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On nearest-neighbor graphs

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Book cover Automata, Languages and Programming (ICALP 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 623))

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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.

The work was done while this author was visiting Xerox Palo Alto Research Center. He is partially supported by the ESPRIT BRA Program of the EC under contract 7141 (ALCOM II).

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Warwick, CV4 7AL, Coventry, England

    Michael S. Paterson

  2. Xerox Palo Alto Research Center, 3333 Coyote Hill Road, 94304, Palo Alto, CA, USA

    F. Frances Yao

Authors
  1. Michael S. Paterson
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  2. F. Frances Yao
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Editor information

W. Kuich

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© 1992 Springer-Verlag Berlin Heidelberg

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Paterson, M.S., Yao, F.F. (1992). On nearest-neighbor graphs. In: Kuich, W. (eds) Automata, Languages and Programming. ICALP 1992. Lecture Notes in Computer Science, vol 623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55719-9_93

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  • DOI: https://doi.org/10.1007/3-540-55719-9_93

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55719-7

  • Online ISBN: 978-3-540-47278-0

  • eBook Packages: Springer Book Archive

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