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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

Acknowledgements

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

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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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