Abstract
Lower bounds for sorting on mesh-connected arrays of processors are presented. For sorting N = n1n2...nr elements on an n1 × n2 × ... × nr array 2(n1 + ... + nr−1) + nr data interchange steps are needed asymptotically. For two dimensions these bounds are asymptotically best possible provided that n1 and n2 are powers of 2. In this case the generalized s2-way merge sort of Thompson and Kung turns out to be asymptotically optimal. The minimal asymptotic bound of 2√2N interchange steps can be obtained only by sorting algorithms suitable for √N/2 × √2N meshes. For r ≥ 3 dimensions an analysis of aspect-ratios also indicates that there might be mesh-connected architectures which are better suited for sorting than simple r-dimensional cubes.
This work was done at the Institut für Informatik und Praktische Mathematik, University of Kiel, West Germany.
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References
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© 1986 Springer-Verlag Berlin Heidelberg
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Kunde, M. (1986). Lower bounds for sorting on mesh-connected architectures. In: Makedon, F., Mehlhorn, K., Papatheodorou, T., Spirakis, P. (eds) VLSI Algorithms and Architectures. AWOC 1986. Lecture Notes in Computer Science, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16766-8_8
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DOI: https://doi.org/10.1007/3-540-16766-8_8
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