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 Td (n, m) denotes the time to find a bichromatic closest pair between n red points and m blue points. The previous bound was O(Td (n, n) log n) and it was proved only for the L2 (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 L1 and L∞-metric. The previous bound was O(n log n log log n).
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