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On the worst case of a minimal spanning tree algorithm for euclidean space

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Abstract

This paper concerns the worst case running time of the minimal spanning tree algorithm presented by Bentley and Friedman.

For a set ofN points ink-dimensional Euclidean space the worst case performance of the algorithm is shown to beΘ(N 2 logN), fork≧2 andΘ(N 2), fork=1.

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References

  1. Jon Bentley and Jerome Friedman,Fast algorithms for constructing minimal spanning trees in coordinate spaces. IEEE Trans. on Computers. Vol. C-27, No. 2 (1978), 97–105.

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  2. Olli Nevalainen, Jarmo Ernvall and Jyrki Katajainen,Finding minimal spanning trees in a Euclidean coordinate space, BIT 21 (1981), 46–54.

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  3. John Zolnowsky,Topics in Computational Geometry, Stanford University, Ph.D. (1978).

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Turku, SF-20500, Turku 50, Finland

    Jyrki Katajainen

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  1. Jyrki Katajainen
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Katajainen, J. On the worst case of a minimal spanning tree algorithm for euclidean space. BIT 23, 1–8 (1983). https://doi.org/10.1007/BF01937321

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  • DOI: https://doi.org/10.1007/BF01937321

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