Locally Checkable Problems Parameterized by Clique-Width

Authors Narmina Baghirova, Carolina Lucía Gonzalez , Bernard Ries , David Schindl

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Author Details

Narmina Baghirova
  • Department of Informatics, University of Fribourg, Switzerland
Carolina Lucía Gonzalez
  • Instituto de Investigación en Ciencias de la Computación (ICC), CONICET-University of Buenos Aires, Argentina
Bernard Ries
  • Department of Informatics, University of Fribourg, Switzerland
David Schindl
  • Department of Informatics, University of Fribourg, Switzerland

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Narmina Baghirova, Carolina Lucía Gonzalez, Bernard Ries, and David Schindl. Locally Checkable Problems Parameterized by Clique-Width. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We continue the study initiated by Bonomo-Braberman and Gonzalez in 2020 on r-locally checkable problems. We propose a dynamic programming algorithm that takes as input a graph with an associated clique-width expression and solves a 1-locally checkable problem under certain restrictions. We show that it runs in polynomial time in graphs of bounded clique-width, when the number of colors of the locally checkable problem is fixed. Furthermore, we present a first extension of our framework to global properties by taking into account the sizes of the color classes, and consequently enlarge the set of problems solvable in polynomial time with our approach in graphs of bounded clique-width. As examples, we apply this setting to show that, when parameterized by clique-width, the [k]-Roman domination problem is FPT, and the k-community problem, Max PDS and other variants are XP.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Graph coloring
  • Mathematics of computing → Combinatorial optimization
  • Mathematics of computing → Combinatorial algorithms
  • Theory of computation → Problems, reductions and completeness
  • locally checkable problem
  • clique-width
  • dynamic programming
  • coloring


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