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.

中文翻译：

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水平顺序优先约束下单位处理时间作业的并行机调度的复杂性

在本文中，我们证明了作业具有单位处理时间和级别顺序优先约束的并行机器调度问题是 NP 完全的，同时最小化了制造跨度或总完成时间。即使允许抢占，这些问题也是 NP 完全的。然后，我们将证明适用于其他具有外树或对立森林优先约束的开放问题。