2015/10/28 by Patrizio Angelini, Giordano Da Lozzo, Angelini, Patrizio +9
Computer Science · #Computational Geometry (cs.CG) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #cs.CG #cs.DS
paper · pdf · doi:10.48550/arxiv.1510.08274
Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016)
arxiv created 2016/08/29 · arxiv updated 2016/08/30
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.