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arXiv · 1908.05015

Sketched Representations and Orthogonal Planarity of Bounded Treewidth Graphs

Emilio Di Giacomo·Giuseppe Liotta·Fabrizio Montecchiani
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Abstract

Given a planar graph $G$ and an integer $b$, OrthogonalPlanarity is the problem of deciding whether $G$ admits an orthogonal drawing with at most $b$ bends in total. We show that OrthogonalPlanarity can be solved in polynomial time if $G$ has bounded treewidth. Our proof is based on an FPT algorithm whose parameters are the number of bends, the treewidth and the number of degree-2 vertices of $G$. This result is based on the concept of sketched orthogonal representation that synthetically describes a family of equivalent orthogonal representations. Our approach can be extended to related problems such as HV-Planarity and FlexDraw. In particular, both OrthogonalPlanarity and HV-Planarity can be decided in $O(n^3 \log n)$ time for series-parallel graphs, which improves over the previously known $O(n^4)$ bounds.

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Emilio Di Giacomo, Giuseppe Liotta, Fabrizio Montecchiani. 2019-08-14. Sketched Representations and Orthogonal Planarity of Bounded Treewidth Graphs. https://arxiv.org/abs/1908.05015

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