable fat-tree.  Essentially
arbitrary channel capacities can be obtained by using two types of
constant-size switches.}
 \label{fig:scalable-fat-tree}
 \end{figure}

The mechanics of routing on fat-trees will be further elaborated in
Chapter~\ref{chap:routing}; the remainder of this chapter sketches the
means by which fat-trees are shown universal in order to motivate the
later analyses of routing time and hardware cost.

\end{document}
