On Bus Graph Realizability

In this paper, we consider the following graph embedding problem: Given a bipartite graph G = (V1, V2; E), where the maximum degree of vertices in V2 is 4, can G be embedded on a two dimensional grid such that each vertex in V1 is drawn as a line segment along a grid line, each vertex in V2 is drawn as a point at a grid point, and each edge e = (u, v) for some u ∈ V1 and v ∈ V2 is drawn as a line segment connecting u and v, perpendicular to the line segment for u? We show that this problem is NP-complete, and sketch how our proof techniques can be used to show the hardness of several other related problems.

• Type: Conference
• Year: 2007
• Where: CCCG
• Authors: Anil Ada, Melanie Coggan, Paul Di Marco, Alain Doyon, Liam Flookes, Samuli Heilala, Ethan Kim, Jonathan Li On Wing, Louis-Francois Preville-Ratelle, Sue Whitesides, Nuo Yu
• Keywords: CCCG 2007, Computational Geometry, Graph Embedding Problem, Grid, Line Segment