Finding Nearest Neighbors in Growth-restricted Metrics

David R. Karger and Matthias Ruhl

ACM Symposium on Theory of Computing (STOC '02)
Montréal, May 2002

[Postscript, 165KB]

[PDF, 146KB]


Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is non-Euclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes of metric spaces that can be tractably searched.

In this paper, we develop an efficient dynamic data structure for nearest neighbor queries in growth-constrained metrics. These metrics satisfy the property that for any point q and distance d the number of points within distance 2d of q is at most a constant factor larger than the number of points within distance d. Spaces of this kind may occur in networking applications, such as the Internet or Peer-to-peer networks, and vector quantization applications, where feature vectors fall into low-dimensional manifolds within high-dimensional vector spaces.

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