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Rectilinear-Upward Planarity Testing of Digraphs

Authors Walter Didimo , Michael Kaufmann , Giuseppe Liotta , Giacomo Ortali , Maurizio Patrignani

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Dynamic programming
  • Theory of computation → Graph algorithms analysis
Keywords
  • Graph drawing
  • orthogonal drawings
  • upward drawings
  • rectilinear planarity
  • upward planarity

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Abstract

A rectilinear-upward planar drawing of a digraph G is a crossing-free drawing of G where each edge is either a horizontal or a vertical segment, and such that no directed edge points downward. Rectilinear-Upward Planarity Testing is the problem of deciding whether a digraph G admits a rectilinear-upward planar drawing. We show that: (i) Rectilinear-Upward Planarity Testing is NP-complete, even if G is biconnected; (ii) it can be solved in linear time when an upward planar embedding of G is fixed; (iii) the problem is polynomial-time solvable for biconnected digraphs of treewidth at most two, i.e., for digraphs whose underlying undirected graph is a series-parallel graph; (iv) for any biconnected digraph the problem is fixed-parameter tractable when parameterized by the number of sources and sinks in the digraph.

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Walter Didimo, Michael Kaufmann, Giuseppe Liotta, Giacomo Ortali, and Maurizio Patrignani. Rectilinear-Upward Planarity Testing of Digraphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ISAAC.2023.26

Author Details

Walter Didimo
  • Department of Engineering, University of Perugia, Italy
Michael Kaufmann
  • Department of Computer Science, University of Tübingen, Germany
Giuseppe Liotta
  • Department of Engineering, University of Perugia, Italy
Giacomo Ortali
  • Department of Engineering, University of Perugia, Italy
Maurizio Patrignani
  • Department of Civil, Computer and Aeronautical Engineering, Roma Tre University, Italy

Funding

  • Didimo, Walter: Project AIDMIX - Artificial Intelligence for Decision Making: Methods for Interpretability and eXplainability - Ricerca di Base 2021.
  • Liotta, Giuseppe: MUR of Italy, PRIN Project n. 2022TS4Y3N - EXPAND: scalable algorithms for EXPloratory Analyses of heterogeneous and dynamic Networked Data.

Acknowledgements

We thank Ignaz Rutter for conversations about the problem 1-2-Switch-Flow.

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