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On Bus Graph Realizability

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
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Abstract

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.

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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. 2006-09-22. On Bus Graph Realizability. https://arxiv.org/abs/cs/0609127

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