generated from sxlxc/pdflatex-note
72 lines
2.2 KiB
TeX
72 lines
2.2 KiB
TeX
\RequirePackage{scrlfile}
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\makeatletter
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\AfterPackage{beamerbasemodes}{\beamer@amssymbfalse}
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\makeatother
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\documentclass[aspectratio=169,handout]{beamer}
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\usefonttheme{professionalfonts}
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\usetheme{moloch} % new metropolis
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% fonts
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\usepackage{fontspec}
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\setsansfont[
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ItalicFont={Fira Sans Italic},
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BoldFont={Fira Sans Medium},
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BoldItalicFont={Fira Sans Medium Italic}
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]{Fira Sans}
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\setmonofont[BoldFont={Fira Mono Medium}]{Fira Mono}
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\AtBeginEnvironment{tabular}{%
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\addfontfeature{Numbers={Monospaced}}
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}
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\usepackage{lete-sans-math}
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\usepackage{booktabs}
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\title{Connectivity Interdiction \& \\ Perturbed Graphic Matroid Cogirth}
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\date{\today}
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\author{Cong Yu}
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\institute{Algorithm \& Logic Group, UESTC}
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\begin{document}
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\maketitle
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\section{Connectivity interdiction}
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\begin{frame}{Connectivity interdiction}
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\textit{What is the maximum change of edge connectivity in a network when some limited set of edges is being removed?}
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\pause
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\medskip
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\begin{problem}[Zenklusen ORL'14]
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Let $G=(V,E)$ be a graph with edge capacity $c:E\to\mathbb{Z}_+$ and edge removal costs $w:E\to\mathbb{Z}_+$ and let $B\in \mathbb Z_+$ be the budget.
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Find $F\subset E$ with $w(F)\leq B$ s.t. the min-cut in $G-F$ is minimized.
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\end{problem}
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\pause
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\medskip
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connectivity interdiction $\approx$ min-cut + knapsack
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Is there an FPTAS?
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\end{frame}
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\begin{frame}{Previous works}
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\begin{table}[h]
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\centering
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\begin{tabular}{c c c c}
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\toprule
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unit cost $w(\cdot)=1$ & general case & random? & ref \\
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\midrule
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$O(m^2n^4\log n)$ & $O(m^{2+1/\varepsilon}n^4\log n)$ & $\times$ & [Zenklusen ORL'14] \\
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$O(mn^4\log^2 n)$ & $O(m^{1+1/\varepsilon}n^4\log^2 n)$ & $\checkmark$ & [Zenklusen ORL'14] \\
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$\tilde O(m+n^4 B)$ & $O(\frac{m^2n^4}{\varepsilon}\log(Bnc_{\max}))$ & $\times$ & [C.-C. Huang et al. IPCO'24]\\
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$\tilde O(n^3m\log c_{\max})$ & - & $\checkmark$ & [Drange et al. AAAI'26]\\
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$\tilde O(m^2+n^3B)$ & $\tilde O(m^2+mn^3+\frac{n^3}{\varepsilon})$ & $\times$ & this work\\
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$\tilde O(m+n^3B)$ & $\tilde O(mn^3+\frac{n^3}{\varepsilon})$ & $\checkmark$ & this work\\
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\bottomrule
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\end{tabular}
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\caption{PTASes for connectivity interdiction}
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\end{table}
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\end{frame}
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\section{Computing cogirth in perturbed graphic matroids}
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\begin{frame}{Perturbed graphic matroids}
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\end{frame}
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\end{document} |