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arXiv · 2203.05364

Parameterized Algorithms for Upward Planarity

Steven Chaplick·Emilio Di Giacomo·Fabrizio Frati·Robert Ganian·Chrysanthi N. Raftopoulou·Kirill Simonov
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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, Kirill Simonov. 2022-03-10. Parameterized Algorithms for Upward Planarity. https://arxiv.org/abs/2203.05364

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