Rectilinear Planarity of Partial 2-Trees
Abstract
A graph is rectilinear planar if it admits a planar orthogonal drawing without bends. While testing rectilinear planarity is NP-hard in general (Garg and Tamassia, 2001), it is a long-standing open problem to establish a tight upper bound on its complexity for partial 2-trees, i.e., graphs whose biconnected components are series-parallel. We describe a new O(n^2)-time algorithm to test rectilinear planarity of partial 2-trees, which improves over the current best bound of O(n^3 \log n) (Di Giacomo et al., 2022). Moreover, for partial 2-trees where no two parallel-components in a biconnected component share a pole, we are able to achieve optimal O(n)-time complexity. Our algorithms are based on an extensive study and a deeper understanding of the notion of orthogonal spirality, introduced several years ago (Di Battista et al, 1998) to describe how much an orthogonal drawing of a subgraph is rolled-up in an orthogonal drawing of the graph.
Cite
@article{arxiv.2208.12558,
title = {Rectilinear Planarity of Partial 2-Trees},
author = {Walter Didimo and Michael Kaufmann and Giuseppe Liotta and Giacomo Ortali},
journal= {arXiv preprint arXiv:2208.12558},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2110.00548 Appears in the Proceedings of the 30th International Symposium on Graph Drawing and Network Visualization (GD 2022)