Jaffke, Lars
[Author];
Kwon, O-joung
[Author];
Strømme, Torstein J. F.
[Author];
Telle, Jan Arne
[Author]
;
Lars Jaffke and O-joung Kwon and Torstein J. F. Strømme and Jan Arne Telle
[Contributor]
Generalized Distance Domination Problems and Their Complexity on Graphs of Bounded mim-width
Footnote:
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Description:
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.