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a/main.tex +++ b/main.tex @@ -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}