The Three Dimensional Logic Engine

We consider the following graph embedding question: given a graph G, is it possible to map its vertices to points in 3D such that G is isomorphic to the mutual nearest neighbor graph of the set P of points to which the vertices are mapped? We show that this problem is NP-hard. We do this by extending the “logic engine” method to three dimensions by using building blocks inpired by the structure of diamond and by constructions of A.G. Bell and B. Fuller.

• Type: Conference
• Year: 2004
• Where: GD
• Authors: Matthew Kitching, Sue Whitesides
• Keywords: GD 2004, Graph Embedding Question, Graph G, Nearest Neighbor Graph