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Two problems of importance for the scheduling of multiprocessing systems composed of identical units are discussed in this paper. 1) Given a partially ordered set of computations represented by the vertices of an acyclic directed graph with their associated execution times, find the minimum number of processors in order to execute them in a time not exceeding the length of the critical path of this graph. 2) Determine the minimum time to process this set of computations when a fixed number of processors is available. A unified formulation for lower bounds on the minimum number of processors and on time is presented. These lower bounds are sharper than previously known values and provide a general framework that gives insight for deriving simplified expressions. A new upper bound on the minimum number of processors is presented, which is sharper than the known bounds. The computational aspects of these bounds are also discussed.
Fernández et al. (Wed,) studied this question.
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