The three dimensional logic engine

Authors:
Matthew Kitching;Sue Whitesides
Affiliations:
Dept. of Comp. Sci., U. of Toronto, Canada;School of Comp. Sci., McGill U., Montreal, Canada
Venue:
GD'04 Proceedings of the 12th international conference on Graph Drawing
Year:
2004

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Abstract

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.