The Three Dimensional Logic Engine
Kitching, Matthew and Whitesides, Sue (2004) The Three Dimensional Logic Engine. In: Graph Drawing 12th International Symposium, GD 2004, September 29-October 2, 2004, New York, NY, USA , pp. 329-339 (Official URL: http://dx.doi.org/10.1007/978-3-540-31843-9_33).
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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.
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