\documentclass[12pt]{article}
\usepackage{../light}

\begin{document}

\pagestyle{empty}

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\mbox{} \vspace{1.5in}

\begin{center}
{\LARGE \textbf{Complete Binary Tree $\mathbf{(N = 4)}$}}
\end{center}

\begin{center}
\includegraphics[width=6.5in]{bintree}
\end{center}

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\newpage \mbox{} \vspace{1in}

\begin{center}
{\LARGE \textbf{Two-Dimenional Array $\mathbf{(N = 4)}$} \\
(a.k.a. Grid, Crossbar)}
\end{center}

\begin{center}
\includegraphics[width=6.5in]{grid}
\end{center}

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\newpage \mbox{} \vspace{1.5in}

\begin{center}
{\LARGE \textbf{Butterfly $\mathbf{(N = 8)}$}}
\end{center}

\begin{center}
\includegraphics[width=6.5in]{butterfly}
\end{center}

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\newpage

\begin{center}
{\LARGE \textbf{Butterfly $\mathbf{(N = 8)}$}}
\end{center}

\begin{center}
\includegraphics[width=6.5in]{butterfly2}
\end{center}

{\LARGE
\noindent Nodes:
\[
\set{(b_1, b_2, \ldots, b_{\log N}, l) \mid b_i = 0 \text{ or } 1, 0 \leq l \leq \log N}
\]
Edges:
\[
(b_1, b_2, \ldots, b_{\log N}, l)
\begin{array}{l}
\nearrow \\
\searrow
\end{array}
\begin{array}{l}
(b_1, \ldots, b_{l+1}, \ldots, b_{\log N}, l + 1) \\
\\
(b_1, \ldots, \overline{b_{l+1}}, \ldots, b_{\log N}, l + 1)
\end{array}
\]
}

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\newpage

\begin{center}
{\LARGE \textbf{Bene\u{s} network $\mathbf{(N = 8)}$}}

\rotatebox{90}{\includegraphics[width=8.25in]{benes}}
\end{center}

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\newpage

\mbox{}
\vspace{0.75in}

\begin{center}
{\LARGE \textbf{Bene\u{s} network $\mathbf{(N = 8)}$}}

\vspace{0.25in}

\includegraphics[width=6.5in]{benes}
\end{center}

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\newpage

\begin{center}
{\LARGE \textbf{Hypercube $\mathbf{(N = 8)}$}}
\end{center}

\begin{center}
\includegraphics[width=5in]{hypercube}
\end{center}

{\LARGE
\noindent Nodes:
\[
\set{(b_1, b_2, \ldots, b_{\log N}) \mid b_i = 0 \text{ or } 1}
\]
Edges:
\begin{multline*}
\bigl\{ ((a_1, \ldots, a_{\log N}), (b_1, \ldots, b_{\log N})) \mid \\
\text{$\vec{a}$ and $\vec{b}$ differ in precisely one bit} \bigr\}
\end{multline*}
}

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\newpage

\begin{center}
{\LARGE \textbf{Butterfly (redrawn)}}
\end{center}

\noindent {\LARGE
\hspace{0.7in} $l = 0$
\hspace{0.9in} $l = 1$
\hspace{0.9in} $l = 2$
\hspace{0.9in} $l = 3$
}

\bigskip
\noindent \includegraphics[width=6.25in]{butterfly3}
\bigskip

{\LARGE Node $(b_1, b_2, \ldots, b_{\log N}, l)$ has been drawn in row:
\[
b_{l+1}, b_{l+2}, \ldots, b_{\log N}, b_1, \ldots, b_l
\]}

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\newpage

\begin{center}
{\LARGE \textbf{De Bruijn Graph $\mathbf{(N = 8)}$}}
\end{center}

\begin{center}
\includegraphics[height=6in]{debruijn}
\end{center}

{\LARGE
\noindent Nodes: \quad 
$\set{(b_1, b_2, \ldots, b_{\log N}) \mid b_i = 0 \text{ or } 1}$

\noindent Edges:
\[
(b_1, b_2, \ldots, b_{\log N})
\begin{array}{l}
\nearrow \\
\searrow
\end{array}
\begin{array}{l}
(b_2, \ldots, b_{\log N}, 0) \\
\\
(b_2, \ldots, b_{\log N}, 1)
\end{array}
\]
}

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\newpage

\mbox{} \vspace{1in}

\begin{center}
{\LARGE \textbf{De Bruijn Graph (redrawn)}}
\end{center}

\begin{center}
\includegraphics[width=6.5in]{debruijn2}
\end{center}

{\LARGE
Edges labels:
\[
(b_1, b_2, \ldots, b_{\log N})
\begin{array}{l}
{\color{red} 0} \\
\nearrow \\
\searrow \\
{\color{red} 1}
\end{array}
\begin{array}{l}
(b_2, \ldots, b_{\log N}, 0) \\
\\
(b_2, \ldots, b_{\log N}, 1)
\end{array}
\]
}

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\end{document}
