unit cost gap is not better
All checks were successful
build pdf / build (push) Successful in 4s

This commit is contained in:
2026-01-11 16:01:57 +08:00
parent 928305623b
commit 979399b211
2 changed files with 63 additions and 1 deletions

View File

@@ -343,7 +343,7 @@ Can we show that the gap is 0 or much smaller than 2?
\begin{enumerate}
\item One cannot do better than $b\lambda^*$ for general costs.
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}}
\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 $1$.
\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}}
\end{enumerate}
\end{remark}