gdea_3The Three Dimensional Logic EngineMatthewKitchingauthorSueWhitesidesauthorWe 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.Z.250 Geometry2004SpringerConference Paper

For work being deposited by its own author: In self-archiving this collection of files and associated bibliographic metadata, I grant gdea the right to store them and to make them permanently available publicly for free on-line. I declare that this material is my own intellectual property and I understand that gdea does not assume any responsibility if there is any breach of copyright in distributing these files or metadata. (All authors are urged to prominently assert their copyright on the title page of their work.)

For work being deposited by someone other than its author: I hereby declare that the collection of files and associated bibliographic metadata that I am archiving at gdea) is in the public domain. If this is not the case, I accept full responsibility for any breach of copyright that distributing these files or metadata may entail.

Clicking on the deposit button indicates your agreement to these terms.