eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
20:1
20:14
10.4230/LIPIcs.IPEC.2020.20
article
Parameterized Complexity of Geodetic Set
Kellerhals, Leon
1
https://orcid.org/0000-0001-6565-3983
Koana, Tomohiro
1
https://orcid.org/0000-0002-8684-0611
Technische Universität Berlin, Faculty IV, Algorithmics and Computational Complexity, Germany
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.20/LIPIcs.IPEC.2020.20.pdf
NP-hard graph problems
Shortest paths
Tree-likeness
Parameter hierarchy
Data reduction
Integer linear programming