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arXiv · 2004.07566

Approximating Independent Set and Dominating Set on VPG graphs

Esther Galby·Andrea Munaro
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Abstract

We consider Independent Set and Dominating Set restricted to VPG graphs (or, equivalently, string graphs). We show that they both remain $\mathsf{NP}$-hard on $B_0$-VPG graphs admitting a representation such that each grid-edge belongs to at most one path and each horizontal path has length at most two. On the other hand, combining the well-known Baker's shifting technique with bounded mim-width arguments, we provide simple PTASes on VPG graphs admitting a representation such that each grid-edge belongs to at most $t$ paths and the length of the horizontal part of each path is at most $c$, for some $c \geq 1$.

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Esther Galby, Andrea Munaro. 2020-04-16. Approximating Independent Set and Dominating Set on VPG graphs. https://arxiv.org/abs/2004.07566

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