There is some evidence that labeling schemes as employed for instance in the famous Coffman-Graham algorithm may provide superior worst-case approximation guarantees than purely path- or level-based list schedules in the presence of (delayed) precedence constraints. In 1989, Bernstein, Rodeh, and Gertner proved that this also holds true for their labeling scheme targeting unit execution time tasks on a single processor provided that all delays imposed by a single task on all of its successors are uniformly either zero or some fixed positive integer. They further conjectured that this superiority is preserved when allowing the delays imposed by a task to differ successor-wise. It is shown in this note however that their labeling scheme as well as more general ones may perform as bad as any list schedule in this case. Moreover, a new lower bound on the worst-case performance of labeling methods in the multiprocessor setting is derived.

有证据表明，在（延迟的）优先约束存在的情况下，例如，著名的Coffman-Graham算法中采用的标记方案可能比纯基于路径或级别的列表计划提供更好的最坏情况近似保证。1989年，Bernstein，Rodeh和Gertner证明，对于以单个处理器上的单位执行时间任务为目标的标签方案，只要单个任务对其所有后继任务施加的所有延迟统一为零或某个固定的正数，这也适用。整数。他们进一步推测，当允许任务所施加的延迟在继承者方面有所不同时，这种优势将得以保留。但是，在此注释中显示，在这种情况下，它们的标记方案以及更通用的标记方案可能会与任何列表计划一样糟糕。而且，