Extending Partial Orthogonal Drawings - Angelini, Patrizio; Rutter, Ignaz; T P, Sandhya (Journal of Graph Algorithms and Applications, 2021)
We study the planar orthogonal drawing style within the framework of partial representation extension. Let (G,H,Γ_H) be a partial orthogonal drawing, i.e., G is a graph, HG is a subgraph, Γ_H is a planar orthogonal drawing of H, and |Γ_H| is the number of vertices and bends in Γ_H. We show that the existence of an orthogonal drawing Γ_G of G that extends Γ_H can be tested in linear time. If such a drawing exists, then there is also one that uses O(|Γ_H|) bends per edge. On the other hand, we show that it is NP-complete to find an extension that minimizes the number of bends or has a fixed number of bends per edge.