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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© 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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