Rolling Upward Planarity Testing of Strongly Connected Graphs
نویسندگان
چکیده
A graph is upward planar if it can be drawn without edge crossings such that all edges point upward. Upward planar graphs have been studied on the plane, the standing and rolling cylinders. For all these surfaces, the respective decision problem NP-hard in general. Efficient algorithms exist if the graph contains a single source and a single sink, but only for the plane and standing cylinder Here we show that there is a linear-time algorithm to test whether a strongly connected graph is upward planar on the rolling cylinder. For our algorithm, we introduce dual and directed SPQR-trees as extensions of SPQR-trees.
منابع مشابه
Upward planar graphs and their duals
We consider upward planar drawings of directed graphs in the plane (UP), and on standing (SUP) and rolling cylinders (RUP). In the plane and on the standing cylinder the edge curves are monotonically increasing in y-direction. On the rolling cylinder they wind unidirectionally around the cylinder. There is a strict hierarchy of classes of upward planar graphs: UP ⊂ SUP ⊂ RUP. In this paper, we ...
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