structcomp/inputs/motivation.tex

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2016-06-26 22:30:37 +00:00
\begin{frame}{General Motivation}
\begin{columns}[c]
\begin{column}{0.5\textwidth}
\begin{enumerate}
\item Choose infeasible problem
\begin{itemize}
\item Combinatorial Problems
\item Computational Biology
\item Constraint Satisfaction
\item \dots{}
\end{itemize}
\item Find FPT$_{tw}$ algorithm
\item Model problem as graph
\item Compute \emph{tree composition} with small \emph{tree width}
\uncover<2>{\alert{\item Tract the intractable}}
\end{enumerate}
\end{column}
\begin{column}{0.8\textwidth}
\begin{center}
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(0,1.25) node[] {FPT}
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(0,2.15) node[] {W[i]}
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\begin{frame}{Why Upper Bounds?}
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\metroset{block=fill}
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\begin{block}{We want (efficiently)}
\begin{itemize}
\item \emph{High} Lower Bound: Tree dec. not the right tool
\item \emph{Low} Upper Bound: Tree dec. works
\item Other combinations? -- Not so useful
\end{itemize}
\end{block}
\begin{block}{What this paper is about}
\smallskip
Exact algorithm: Huge constant factor \cite{roehrig1998}
\begin{itemize}
\item[$\rightarrow$] Find a non-optimal tree decomposition
\item[$\rightarrow$] This is also an Upper Bound
\end{itemize}
\end{block}
\end{frame}
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