Preemptive Scheduling of. Precedence-Constrained Jobs on Parallel Machines
Polynomial time-bounded algorithms are presented for solving three problems involving the preemptive scheduling of precedence-constrained jobs on parallel machines: the “intree problem”, the “two-machine problem with equal release dates”, and the “general two-machine problem”. These problems are preemptive counterparts of problems involving the nonpreemptive scheduling of unit-time jobs previously solved by Brucker, Garey and Johnson and by Garey and Johnson. The algorithms and proofs (and the running times of the algorithms) closely parallel those presented in their papers. These results improve on previous results in preemptive scheduling and also suggest a close relationship between preemptive scheduling problems and problems in nonpreemptive scheduling of unit-time jobs.
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