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- W2953023571 abstract "We study treewidth sparsifiers. Informally, given a graph $G$ of treewidth $k$, a treewidth sparsifier $H$ is a minor of $G$, whose treewidth is close to $k$, $|V(H)|$ is small, and the maximum vertex degree in $H$ is bounded. Treewidth sparsifiers of degree $3$ are of particular interest, as routing on node-disjoint paths, and computing minors seems easier in sub-cubic graphs than in general graphs. In this paper we describe an algorithm that, given a graph $G$ of treewidth $k$, computes a topological minor $H$ of $G$ such that (i) the treewidth of $H$ is $Omega(k/text{polylog}(k))$; (ii) $|V(H)| = O(k^4)$; and (iii) the maximum vertex degree in $H$ is $3$. The running time of the algorithm is polynomial in $|V(G)|$ and $k$. Our result is in contrast to the known fact that unless $NP subseteq coNP/{sf poly}$, treewidth does not admit polynomial-size kernels. One of our key technical tools, which is of independent interest, is a construction of a small minor that preserves node-disjoint routability between two pairs of vertex subsets. This is closely related to the open question of computing small good-quality vertex-cut sparsifiers that are also minors of the original graph." @default.
- W2953023571 created "2019-06-27" @default.
- W2953023571 creator A5036503505 @default.
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- W2953023571 date "2014-10-04" @default.
- W2953023571 modified "2023-09-27" @default.
- W2953023571 title "Degree-3 Treewidth Sparsifiers" @default.
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