Parameterized Algorithms for Upward Planarity

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

doi:10.48550/arXiv.2203.05364

Parameterized Algorithms for Upward Planarity

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

Research output: Working paper / Preprint › Preprint

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.

Original language	English
DOIs	https://doi.org/10.48550/arXiv.2203.05364
Publication status	Published - 10 Mar 2022

Keywords

cs.CG
cs.DS

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10.48550/arXiv.2203.05364Licence: CC BY

1 Chapter

Parameterized Algorithms for Upward Planarity
Chaplick, S., Giacomo, E. D., Frati, F., Ganian, R., Raftopoulou, C. N. & Simonov, K., 1 Jun 2022, 38th International Symposium on Computational Geometry, SoCG 2022. Goaoc, X. & Kerber, M. (eds.). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Vol. 224. p. 26:1-26:16 26. (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 224).
Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

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title = "Parameterized Algorithms for Upward Planarity",

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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author = "Steven Chaplick and Giacomo, {Emilio Di} and Fabrizio Frati and Robert Ganian and Raftopoulou, {Chrysanthi N.} and Kirill Simonov",

note = "Short version appeared at the 38th International Symposium on Computational Geometry (SoCG 2022)",

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AU - Chaplick, Steven

AU - Giacomo, Emilio Di

AU - Frati, Fabrizio

AU - Ganian, Robert

AU - Raftopoulou, Chrysanthi N.

AU - Simonov, Kirill

N1 - Short version appeared at the 38th International Symposium on Computational Geometry (SoCG 2022)

PY - 2022/3/10

Y1 - 2022/3/10

N2 - 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.

AB - 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.

KW - cs.CG

KW - cs.DS

U2 - 10.48550/arXiv.2203.05364

DO - 10.48550/arXiv.2203.05364

M3 - Preprint

BT - Parameterized Algorithms for Upward Planarity

ER -

Parameterized Algorithms for Upward Planarity

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Parameterized Algorithms for Upward Planarity

Cite this