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fix bug

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Yu Cong 2025-04-13 13:19:25 +08:00
parent 5c6f64542f
commit 0d69b8bf80
2 changed files with 3 additions and 2 deletions
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@ -166,7 +166,8 @@ s.t.& & \sum_{e\in T} x_e+y_e&\geq 1 & &\forall T\quad \text{($x$ fo
Note that now this is almost a positive covering LP. Let $L(\lambda)= \min \{ w(C\setminus F)-\lambda(b-c(F)) | \forall \text{cut $C$}\;\forall F\subset C
% \land c(F)\leq b
\}$ Consider the Lagrangian dual,
\}$.
Consider the Lagrangian dual,
\begin{equation*}
\max_{\lambda\geq 0} L(\lambda)= \max_{\lambda\geq 0} \min \left\{ w(C\setminus F)-\lambda(b-c(F)), \forall \text{cut $C$}\;\forall F\subset C
% \land c(F)\leq b
@ -174,7 +175,7 @@ Note that now this is almost a positive covering LP. Let $L(\lambda)= \min \{ w(
\end{equation*}
At this point, it becomes clear how the normalized min-cut is implicated in \cite{vygen_fptas_2024}. The optimum of normalized min-cut is exactly the value of $\lambda$ when $L(\lambda)$ is 0.
% At this point, it becomes clear how the normalized min-cut is implicated in \cite{vygen_fptas_2024}. The optimum of normalized min-cut is exactly the value of $\lambda$ when $L(\lambda)$ is 0.
\section{Random Stuff}