Abstract
Minimum spanning forests (MSFs) can be computed in time O(n 2/l) on a 1-dimensional processor array of length l ≤ n. For this result we apply a new algorithmic approach different from e.g. Sollin's. It holds for arbitrary input conventions if we only count communication rounds. If we also take internal computation into account it still holds for a wide class of input conventions, generalizing a result by Doshi and Varman. For l × l-meshes, √n ≤ l ≤ n, we present two input conventions for which computing MSFs needs different numbers of communication rounds. For one of them we prove the interesting phenomenon that the complexity is not monotone in l: It is ≈ n for l=√n and l=n, but takes its minimum, ≈ n 3/4, for l= 3/4n .
Supported in part by DGF-Grants ME-872/1-2 and WE 1066/2-1
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© 1989 Springer-Verlag Berlin Heidelberg
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Meyer auf der Heide, F. (1989). Computing minimum spanning forests on 1- and 2-dimensional processor arrays. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028983
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DOI: https://doi.org/10.1007/BFb0028983
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