具有两个非单位任务长度的排序问题是NP完全问题
Scheduling with two non-unit task lengths is NP-complete
摘要：
单机上带释放时间和截止期的非抢占式作业调度问题是许多调度问题的基础。我们通过作业可以具有的作业长度的集合来参数化这个问题。已知所有作业长度相同的情况在多项式时间内是可解的。我们证明了两个工作长度的问题是NP-完全的，除了在短的工作有单位的工作长度，这是已知的是有效地解决的情况。证明使用减少满足性的辅助调度问题，其中包括一组成对的工作，每个都有一个早期和晚期的最后期限，其中至少有一个应该在早期的最后期限之前进行调度。这种减少不仅是使这些成对的依赖关系之间的工作，但也由专门构造的工作，具有彼此接近的最后期限集的依赖关系。通过用四个不同的工件来表示每对具有两个截止期的工件，辅助排序问题又可以归结为具有两个工件长度的排序问题。
英文摘要：
The non-preemptive job scheduling problem with release times and deadlines on a single machine is fundamental to many scheduling problems. We parameterize this problem by the set of job lengths the jobs can have. The case where all job lengths are identical is known to be solvable in polynomial time. We prove that the problem with two job lengths is NP-complete, except for the case in which the short jobs have unit job length, which was already known to be efficiently solvable. The proof uses a reduction from satisfiability to an auxiliary scheduling problem that includes a set of paired jobs that each have both an early and a late deadline, and of which at least one should be scheduled before the early deadline. This reduction is enabled by not only these pairwise dependencies between jobs, but also by dependencies introduced by specifically constructed sets of jobs which have deadlines close to each other. The auxiliary scheduling problem in its turn can be reduced to the scheduling problem with two job lengths by representing each pair of jobs with two deadlines by four different jobs.
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