Abstract
We prove an Ω(lg2 n/lg lgn) lower bound for the depth ofn-input sorting networks based on the shuffle permutation. The best previously known lower bound was the trivial Ω(lgn) bound, while the best upper bound is given by Batcher's Θ(lg2 n)-depth bitonic sorting network. The proof technique employed in the lower bound argument may be of independent interest.
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C. G. Plaxton was supported by NSF Research Initiation Award CCR-9111591, and the Texas Advanced Research Program under Grant No. 003658-480. T. Suel was supported by the Texas Advanced Research Program under Grant No. 003658-480, and by an MCD Fellowship of the University of Texas at Austin.
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Plaxton, C.G., Suel, T. A lower bound for sorting networks based on the shuffle permutation. Math. Systems Theory 27, 491–508 (1994). https://doi.org/10.1007/BF01184936
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DOI: https://doi.org/10.1007/BF01184936