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The lower and upper bounds on the minimum time needed to process a given directed acyclic task graph for a given number of processors are derived. It is proved that the proposed lower bound on time is not only sharper than the previously known values but also easier to calculate. The upper bound on time, which is useful in determining the worst case behavior of a given task graph, is presented for the first time. The lower and upper bounds on the minimum number of processors required to processdoi:10.1109/71.298216 fatcat:3gaqt7w6yfapnkkejhmjmqeygm