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Discrete & Computational Geometry

, Volume 17, Issue 3, pp 263–282 | Cite as

On Nearest-Neighbor Graphs

  • D. EppsteinEmail author
  • M. S. PatersonEmail author
  • F. F. YaoEmail author
Article

Abstract

The “nearest-neighbor” relation, or more generally the “k-nearest-neighbors” relation, defined for a set of points in a metric space, has found many uses in computational geometry and clustering analysis, yet surprisingly little is known about some of its basic properties. In this paper we consider some natural questions that are motivated by geometric embedding problems. We derive bounds on the relationship between size and depth for the components of a nearest-neighbor graph and prove some probabilistic properties of the k-nearest-neighbors graph for a random set of points.

Keywords

Minimum Span Tree Computational Geometry Related Edge Outer Vertex Rectilinear Steiner Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  1. 1.Department of Information and Computer ScienceUniversity of CaliforniaIrvineUSA
  2. 2.Department of Computer ScienceUniversity of WarwickCoventryEngland
  3. 3.Xerox Palo Alto Research CenterPalo AltoUSA

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