On Nearest-Neighbor Graphs
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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.
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- 4.P. B. Callahan. Optimal parallel all-nearest-neighbors using the well-separated pair decomposition. Proc. 34 th IEEE Symp. on Foundations of Computer Science (1993), pp. 332–340.Google Scholar
- 5.P. B. Callahan and S. R. Kosaraju. A decomposition of multi-dimensional point-sets with applications to k-nearest-neighbors and n-body potential fields. Proc. 24th ACM Symp. on Theory of Computing (1992), pp. 546–556.Google Scholar
- 6.K. L. Clarkson. Fast algorithms for the all-nearest-neighbors problem. Proc. 24th IEEE Symp. on Foundations of Computer Science (1983), pp. 226–232.Google Scholar
- 10.P. Eades and S. Whitesides. The realization problem for Euclidean minimum spanning trees is NP-hard. Proc. 10th ACM Symp. on Computational Geometry (1994), pp. 49–56.Google Scholar
- 13.C. Monma and S. Suri. Transitions in geometric spanning trees. Proc. 7th ACM Symp. on Computational Geometry (1991), pp. 239–249.Google Scholar
- 14.M. S. Paterson and F. F. Yao. On nearest-neighbor graphs. Proc. 19th Internat. Coll. on Automata, Languages and Programming. LNCS, 623. Springer-Verlag, Berlin, 1992, pp. 416–426.Google Scholar
- 15.S.-H. Teng and F. F. Yao. Percolation and k-nearest neighbor clustering. Manuscript, 1993.Google Scholar