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A Multiway Merge Sorting Network
February 1995 (vol. 6 no. 2)
pp. 211-215

Abstract—A multiway merge sorting network is presented, which generalizes the technique used in the odd-even merge sorting network. The merging network described here is composed of $m\ k$-way mergers and a combining network. It arranges $k$ ordered lists of length $n$ each into one ordered lists in $T(k) + \lceil \log_m n\rceil \lceil \log_2 k\rceil \lceil \log_2 m\rceil$ steps, where $T(k)$ is the number of steps needed to sort $k$ keys in order; and $k$ and $m$ are any integers no longer restricted to 2.

Index Terms—Sorting networks, odd-even merge, multiway merge, parallel processing.

[1] K. E. Batcher,“Sorting networks and their applications,”inAFIPS Proc. Spring Joint Comput. Conf., 1968, pp. 307–314.
[2] K. E. Batcher,“On bitonic sorting networks,”inProc. 19th Int. Conf. Parallel Process., 1990, pp. 376–379.
[3] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. Addison-Wesley, 1973.

De-Lei Lee, Kenneth E. Batcher, "A Multiway Merge Sorting Network," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 2, pp. 211-215, Feb. 1995, doi:10.1109/71.342136
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