The Three Dimensional Logic Engine

  • Matthew Kitching
  • Sue Whitesides
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Matthew Kitching
    • 1
  • Sue Whitesides
    • 2
  1. 1.Dept. of Comp. Sci.U. of TorontoCanada
  2. 2.School of Comp. Sci.McGill U.MontrealCanada

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