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Progressive Algorithms for Domination and Independence

Authors Grzegorz Fabiański, Michał Pilipczuk, Sebastian Siebertz, Szymon Toruńczyk

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Author Details

Grzegorz Fabiański
  • Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland
Michał Pilipczuk
  • Institute of Informatics, University of Warsaw, Poland
Sebastian Siebertz
  • Institute of Informatics, Humboldt-Universität zu Berlin, Germany
Szymon Toruńczyk
  • Institute of Informatics, University of Warsaw, Poland

Funding

The work of M. Pilipczuk and S. Siebertz is supported by the National Science Centre of Poland via POLONEZ grant agreement UMO-2015/19/P/ST6/03998, which has received funding from the European Union’s Horizon 2020 research and innovation programme (Marie Skłodowska-Curie grant agreement No. 665778). G. Fabia{ń}ski and Sz. Toru{ń}czyk are supported by the NCN grant 2016/21/D/ST6/01485.

Acknowledgements

We thank Ehud Hrushovski for pointing us to the nfcp property.

Cite As Get BibTex

Grzegorz Fabiański, Michał Pilipczuk, Sebastian Siebertz, and Szymon Toruńczyk. Progressive Algorithms for Domination and Independence. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.STACS.2019.27

Abstract

We consider a generic algorithmic paradigm that we call progressive exploration, which can be used to develop simple and efficient parameterized graph algorithms. We identify two model-theoretic properties that lead to efficient progressive algorithms, namely variants of the Helly property and stability. We demonstrate our approach by giving linear-time fixed-parameter algorithms for the Distance-r Dominating Set problem (parameterized by the solution size) in a wide variety of restricted graph classes, such as powers of nowhere dense classes, map graphs, and (for r=1) biclique-free graphs. Similarly, for the Distance-r Independent Set problem the technique can be used to give a linear-time fixed-parameter algorithm on any nowhere dense class. Despite the simplicity of the method, in several cases our results extend known boundaries of tractability for the considered problems and improve the best known running times.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Finite Model Theory
Keywords
  • Dominating Set
  • Independent Set
  • nowhere denseness
  • stability
  • fixed-parameter tractability

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