发表机构
New York University; Tel Aviv University; Technische Universität Berlin; University of Southern Denmark; ETH Zürich（纽约大学; 特拉维夫大学; 柏林工业大学; 南丹麦大学; 苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对单机在线流时间调度，提出一种参数无关的MLF变体算法，在作业处理中段获得近似估计，实现O(μ/ε)竞争比且渐近最优。
AI 中文摘要
在经典的单机在线流时间调度问题中，作业随时间到达，必须进行处理以最小化它们在系统中花费的总时间：五十多年来，我们已知SRPT是最优的在线算法。但该算法在两个方面需要精确性：(a) 作业大小必须精确已知，(b) 它们必须在作业到达时立即被揭示。最近的工作分别放宽了这些假设：有基于知道近似大小（在作业到达时给出）的算法，或者基于在剩余大小变得过小之前的某个时刻知道（精确）大小的算法。尽管如此，在本工作之前，没有已知方法能同时放宽这两个假设。在本工作中，我们考虑一个要求低得多的模型：当我们处理一个作业时，在完成其未知处理需求的ε比例和(1-ε)比例之间的某个时间点，我们被告知该作业“处于中间某处”。最后，当作业获得其期望的处理量时，我们被告知其完成。关于该作业不共享其他信息。我们为这个模型给出了一个O(1/ε²)竞争的算法。稍微更一般地，我们假设算法在完成每个作业处理的(1-ε)比例之前的某个时间收到其处理时间的μ近似估计。我们的算法是O(μ/ε)竞争的，并且我们证明这是渐近最优的。它是多级反馈算法（MLF）的一个令人惊讶的自然变体，并且是参数无关的：它不需要预先知道μ或ε。核心分析贡献是为该问题强化对偶拟合框架，以处理我们尚未收到估计的作业。
英文摘要
In the classical online flow-time scheduling problem on a single machine, jobs arrive over time and must be processed to minimize the total time they spend in the system: for over fifty years, we have known that SRPT is an optimal online algorithm. But this algorithm requires exactness in two different ways: (a) job sizes must be known exactly, and (b) they must be revealed as soon as the job arrives. Recent work relaxed each of these assumptions separately: there are algorithms based on knowing approximate sizes (given when the job arrives), or based on knowing (exact) sizes at some point before the remaining size gets too small. Nonetheless, prior to this work, there was no known approach to relax both assumptions simultaneously. In this work, we consider a model that demands much less: When we process a job, at some point in time between when we complete an $\varepsilon$-fraction and a $(1-\varepsilon)$-fraction of its unknown processing requirement, we are informed that the job is ``somewhere in the middle''. Finally, when the job has received its desired amount of processing, we are informed of its completion. No other information is shared about the job. We give an $O(1/\varepsilon^2)$-competitive algorithm for this model. Slightly more generally, we assume that an algorithm receives a $μ$-approximate estimate of each job's processing time at some time before we complete a $(1-\varepsilon)$-fraction of its processing. Our algorithm is $O(μ/\varepsilon)$-competitive, and we show that this is asymptotically optimal. It is a surprisingly natural variant of the multilevel feedback algorithm (MLF) and it is parameter-oblivious: it does not need to know $μ$ or $\varepsilon$ upfront. The core analytical contribution is to robustify the dual-fitting framework for this problem to handle jobs for which we have not yet received estimates.
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