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. © Springer-Verlag Berlin Heidelberg 2004.
CITATION STYLE
Kitching, M., & Whitesides, S. (2004). The three dimensional logic engine. In Lecture Notes in Computer Science (Vol. 3383, pp. 329–339). Springer Verlag. https://doi.org/10.1007/978-3-540-31843-9_33
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