# Tag Info

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A linear bound is impossible. Suppose your graph is a star, with half of the edges oriented towards the universal vertex $u$ and the rest oriented outward. In the transitive closure, the maximal cliques will be triangles, each of them containing $u$ and exactly one of its inneighbors and one of its outneighbors. This gives a quadratic number of maximal (and ...

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After a bit more searching, it appears that what I'm looking for is unlikely to exist. In [1], it is proven that approximating the minimum maximal independence number (which is equivalent to the minimum size of an independent dominating set) within a factor of $O(n^{1-\epsilon})$ is $\mathrm{NP}$-hard for any $\epsilon > 0$. This remains true even when ...

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Per the section quoted in the comments, it appears that one of the cited documents takes input in the form of an adjacency matrix. In this scenario, taking $s$ and $t$ to correspond to the first and last indices respectively, we can prove that $\Omega(n^2)$ bits of the matrix may need to be read to decide STCONN even under the promise that the \$(n/2)\times(n/...

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