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The geometric mean distance

Published:01 July 1976Publication History
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Abstract

Given N points in K-space, the O(N2) distances between them may be characterized by their minimum[1, 2], maximum [3], mean[4, 5, 6], or median [7]; since these problems are geometrical, it may be Interesting to consider the geometric mean - or, which is equivalent, the product - of the distances between all pairs.

References

  1. G. Yuval, "Finding nearest neighbours". Information Processing Letters, to appear.Google ScholarGoogle Scholar
  2. M. Shamos and J. Bentley, "Divide-and-conquer in multidimensional space", SIGACT, april 1976. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. M. Shamos, Problems in computational geometry. Springer, to appear.Google ScholarGoogle Scholar
  4. G. Yuval, "The complexity of the mean distance in 2-space", submitted to Information Processing Letters.Google ScholarGoogle Scholar
  5. G. Yuval, The mean distance in 2-space, technical report, Carnegie-Mellon University, June 1976.Google ScholarGoogle Scholar
  6. M. Shamos and G. Yuval, "Lower bounds from complex function theory", FOCS, October 1976. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. G. Yuval, "Ranking a distance", submitted to Information Processing Letters.Google ScholarGoogle Scholar
  8. H. T. Kung, Fast evaluation and interpolation, technical report, Carnegie-Mellon University, 1973.Google ScholarGoogle Scholar
  9. Aho, Hopcroft and Ullman, The design and analysis of computer algorithms. Reading, Mass., 1974, pp. 278--313.Google ScholarGoogle Scholar

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  • Published in

    cover image ACM SIGACT News
    ACM SIGACT News  Volume 8, Issue 3
    July-September 1976
    24 pages
    ISSN:0163-5700
    DOI:10.1145/1810926
    Issue’s Table of Contents

    Copyright © 1976 Author

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    • Published: 1 July 1976

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