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URN: urn:nbn:de:0030-drops-133237
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Parameterized Complexity of Geodetic Set

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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 ∈ 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.

BibTeX - Entry

@InProceedings{kellerhals_et_al:LIPIcs:2020:13323,
  author =	{Leon Kellerhals and Tomohiro Koana},
  title =	{{Parameterized Complexity of Geodetic Set}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Yixin Cao and Marcin Pilipczuk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13323},
  URN =		{urn:nbn:de:0030-drops-133237},
  doi =		{10.4230/LIPIcs.IPEC.2020.20},
  annote =	{Keywords: NP-hard graph problems, Shortest paths, Tree-likeness, Parameter hierarchy, Data reduction, Integer linear programming}
}

Keywords: NP-hard graph problems, Shortest paths, Tree-likeness, Parameter hierarchy, Data reduction, Integer linear programming
Seminar: 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)
Issue date: 2020
Date of publication: 04.12.2020


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