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main.tex

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