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Related to matrix transposition: matrix addition, matrix multiplication
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The FFT, permutation network, and matrix transposition problems have no input distribution, so the average-case and worst-case models are the same.
For the last case quoted in Section 3, the matching lower bound follows by an analysis of matrix transposition, which we do later in this section.
We first discuss the sorting problem and then apply our results to get optimum algorithms for permuting, FFT, permutation networks, and matrix transposition. Without loss of generality, we can assume that B, M, and N are powers of 2 and that B < M < N.