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Generalized Distance Domination Problems and Their Complexity on Graphs of Bounded mim-width

Authors Lars Jaffke , O-joung Kwon , Torstein J. F. Strømme , Jan Arne Telle



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Author Details

Lars Jaffke
  • Department of Informatics, University of Bergen, Norway
O-joung Kwon
  • Department of Mathematics, Incheon National University, Incheon, South Korea
Torstein J. F. Strømme
  • Department of Informatics, University of Bergen, Norway
Jan Arne Telle
  • Department of Informatics, University of Bergen, Norway

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Lars Jaffke, O-joung Kwon, Torstein J. F. Strømme, and Jan Arne Telle. Generalized Distance Domination Problems and Their Complexity on Graphs of Bounded mim-width. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 6:1-6:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.IPEC.2018.6

Abstract

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Graph Width Parameters
  • Graph Classes
  • Distance Domination Problems
  • Parameterized Complexity

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References

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