2018/03/09 by Jaffke, Lars, Kwon, O-joung, Strømme, Torstein J. F. +1
#Combinatorics (math.CO) #Computational Complexity (cs.CC) #Discrete Mathematics (cs.DM) #F.2 #FOS: Computer and information sciences #FOS: Mathematics #G.2.2
paper · doi:10.48550/arxiv.1803.03514
We generalize the family of (σ, ρ)-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) (σ, ρ)-problems are W[1]-hard parameterized by mim-width + solution size.