Drawing HV-Restricted Planar Graphs
A strict orthogonal drawing of a graph G = (V, E) in ℝ2 is a drawing of G such that each vertex is mapped to a distinct point and each edge is mapped to a horizontal or vertical line segment. A graph G is HV-restricted if each of its edges is assigned a horizontal or vertical orientation. A strict orthogonal drawing of an HV-restricted graph G is good if it is planar and respects the edge orientations of G. In this paper we give a polynomial-time algorithm to check whether a given HV-restricted plane graph (i.e., a planar graph with a fixed combinatorial embedding) admits a good orthogonal drawing preserving the input embedding, which settles an open question posed by Maňuch, Patterson, Poon and Thachuk (GD 2010). We then examine HV-restricted planar graphs (i.e., when the embedding is not fixed). Here we completely characterize the 2-connected maximum-degree-three HV-restricted outerplanar graphs that admit good orthogonal drawings.
Unable to display preview. Download preview PDF.
- 2.Borradaile, G., Klein, P.N., Mozes, S., Nussbaum, Y., Wulff-Nilsen, C.: Multiple-source multiple-sink maximum flow in directed planar graphs in near-linear time. In: Ostrovsky, R. (ed.) IEEE 52nd Annual Symposium on Foundations of Computer Science (FOCS), pp. 170–179. IEEE (2011)Google Scholar