On Bus Graph Realizability
Anil Ada, Melanie Coggan, Paul Di Marco, Alain Doyon, Liam Flookes, Samuli Heilala, Ethan Hyungkeun Kim, Jonathan Li On Wing, Louis-François Préville-Ratelle, Sue H. Whitesides, Nuo Yu · arXiv (Cornell University) · 2006
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 2 V1 and v 2 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.