论文标题
与处理时间Oracle进行安排
Scheduling with a processing time oracle
论文作者
论文摘要
在本文中，我们研究了一个机器调度问题，目的是最大程度地减少完成时间的总和。给定的每个工作都是短或长的。但是，处理时间最初被隐藏在算法上，但可以进行测试。这是通过执行处理时间Oracle来完成的，该时间揭示了给定作业的处理时间。每个测试都占据时间表中的一个时间单元，因此该算法必须决定将其称为处理时间Oracle的工作。将结果时间表的客观值与最佳时间表的客观值进行了比较，该时间表是使用完整信息计算的。最终的竞争比率衡量了隐藏处理时间的价格，目标是设计具有最小竞争比率的算法。 本文研究了两种模型。在非自适应模型中，该算法需要事先决定要测试哪些作业以及执行未经测试的工作。但是，在自适应模型中，算法可以根据工作测试的结果自适应地做出这些决定。在这两种模型中，我们都按照两相策略提供了最佳的多项式时间算法，该策略由测试作业的第一阶段和第二阶段组成，第二阶段的工作被遗忘了。实验提供了有力的证据，表明最佳算法具有这种结构。证明此属性是一个空旷的问题。
In this paper we study a single machine scheduling problem with the objective of minimizing the sum of completion times. Each of the given jobs is either short or long. However the processing times are initially hidden to the algorithm, but can be tested. This is done by executing a processing time oracle, which reveals the processing time of a given job. Each test occupies a time unit in the schedule, therefore the algorithm must decide for which jobs it will call the processing time oracle. The objective value of the resulting schedule is compared with the objective value of an optimal schedule, which is computed using full information. The resulting competitive ratio measures the price of hidden processing times, and the goal is to design an algorithm with minimal competitive ratio. Two models are studied in this paper. In the non-adaptive model, the algorithm needs to decide beforehand which jobs to test, and which jobs to execute untested. However in the adaptive model, the algorithm can make these decisions adaptively depending on the outcomes of the job tests. In both models we provide optimal polynomial time algorithms following a two-phase strategy, which consist of a first phase where jobs are tested, and a second phase where jobs are executed obliviously. Experiments give strong evidence that optimal algorithms have this structure. Proving this property is left as an open problem.
