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zO7vYoQKb+A0SDUP05qh5ANC;~GN2vyAQN1W1#ZZO9LR+{@IXEkKp_-CG1NglG(e3g z<*`SWfEU7lPzEco16!~O5m<*cSOp(!!v>T?1yn*6RKqUxKqE9kGju?$sO)EZOAE9@ zH*`S|Iz{=Cb|e73&9Wh0AcYWw<^!-251B-F7z$hY*J&NWd{9MW;T^@WYq-15}kQ2bY_a10D-9IW#f~ JB_%~qMhdhB9aI1S diff --git a/main.tex b/main.tex index 2a65e27..22dc1b4 100644 --- a/main.tex +++ b/main.tex @@ -115,6 +115,30 @@ Authors of \cite{vygen_fptas_2024} $\subset$ authors of How to derive normalized min cut for connectivity interdiction? +\begin{equation*} +\begin{aligned} +\max& & z& & & \\ +s.t.& & \sum_{e} y_e c(e) &\leq B & &\text{(budget for $F$)}\\ +& & \sum_{e\in T} x_e&\geq 1 & &\forall T\quad \text{($x$ forms a cut)}\\ +& & \sum_{e} \min(0,x_e-y_e) w(e)&\geq z & &\\ +& & y_e,x_e&\in\{0,1\} & &\forall e +\end{aligned} +\end{equation*} + +we can assume that $y_e\leq x_e$. + +\begin{equation*} +\begin{aligned} +\min& & \sum_{e} (x_e&-y_e) w(e) & & \\ +% s.t.& & \sum_{e} (x_e-y_e) w(e)&\geq z & &\\ +s.t.& & \sum_{e\in T} x_e&\geq 1 & &\forall T\quad \text{($x$ forms a cut)}\\ +& & \sum_{e} y_e c(e) &\leq B & &\text{(budget for $F$)}\\ +& & x_e&\geq y_e & &\forall e\quad(F\subset C)\\ +& & y_e,x_e&\in\{0,1\} & &\forall e +\end{aligned} +\end{equation*} + +Now this LP looks similar to the normalized min-cut problem. \section{Random Stuff}