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We provide the rst optimal algorithms in terms of the number of input outputs I Os required between internal memory and multiple secondary storage devices for the problems of sorting, FFT, matrix transposition, standard matrix multiplication, and related problems. Our two-level memory model is new and gives a realistic treatment o f p arallel block transfer, in which during a single I O each of the P secondary storage devices can simultaneously transfer a contiguous block o f B records. Thedoi:10.1007/bf01185207 fatcat:linktjnicze2zm2zbn7doefbjy