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Algorithms and Architectures for Parallel Processing
Let m(n) be the minimum positive integer k so that the Shuffle-Exchange network with k stages, N = 2 n inputs and N outputs is rearrangeable. Beneš conjectured that m(n) = 2n ? 1. The best bounds known so far are 2n ? 1 m(n) 3n ? 4. In this paper, we verify Beneš conjecture for n = 4, and use this result to show that m(n) 3n ? 5. The n = 4 case is considerably more complex than the n = 3 case, which have been done in the literature. We believe that hidden in our proof there is some generaldoi:10.1142/9789812792037_0008 fatcat:pt3zlp3ibvhl7fxeo7dpruqfoy