Abstract.
We give an algorithm to find a minimum spanning tree in the k-dimensional space under rectilinear metric. The running time is \(O((8^k/\sqrt{k})n(\lg n)^{k-2} \lg\lg n)\) for k≥ 3. This improves the previous bound by a factor \(\sqrt{k}\lg^2 n/4^k\) .
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Received January 10, 1995; revised December 21, 1995.
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Bespamyatnikh, S. On Constructing Minimum Spanning Trees in R k 1 . Algorithmica 18, 524–529 (1997). https://doi.org/10.1007/PL00009170
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DOI: https://doi.org/10.1007/PL00009170