This paper describes practical optimization/ approximation algorithms for scheduling a set of partially ordered computational tasks onto a multiprocessor system so that the schedule length will be minimized. Since this problem belongs to the class of “strong” NP-hard problems, we must foreclose the possibility of constructing not only pseudopolynomial time optimization algorithms but also fully polynomial time approximation schemes unless P = NP. This paper proposes a heuristic algorithm named CP/MISF (critical path/most immediate successors first) and an optimization/approximation algorithm named DF/IHS (depth-first/implicit heuristic search). DF/IHS is an excellent scheduling method which can reduce markedly space complexity and average computation time by combining the branch-and-bound method with CP/MISF; it allows us to solve very large scale problems with a few hundred tasks. Numerical examples are included to demonstrate the effectiveness of the proposed algorithms.
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