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z+M5wZr=h%?XsfC9U{F^Pso(I3$l5PQALJ(!h^rxhO#fFO=&&2S{C-BfP*c1RRo6g~ z%R{!5NaM^=>Qq5_OpJGydQSS@i{~EtTYz+C`3Nd4vk5YHH-zJO8!27FSgV9b*u-lF>D3buv6Q}|$K*1_tBO~O{iIwbuwjL8TAR8{=9ewR} zN_Fxl{ZJVanB8E~<-b5?^v)-V7g4YGC*-@X%q>`O6F`E<#=*vpKus;FEQRnNp?ArZ diff --git a/main.tex b/main.tex index 53e50d5..40170b9 100644 --- a/main.tex +++ b/main.tex @@ -196,6 +196,11 @@ The number of breakpoints on $L(\lambda)$ is at most $n-1$. (there is a $\pm1$ difference between principal partition and graph strength... but we dont care those $c\lambda$ terms since the difficult part is minimize $L(\lambda)$ for fixed $\lambda$) +\subsection{principal sequence of partitions for cut interdiction} +I don't expect similar results hold. + +\subsection{integrality gap} +I guess the 2 approximation cut enumeration algorithm implies a integrality gap of 2 for cut interdiction problem. \section{Random Stuff} @@ -220,7 +225,7 @@ s.t.& & \sum_{e\in T} c(e)x_e&\geq k & &\forall T\\ \end{aligned} \end{equation*} -These two LPs have the same optimum. One can see that any feasible solution to +These two LPs have the same optimum. Any feasible solution to LP1 is feasible in LP2. Thus $\opt(LP1) \geq \opt(LP2)$. Next we show that any $x_e$ in the optimum solution to LP2 is always in $[0,c(e)]$. Let $x^*$ be the optimum and