eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-02-05
6:1
6:14
10.4230/LIPIcs.IPEC.2018.6
article
Generalized Distance Domination Problems and Their Complexity on Graphs of Bounded mim-width
Jaffke, Lars
1
https://orcid.org/0000-0003-4856-5863
Kwon, O-joung
2
https://orcid.org/0000-0003-1820-1962
Strømme, Torstein J. F.
1
https://orcid.org/0000-0002-3896-3166
Telle, Jan Arne
1
Department of Informatics, University of Bergen, Norway
Department of Mathematics, Incheon National University, Incheon, South Korea
We generalize the family of (sigma, rho)-problems and locally checkable vertex partition problems to their distance versions, which naturally captures well-known problems such as distance-r dominating set and distance-r independent set. We show that these distance problems are XP parameterized by the structural parameter mim-width, and hence polynomial on graph classes where mim-width is bounded and quickly computable, such as k-trapezoid graphs, Dilworth k-graphs, (circular) permutation graphs, interval graphs and their complements, convex graphs and their complements, k-polygon graphs, circular arc graphs, complements of d-degenerate graphs, and H-graphs if given an H-representation. To supplement these findings, we show that many classes of (distance) (sigma, rho)-problems are W[1]-hard parameterized by mim-width + solution size.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol115-ipec2018/LIPIcs.IPEC.2018.6/LIPIcs.IPEC.2018.6.pdf
Graph Width Parameters
Graph Classes
Distance Domination Problems
Parameterized Complexity