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\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}
\textit{What is the maximum change of edge connectivity in a network when some limited set of edges is being removed?}
\pause

\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}
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\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}
\end{frame}
\end{document}