Abstract
The k-selection problem asks for the k-th smallest element in a set S of n unordered items to be identified. We present two k-selection randomized SIMD algorithms for two-dimensional processor arrays with reconfigurable bus systems, RM for short. First we use an efficient prefix sums computation to develop O(log log n log n) time implementations on a √n×√n RM. We then show that pipelining the operation of counting n binary numbers can be efficiently implemented on the RM to achieve a running time of O(log log n log log log n/log n).
This research is supported by a grant from the Research Management Committee, The University of Newcastle.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A.V. Aho, J.E. Hopcroft and J.D. Ullman, The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company, 1975.
Y.C. Chen, W.T. Chen, and G.H. Chen, “Two-variable linear programming on mesh connected computers with multiple broadcasting,” Proc. of 1990 International Conference on Parallel Processing, August 1990.
R. Cole, “An optimally efficient selection algorithm,” Information Processing Letters, 26, 295–299 (1987/88)
H. ElGindy and P. Wegrowicz, “Selection on the reconfigurable mesh,” Proc. of 1991 International Conference on Parallel Processing, August 1991, pp. III-26–33.
A.G. Greenberg and U. Manber, “A probabilistic pipeline algorithm for k-selection on the tree machine,” Proc. of 1985 International Conference on Parallel Processing, 1985, pp. 1–5.
Ju-Wook Jang and Viktor K. Prasanna, “An optimal sorting algorithm on reconfigurable mesh,” Proc. of 6th International Parallel Processing Symposium, pp. 130–137.
D.E. Knuth, The Art of Computer Programming: Sorting and Searching. Addison-Wesley, 1973.
R. Miller, V.K. Prasanna-Kumar, D.I. Reisis and Q.F. Stout, “Meshes with reconfigurable buses,” MIT Conference on Advanced Research in VLSI, 1988, pp. 163–178.
R. Miller, V.K. Prasanna-Kumar, D.I. Reisis and Q.F. Stout, “Parallel computations on reconfigurable meshes,” manuscript.
J.I. Munro and M.S. Paterson, “Selection and sorting with limited storage,” Theoretical Computer Science, 12, 315–323 (1980).
A. Olariu, J.L. Schwing, and J. Zhang, “Fast computer vision algorithms for reconfigurable meshes,” Proc. of 6th International Parallel Processing Symposium, 1992, pp. 258–261.
V.K. Prasanna Kumar and C.S. Raghavendra, “Array processors with multiple broadcasting,” Journal of Parallel and Distributed Computing, 4, 173–190 (1987).
D.S. Richards, “VLSI median filters,” IEEE Trans. on ASSP, vol. 38, January 1990, pp. 145–153.
L. Shrira, N. Francez and M. Rodeh, “Distributed k-selection: From a sequential toa distributed algorithm,” Proc. ACM Symposium on Principles of Distributed Computing, August 1983, pp. 143–153.
Q.F. Stout, “Mesh-connected computers with broadcasting” IEEE Transactions on Computers, 9, 826–830 (1983).
P. Wegrowicz, “Linear programming on the reconfigurable mesh and the CREW PRAM,” Masters Thesis, McGill University (1991).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
ElGindy, H. (1993). Pipelining computations on processor arrays with reconfigurable bus systems. In: Volkert, J. (eds) Parallel Computation. ACPC 1993. Lecture Notes in Computer Science, vol 734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57314-3_5
Download citation
DOI: https://doi.org/10.1007/3-540-57314-3_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57314-2
Online ISBN: 978-3-540-48055-6
eBook Packages: Springer Book Archive