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Classes of Intersection Digraphs with Good Algorithmic Properties

Authors Lars Jaffke , O-joung Kwon , 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, South Korea
  • Institute for Basic Science, South Korea
Jan Arne Telle
  • Department of Informatics, University of Bergen, Norway

Funding

  • Jaffke, Lars: Supported by the Norwegian Research Council via project 274526.
  • Kwon, O-joung: Supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. NRF-2018R1D1A1B07050294) and by Institute for Basic Science (IBS-R029-C1).

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Lars Jaffke, O-joung Kwon, and Jan Arne Telle. Classes of Intersection Digraphs with Good Algorithmic Properties. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.STACS.2022.38

Abstract

While intersection graphs play a central role in the algorithmic analysis of hard problems on undirected graphs, the role of intersection digraphs in algorithms is much less understood. We present several contributions towards a better understanding of the algorithmic treatment of intersection digraphs. First, we introduce natural classes of intersection digraphs that generalize several classes studied in the literature. Second, we define the directed locally checkable vertex (DLCV) problems, which capture many well-studied problems on digraphs such as (Independent) Dominating Set, Kernel, and H-Homomorphism. Third, we give a new width measure of digraphs, bi-mim-width, and show that the DLCV problems are polynomial-time solvable when we are provided a decomposition of small bi-mim-width. Fourth, we show that several classes of intersection digraphs have bounded bi-mim-width, implying that we can solve all DLCV problems on these classes in polynomial time given an intersection representation of the input digraph. We identify reflexivity as a useful condition to obtain intersection digraph classes of bounded bi-mim-width, and therefore to obtain positive algorithmic results.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • intersection digraphs
  • H-digraphs
  • reflexive digraphs
  • directed domination
  • directed H-homomorphism

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