2026-08-06T00:31:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17316 2024-03-06T10:59:26Z ddc:004 open_access

Locally Checkable Problems Parameterized by Clique-Width Baghirova, Narmina Gonzalez, Carolina Lucía Ries, Bernard Schindl, David locally checkable problem clique-width dynamic programming coloring 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Narmina Baghirova and Carolina Lucía Gonzalez and Bernard Ries and David Schindl 2022 Is Part Of LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2022.31 urn:nbn:de:0030-drops-173167 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.31 eng https://creativecommons.org/licenses/by/4.0/legalcode