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Solving Partial Dominating Set and Related Problems Using Twin-Width

Authors Jakub Balabán , Daniel Mock , Peter Rossmanith

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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Partial Dominating Set
  • Partial Vertex Cover
  • meta-algorithm
  • counting logic
  • twin-width

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Abstract

Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are W[1]-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including nowhere-dense classes. In this paper, we demonstrate that these problems are also fixed-parameter tractable with respect to the twin-width of a graph. Indeed, we establish a more general result: every graph property that can be expressed by a logical formula of the form ϕ≡∃ x₁⋯ ∃ x_k ∑_{α ∈ I} #y ψ_α(x₁,…,x_k,y) ≥ t, where ψ_α is a quantifier-free formula for each α ∈ I, t is an arbitrary number, and #y is a counting quantifier, can be evaluated in time f(d,k)n, where n is the number of vertices and d is the width of a contraction sequence that is part of the input. In addition to the aforementioned problems, this includes also connected partial dominating set and independent partial dominating set.

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Jakub Balabán, Daniel Mock, and Peter Rossmanith. Solving Partial Dominating Set and Related Problems Using Twin-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.13

Author Details

Jakub Balabán
  • Faculty of Informatics, Masaryk University, Brno, Czech Republic
Daniel Mock
  • Dept. of Computer Science, RWTH Aachen University, Germany
Peter Rossmanith
  • Dept. of Computer Science, RWTH Aachen University, Germany

Funding

Daniel Mock and Peter Rossmanith: Supported by the Deutsche Forschungsgemeinschaft (DFG, German Science Foundation) - DFG-927/15-2
  • Balabán, Jakub: Brno Ph.D. Talent Scholarship Holder – Funded by the Brno City Municipality.

Acknowledgements

We would like to thank one of the anonymous reviewers for suggesting a generalization of the logic we considered that also captures the Partial Vertex Cover problem.

References

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