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 and Torus Level Planarity, are polynomial-time solvable. Moreover, we show a complexity dichotomy for testing the Simultaneous Level Planarity of a set of level graphs, with respect to both the number of level graphs and the number of levels.
CITATION STYLE
Angelini, P., Da Lozzo, G., Di Battista, G., Frati, F., Patrignani, M., & Rutter, I. (2016). Beyond level planarity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9801 LNCS, pp. 482–495). Springer Verlag. https://doi.org/10.1007/978-3-319-50106-2_37
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