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Parameterized Algorithms for Upward Planarity

Authors Steven Chaplick , Emilio Di Giacomo , Fabrizio Frati , Robert Ganian , Chrysanthi N. Raftopoulou , Kirill Simonov

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LIPIcs.SoCG.2022.26.pdf
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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Human-centered computing → Graph drawings
Keywords
  • Upward planarity
  • parameterized algorithms
  • SPQR trees
  • treewidth
  • treedepth

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Abstract

We obtain new parameterized algorithms for the classical problem of determining whether a directed acyclic graph admits an upward planar drawing. Our results include a new fixed-parameter algorithm parameterized by the number of sources, an XP-algorithm parameterized by treewidth, and a fixed-parameter algorithm parameterized by treedepth. All three algorithms are obtained using a novel framework for the problem that combines SPQR tree-decompositions with parameterized techniques. Our approach unifies and pushes beyond previous tractability results for the problem on series-parallel digraphs, single-source digraphs and outerplanar digraphs.

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Steven Chaplick, Emilio Di Giacomo, Fabrizio Frati, Robert Ganian, Chrysanthi N. Raftopoulou, and Kirill Simonov. Parameterized Algorithms for Upward Planarity. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.SoCG.2022.26

Author Details

Steven Chaplick
  • Maastricht University, The Netherlands
Emilio Di Giacomo
  • Università degli Studi di Perugia, Italy
Fabrizio Frati
  • Roma Tre University, Rome, Italy
Robert Ganian
  • Technische Universität Wien, Austria
Chrysanthi N. Raftopoulou
  • National Technical University of Athens, Greece
Kirill Simonov
  • Technische Universität Wien, Austria

Funding

  • Di Giacomo, Emilio: MIUR, grant 20174LF3T8, Dip. Ing. - UNIPG, grants RICBA19FM and RICBA20EDG.
  • Frati, Fabrizio: MIUR, grant 20174LF3T8.
  • Ganian, Robert: Austrian Science Fund (FWF) Project Y1329.
  • Raftopoulou, Chrysanthi N.: NTUA research program ΠEBE 2020.
  • Simonov, Kirill: Austrian Science Fund (FWF) Project P31336.

Acknowledgements

The authors thank Fabrizio Montecchiani and Giuseppe Liotta for fruitful discussions on the topic of upward planarity. This research was initiated at Dagstuhl Seminar 21293: Parameterized Complexity in Graph Drawing [Ganian et al., 2021].

References

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