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European Symposium on Algorithms

ESA 1997: Algorithms — ESA '97 pp 341–349Cite as

Minimum spanning trees in d dimensions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1284))

Abstract

It is shown that a minimum spanning tree of n points in ℝd can be computed in optimal O(Td(n,n)) time under any fixed Lt−metric, where T d (n, m) denotes the time to find a bichromatic closest pair between n red points and m blue points. The previous bound was O(T d (n, n) log n) and it was proved only for the L 2 (Euclidean) metric. Furthermore, for d = 3 it is shown that a minimum spanning tree can be found in optimal O(n log n) time under the L 1 and L ∞-metric. The previous bound was O(n log n log log n).

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Authors and Affiliations

  1. Department of Computer Science, Lund University, Box 118, S-22100, Lund, Sweden

    Drago Krznaric, Christos Levcopoulos & Bengt J. Nilsson

Authors
  1. Drago Krznaric
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  2. Christos Levcopoulos
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  3. Bengt J. Nilsson
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Editor information

Rainer Burkard Gerhard Woeginger

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© 1997 Springer-Verlag Berlin Heidelberg

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Krznaric, D., Levcopoulos, C., Nilsson, B.J. (1997). Minimum spanning trees in d dimensions. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_26

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  • DOI: https://doi.org/10.1007/3-540-63397-9_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63397-6

  • Online ISBN: 978-3-540-69536-3

  • eBook Packages: Springer Book Archive

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