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22 files changed, 29 insertions, 2 deletions
diff --git a/chapters/design-space.tex b/chapters/design-space.tex index 9865b26..321c638 100644 --- a/chapters/design-space.tex +++ b/chapters/design-space.tex @@ -592,10 +592,10 @@ reconstructions, one per level. \begin{tabular}{|l l l l|} \hline & \textbf{Gen. BSM} & \textbf{Leveling} & \textbf{Tiering} \\ \hline +$I_A(n)$ & $\Theta\left(\frac{B(n)}{n} s\log_s n)\right)$ & $\Theta\left(\frac{B(n)}{n} s\log_s n\right)$& $\Theta\left(\frac{B(n)}{n} \log_s n\right)$ \\ \hline $\mathscr{Q}(n)$ &$O\left(\log_s n \cdot \mathscr{Q}_S(n)\right)$ & $O\left(\log_s n \cdot \mathscr{Q}_S(n)\right)$ & $O\left(s \log_s n \cdot \mathscr{Q}_S(n)\right)$\\ \hline -$\mathscr{Q}_B(n)$ & $\Theta(\mathscr{Q}_S(n))$ & $O(\log_s n \cdot \mathscr{Q}_S(n))$ & $O(\log_s n \cdot \mathscr{Q}_S(n))$ \\ \hline +%$\mathscr{Q}_B(n)$ & $\Theta(\mathscr{Q}_S(n))$ & $O(\log_s n \cdot \mathscr{Q}_S(n))$ & $O(\log_s n \cdot \mathscr{Q}_S(n))$ \\ \hline $I(n)$ & $\Theta(B(n))$ & $\Theta\left(B\left(\frac{s-1}{s} \cdot n\right)\right)$ & $ \Theta\left(\sum_{i=0}^{\log_s n} B(s^i)\right)$ \\ \hline -$I_A(n)$ & $\Theta\left(\frac{B(n)}{n} s\log_s n)\right)$ & $\Theta\left(\frac{B(n)}{n} s\log_s n\right)$& $\Theta\left(\frac{B(n)}{n} \log_s n\right)$ \\ \hline \end{tabular} \caption{Comparison of cost functions for various layout policies for DSPs} @@ -438,6 +438,33 @@ of Engineering Science and Mechanics \backmatter +\newpage +\begin{align*} + B(n) &\in \Theta(n \log n) \\ + \mathscr{Q}_S(n) &\in \Theta(\log n + k) +\end{align*} + +\begin{align} +I(n) \in \Theta\left(B\left(\frac{n}{2}\right)\right) \\ +I(n) \in \Theta(n \log n) +\end{align} + +\begin{equation} +\mathscr{Q}(n) = \mathscr{Q}_S\left(\frac{n}{2}\right) + \mathscr{Q}_S\left(\frac{n}{2}\right) +\end{equation} + +\begin{equation} +\mathscr{Q}(n) \in \Theta\left(\log^2n + k\log n\right) +\end{equation} + + + + + +\begin{align*} +I_A(n) \in \Theta \left(\frac{B(n)}{n}\cdot \log n\right) \\ +\mathscr{Q}(n) \in O \left(\mathscr{Q}_S(n) \cdot \log n\right) +\end{align*} %Vita \vita{chapters/vita} diff --git a/presentation/comp-presentation.odp b/presentation/comp-presentation.odp Binary files differindex af6a5b9..3ec3f64 100644 --- a/presentation/comp-presentation.odp +++ 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