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The problem of identifying the point from a set of points which is nearest to a given point according to some measure of distance. The nearest neighborhood problem involves identifying the locus of points lying nearer to the query point than to any other point in the set.
References
Martin, E. C. ``Computational Geometry.''
http://www.mathsource.com/cgi-bin/MathSource/Enhancements/DiscreteMath/0200-181.