eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-03-02
14:1
14:12
10.4230/LIPIcs.IPEC.2017.14
article
The Dominating Set Problem in Geometric Intersection Graphs
de Berg, Mark
Kisfaludi-Bak, Sándor
Woeginger, Gerhard
We study the parameterized complexity of dominating sets in geometric intersection graphs. In one dimension, we investigate intersection graphs induced by translates of a fixed pattern Q that consists of a finite number of intervals and a finite number of isolated points. We prove that Dominating Set on such intersection graphs is polynomially solvable whenever Q contains at least one interval, and whenever Q contains no intervals and for any two point pairs in Q the distance ratio is rational. The remaining case where Q contains no intervals but does contain an irrational distance ratio is shown to be NP-complete and contained in FPT (when parameterized by the solution size). In two and higher dimensions, we prove that Dominating Set is contained in W[1] for intersection graphs of semi-algebraic sets with constant description complexity. This generalizes known results from the literature. Finally, we establish W[1]-hardness for a large class of intersection graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol089-ipec2017/LIPIcs.IPEC.2017.14/LIPIcs.IPEC.2017.14.pdf
dominating set
intersection graph
W-hierarchy