This paper studies the online machine minimization problem, where the jobs have real release times, uniform processing times and a common deadline. We investigate how the lookahead ability improves the performance of online algorithms. Two lookahead models are studied, that is, the additive lookahead and the multiplicative lookahead. At any time t, the online algorithm knows all the jobs to be released before time \(t+L\) (or \(\beta \cdot t\)) in the additive (or multiplicative) lookahead model. We propose a \(\frac{e}{\alpha (e-1)+1}\)-competitive online algorithm with the additive lookahead, where \(\alpha = \frac{L}{T} \le 1\) and T is the common deadline of the jobs. For the multiplicative lookahead, we provide an online algorithm with a competitive ratio of \(\frac{\beta e}{(\beta -1) e +1}\), where \(\beta \ge 1\). Lower bounds are also provided for both of the two models, which show that our algorithms are optimal for two extreme cases, that is, \(\alpha = 0\) (or \(\beta = 1\)) and \(\alpha = 1\) (or \(\beta \rightarrow \infty \)), and remain a small gap for the cases in between. Particularly, for \(\alpha = 0\) (or \(\beta = 1\)), the competitive ratio is e, which corresponds to the problem without lookahead. For \(\alpha = 1\) (or \(\beta \rightarrow \infty \)), the competitive ratio is 1, which corresponds to the offline version (with full information).

本文研究在线机器最小化问题，其中作业具有实际的发布时间，统一的处理时间和共同的期限。我们研究了超前能力如何提高在线算法的性能。研究了两个超前模型，即加性超前和乘法超前。在任何时间t，在线算法都知道在加性（或乘法）超前模型中的时间\（t + L \）（或\（\ beta \ cdot t \））之前要释放的所有作业。我们提出了具有竞争性的\（\ frac {e} {\ alpha（e-1）+1} \）在线竞争算法，其中\（\ alpha = \ frac {L} {T} \ le 1 \ ）和T是工作的最后期限。为了提前进行乘法运算，我们提供了一种竞争比为\（\ frac {\ beta e} {（\ beta -1）e +1} \）的在线算法，其中\（\ beta \ ge 1 \）。还为两个模型都提供了下界，这表明我们的算法对于两种极端情况是最优的，即\（\ alpha = 0 \）（或\（\ beta = 1 \））和\（\ alpha = 1 \）（或\（\ beta \ rightarrow \ infty \）），并且在两者之间的情况下保持很小的差距。特别是，对于\（\ alpha = 0 \）（或\（\ beta = 1 \）），竞争比率为e，这对应于无前瞻性的问题。对于\（\ alpha = 1 \）（或\（\ beta \ rightarrow \ infty \）），竞争比率为1，与离线版本相对应（具有完整的信息）。