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arXiv · 2008.03784

Rectilinear Planarity Testing of Plane Series-Parallel Graphs in Linear Time

Walter Didimo·Michael Kaufmann·Giuseppe Liotta·Giacomo Ortali
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Abstract

A plane graph is rectilinear planar if it admits an embedding-preserving straight-line drawing where each edge is either horizontal or vertical. We prove that rectilinear planarity testing can be solved in optimal $O(n)$ time for any plane series-parallel graph $G$ with $n$ vertices. If $G$ is rectilinear planar, an embedding-preserving rectilinear planar drawing of $G$ can be constructed in $O(n)$ time. Our result is based on a characterization of rectilinear planar series-parallel graphs in terms of intervals of orthogonal spirality that their components can have, and it leads to an algorithm that can be easily implemented.

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Walter Didimo, Michael Kaufmann, Giuseppe Liotta, Giacomo Ortali. 2020-08-09. Rectilinear Planarity Testing of Plane Series-Parallel Graphs in Linear Time. https://arxiv.org/abs/2008.03784

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