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main.tex
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main.tex
@@ -343,7 +343,7 @@ Can we show that the gap is 0 or much smaller than 2?
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\begin{enumerate}
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\item One cannot do better than $b\lambda^*$ for general costs.
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There are examples (a 4-vertex path with parallel edges) where the gap is almost $b\lambda^*$.\footnote{see \url{https://gitea.talldoor.uk/sxlxc/edge_conn_interdiction/src/branch/master/gap.py}}
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\item Unit cost. We can assume WLOG that $|C^*|>b$ and that $F^*$ is the set of $b$ edges in $C^*$ with largest weights. By the complementary slackness condition, $(C^{LD},F^{LD})$ is optimal for connectivity interdiction IP. Thus we can see the gap is $1$.
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\item Unit cost. There is still a gap between $L(\lambda^*)$ and $w(C^*\setminus F^*)$.\footnote{see \url{https://gitea.talldoor.uk/sxlxc/edge_conn_interdiction/src/branch/master/plot.py}}
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\end{enumerate}
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\end{remark}
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