This Article 
 Bibliographic References 
 Add to: 
An Optimal Hardware-Algorithm for Sorting Using a Fixed-Size Parallel Sorting Device
December 2000 (vol. 49 no. 12)
pp. 1310-1324

Abstract—We present a hardware-algorithm for sorting $N$ elements using either a p-sorter or a sorting network of fixed I/O size $p$ while strictly enforcing conflict-free memory accesses. To the best of our knowledge, this is the first realistic design that achieves optimal time performance, running in $\Theta ( {\frac{N \log N}{p \log p}})$ time for all ranges of $N$. Our result completely resolves the problem of designing an implementable, time-optimal algorithm for sorting $N$ elements using a p-sorter. More importantly, however, our result shows that, in order to achieve optimal time performance, all that is needed is a sorting network of depth $O(\log^2 p)$ such as, for example, Batcher's classic bitonic sorting network.

[1] K.E. Batcher, “Sorting Networks and Their Applications,” Proc. Am. Federation Inforimation Processing Socs. Conf., pp. 307-314, 1968.
[2] R. Beigel and J. Gill, “Sorting$n$Objects with ak-Sorter,” IEEE Trans. Computers, vol. 39, pp. 714-716, 1990.
[3] J. Jang and V.K. Prasanna, ”An Optimal Sorting Algorithm on Reconfigurable Mesh,“ J. Parallel and Distributed Computing, vol. 25, pp. 31-41, 1995.
[4] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. Addison-Wesley, 1973.
[5] T. Leighton, "Tight Bounds on the Complexity of Parallel Sorting," IEEE Trans. Computers, vol. 34, no. 4, pp. 344-354, Apr. 1985.
[6] F.T. Leighton,Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes.San Mateo, Calif.: Morgan Kaufmann, 1992.
[7] R. Lin, S. Olariu, J. Schwing, and J. Zhang, “Sorting in O(1) Time on a Reconfigurable Mesh of Size$n \times n$,” Parallel Computing: From Theory to Sound Practice, Proc. European Workshop Parallel Computing (EQPC '92), plenary address, pp. 16-27, 1992.
[8] M. Nigam and S. Sahni, "Sorting n Numbers on n x n Reconfigurable Meshes With Buses," Proc. Int'l Parallel Processing Symp., pp. 174-181, 1993.
[9] S. Olariu, M.C. Pinotti, and S.Q. Zheng, “How to Sort N Items Using a Sorting Network of Fixed I/O Size,” IEEE Trans. Parallel and Distributed Systems, vol. 10, no. 5, pp. 487-499, May 1999.
[10] Y. Zhang and S.Q. Zheng, “An Efficient Parallel Sorting Architecture,” VLSI Design, vol. 11, no. 2, pp. 137-147, 2000.

Index Terms:
Special-purpose architectures, hardware-algorithms, sorting networks, columnsort, VLSI.
Stephan Olariu, M. Cristina Pinotti, Si Qing Zheng, "An Optimal Hardware-Algorithm for Sorting Using a Fixed-Size Parallel Sorting Device," IEEE Transactions on Computers, vol. 49, no. 12, pp. 1310-1324, Dec. 2000, doi:10.1109/12.895849
Usage of this product signifies your acceptance of the Terms of Use.