Finding nearest neighbors in growth-restricted metrics

  • Authors:
  • David R. Karger;Matthias Ruhl

  • Affiliations:
  • MIT, Cambridge, MA;MIT, Cambridge, MA

  • Venue:
  • STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
  • Year:
  • 2002

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Abstract

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 number r the ratio between numbers of points in balls of radius 2r and r is bounded by a constant. 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.