English

Beyond Level Planarity

Data Structures and Algorithms 2016-08-30 v4 Computational Geometry

Abstract

In this paper we settle the computational complexity of two open problems related to the extension of the notion of level planarity to surfaces different from the plane. Namely, we show that the problems of testing the existence of a level embedding of a level graph on the surface of the rolling cylinder or on the surface of the torus, respectively known by the name of Cyclic Level Planarity\textit{Cyclic Level Planarity} and Torus Level Planarity\textit{Torus Level Planarity}, are polynomial-time solvable. Moreover, we show a complexity dichotomy for testing the Simultaneous Level Planarity\textit{Simultaneous Level Planarity} of a set of level graphs, with respect to both the number of level graphs and the number of levels.

Keywords

Cite

@article{arxiv.1510.08274,
  title  = {Beyond Level Planarity},
  author = {Patrizio Angelini and Giordano Da Lozzo and Giuseppe Di Battista and Fabrizio Frati and Maurizio Patrignani and Ignaz Rutter},
  journal= {arXiv preprint arXiv:1510.08274},
  year   = {2016}
}

Comments

Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016)

R2 v1 2026-06-22T11:30:58.208Z