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arXiv · 2001.03098

Parameterized Complexity of Geodetic Set

Leon Kellerhals·Tomohiro Koana
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Abstract

A vertex set $S$ of a graph $G$ is geodetic if every vertex of $G$ lies on a shortest path between two vertices in $S$. Given a graph $G$ and $k \in \mathbb N$, the NP-hard Geodetic Set problem asks whether there is a geodetic set of size at most $k$. Complementing various works on Geodetic Set restricted to special graph classes, we initiate a parameterized complexity study of Geodetic Set and show, on the negative side, that Geodetic Set is W[1]-hard when parameterized by feedback vertex number, path-width, and solution size, combined. On the positive side, we develop fixed-parameter algorithms with respect to the feedback edge number, the tree-depth, and the modular-width of the input graph.

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Leon Kellerhals, Tomohiro Koana. 2020-01-09. Parameterized Complexity of Geodetic Set. https://arxiv.org/abs/2001.03098

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