Abstract
A general method for generating 3-dimensional sorting algorithms by using 2-dimensional algorithms is presented. The main advantage is that from a large class of sorting algorithms suitable for mesh-connected rectangles of processors we efficiently obtain sorting algorithms suitable for 3-dimensional meshes. It is shown that by using the s2-way merge sort of Thompson and Kung sorting n3 elements can be performed on an n × n × n cube with 12n+0(n2/3 log n) data interchange steps. Further improvements lead to an algorithm for an n/2 × n × 2n mesh sorting n3 items within 10.5n+O (n2/3log n) interchange steps. By a generalization of the method to r-dimensional cubes one can obtain algorithms sorting nΓ elements with 0(r3n) interchange steps.
This work was partially done at the Institut für Informatik, University of Kiel, and partially supported by the Siemens AG, München.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Foster, M.J., Kung, H.T., The design of special-purpose VLSI-chips. IEEE Computer (1980), 26–40.
M. Kumar and D.S. Hirschberg, An efficient implementation of Batcher's odd-even merge algorithm and its application in parrallel sorting schemes, IEEE Trans. Comp., Vol. C-32, 254–264 (1983)
Kung, H.T., Leiserson, C.E., Systolic arrays for VLSI. Symposium on Sparse Matrix Computation 1978, Proceedings, eds: I.S. Duff, C.G. Stewart, (1978).
M. Kunde, H.-W. Lang, M. Schimmler, H. Schmeck and H. Schroeder, The instruction systolic array and its relation to other models of parallel computers, in Proc. Parallel Computing '85, (1985)
D.E. Knuth, The art of computer programming, Vol. 3: Sorting and Searching, Addison Wesley, Reading, 1973, pp 224–225.
M. Kunde, Lower bounds for sorting on mesh-connected architectures, Proceedings AWOC 86 VLSI Algorithms and Architectures, LNCS 227, Springer, Berlin, 1986, 84–95.
H.-W. Lang, The instruction systolic array, a parallel architecture for VLSI, to appear in Integration
H.-W. Lang, M. Schimmler, H. Schmeck and H. Schroeder, Schroeder, Systolic sorting on a mesh-connected network, IEEE Trans. Comp., Vol. C-34, 652–658 (1985)
D. Nassimi and S. Sahni, Bitonic sort on a mesh-connected parallel computer, IEEE Trans. Comp., Vol. C-28, 2–7 (1979)
M. Schimmler, Fast sorting on a three dimensional cube grid, Bericht 86O4, Institut fuer Informatik, University of Kiel, Germany, 1986
K. Sado and Y. Igarashi, A fast parallel pesudo-merge sort algorithm, Technical Report, Gunma University Japan, 1985
C.D. Thompson and H.T. Kung, Sorting on a mesh-connected parallel computer, CACM, vol. 20, 263–271 (1977)
J.D. Ullmann, Computational aspects of VLSI, Computer Science Press, Rockville, 1984
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kunde, M. (1986). A general approach to sorting on 3-dimensionally mesh-connected arrays. In: Händler, W., Haupt, D., Jeltsch, R., Juling, W., Lange, O. (eds) CONPAR 86. CONPAR 1986. Lecture Notes in Computer Science, vol 237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16811-7_187
Download citation
DOI: https://doi.org/10.1007/3-540-16811-7_187
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16811-9
Online ISBN: 978-3-540-44856-3
eBook Packages: Springer Book Archive