Rectilinear Planarity Testing of Plane Series-Parallel Graphs in Linear Time
Walter Didimo, Michael Kaufmann, Giuseppe Liotta, Giacomo Ortali

TL;DR
This paper presents an optimal linear-time algorithm for testing rectilinear planarity of plane series-parallel graphs and constructing such drawings if they exist, based on a new characterization involving orthogonal spirality intervals.
Contribution
It introduces a novel characterization of rectilinear planar series-parallel graphs and provides an efficient linear-time algorithm for testing and constructing rectilinear drawings.
Findings
Rectilinear planarity testing is solvable in O(n) time for plane series-parallel graphs.
An embedding-preserving rectilinear drawing can be constructed in O(n) time if the graph is rectilinear planar.
The characterization involves intervals of orthogonal spirality of graph components.
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 time for any plane series-parallel graph with vertices. If is rectilinear planar, an embedding-preserving rectilinear planar drawing of can be constructed in 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
