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DOI: 10.4230/LIPIcs.IPEC.2020.20
URN: urn:nbn:de:0030-drops-133237
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13323/
Kellerhals, Leon ; Koana, Tomohiro
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 |
