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The st-Planar Edge Completion Problem Is Fixed-Parameter Tractable

Authors Liana Khazaliya , Philipp Kindermann , Giuseppe Liotta , Fabrizio Montecchiani , Kirill Simonov

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Author Details

Liana Khazaliya
  • Technische Universität Wien, Austria
Philipp Kindermann
  • FB IV - Informatikwissenschaften, Universität Trier, Germany
Giuseppe Liotta
  • Department of Engineering, University of Perugia, Italy
Fabrizio Montecchiani
  • Department of Engineering, University of Perugia, Italy
Kirill Simonov
  • Hasso Plattner Institute, Universität Potsdam, Germany

Funding

Research of LK supported by WWTF (Project ICT22-029); European Union’s Horizon 2020 COFUND programme [LogiCS@TUWien, grant agreement No.101034440]. Research of GL and FM partially supported by MUR of Italy, under PRIN Project n. 2022ME9Z78 - NextGRAAL: Next-generation algorithms for constrained GRAph visuALization, and under PRIN Project n. 2022TS4Y3N - EXPAND: scalable algorithms for EXPloratory Analyses of heterogeneous and dynamic Networked Data.

Acknowledgements

This research was initiated at Dagstuhl Seminar 23162: New Frontiers of Parameterized Complexity in Graph Drawing.

Cite As Get BibTex

Liana Khazaliya, Philipp Kindermann, Giuseppe Liotta, Fabrizio Montecchiani, and Kirill Simonov. The st-Planar Edge Completion Problem Is Fixed-Parameter Tractable. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ISAAC.2023.46

Abstract

The problem of deciding whether a biconnected planar digraph G = (V,E) can be augmented to become an st-planar graph by adding a set of oriented edges E' ⊆ V × V is known to be NP-complete. We show that the problem is fixed-parameter tractable when parameterized by the size of the set E'.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Mathematics of computing → Graph algorithms
Keywords
  • st-planar graphs
  • parameterized complexity
  • upward planarity

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References

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