Abstract.
Shuffle-unshuffle sorting networks are a class of comparator networks whose structure maps efficiently to the hypercube and any of its bounded degree variants. Recently, n -input shuffle-unshuffle sorting networks with depth \(2^{O(\sqrt{ lg lg n})} lg n\) have been discovered. These networks are the only known sorting networks of depth o( lg2 n) that are not based on expanders, and their existence raises the question of whether a depth of O( lg n) can be achieved by any shuffle-unshuffle sorting network. In this paper we resolve this question by establishing an Ω( lg n lg lg n/lg lg lg n) lower bound on the depth of any n -input shuffle-unshuffle sorting network. Our lower bound can be extended to certain restricted classes of nonoblivious sorting algorithms on hypercubic machines.
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Received September 9, 1999, and in final form December 20, 1999.
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Plaxton, C., Suel, T. A Superlogarithmic Lower Bound for Shuffle-Unshuffle Sorting Networks . Theory Comput. Systems 33, 233–254 (2000). https://doi.org/10.1007/s002240010001
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DOI: https://doi.org/10.1007/s002240010001