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Yu Cong 2025-04-19 14:20:32 +08:00
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@ -13,7 +13,7 @@
\section{``Cut-free'' Proof} \section{``Cut-free'' Proof}
\begin{problem}[b-free knapsack]\label{bfreeknap} \begin{problem}[b-free knapsack]\label{bfreeknap}
Consider a set of elements $E$ and two weights $w:E\to \Z_+$ and Consider a set of elements $E$ and two weights $w:E\to \Z_+$ and
$c:E\to Z_+$ and a budget $b\in \Z_+$. Given a feasible set $\mathcal $c:E\to \Z_+$ and a budget $b\in \Z_+$. Given a feasible set $\mathcal
F\subset 2^E$, find $\min_{X F\subset 2^E$, find $\min_{X
\in \mathcal F, F\subset E} w(X\setminus F)$ such that $c(F)\leq b$. \in \mathcal F, F\subset E} w(X\setminus F)$ such that $c(F)\leq b$.
\end{problem} \end{problem}