The Complexity of Parallel Machine Scheduling of Unit-Processing-Time Jobs under Level-Order Precedence Constraints
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In this paper, we prove that parallel machine scheduling problems where jobs have unit processing time and level-order precedence constraints are NP-complete, while minimizing the makespan or the total completion time. These problems are NP-complete even when preemption is allowed. We then adapt the proof to other open problems with out-tree or opposing-forests precedence constraints.
KeywordsParallel machine scheduling Level-order Precedence constraints
This work was supported by the China Scholarship Council (Grant No. 201404490037).
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