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\title[Edge Conn Interdiction]{Faster FPTAS for Edge Connectivity Interdiction}
\date{\today}
\author{丛宇}
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\section{Connectivity Interdiction}

\begin{frame}{Edge Connectivity \& Cut}
\begin{definition}
Let $G=(V,E)$ be a undirected connected graph. The minimum cut of $G$ is the minimum set of edges whose removal breaks the connectivity of $G$.
\end{definition}

The edge connectivity of $G$ = $|\text{mincut of $G$}|-1$.
\newline

Edge connectivity is an important measure of network reliability. The greater the edge connectivity, the more difficult it is to break the network's connectivity.
\newline

Now suppose that we want to attack the network. To what extent can we decrease the size of the min-cut by removing a limited set of edges?
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\begin{frame}{Interdiction}
\begin{problem}[edge connectivity interdiction]
The input is a graph $G=(V,E)$ with edge weights $w:E\to \Z_+$ and edge removal cost $c:E\to \Z_+$ and a budget $b\in \Z_+$. The goal is to find a interdiction set $F\subset E$ with $c(F)\leq b$ that minimizes the mincut in $G-F$.
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\begin{frame}{Examples}
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Examples for containing knapsack and for unweighted easy case.
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\begin{frame}{Prevous Works}
Zenklusen \citep{zenklusen_connectivity_2014} first studied this problem and showed the following results:
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\item A PTAS\footnote{polynomial time approximation scheme} for edge connectivity interdiction;
\item A $\tilde{O}(m^2 n^4)$ algorithm for the unit cost case\footnote{$\tilde{O}$ hides polylog factors}.
\end{itemize}

Later \citep{vygen_fptas_2024} discovered an FPTAS\footnote{fully PTAS} with time complexity $\tilde{O}(m^2 n^4/\epsilon)$.
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\section{FPTAS}

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\section{LP Perspective}

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