最小化流时间的不失真算法
Distortion-Oblivious Algorithms for Minimizing Flow Time
摘要：
我们考虑经典的在线调度问题，在一台机器上，以尽量减少总流时间。在STOC 2021中，引入了对处理时间中的失真的鲁棒性的概念：对于每个失真因子$μ$，提出了处理高达$μ$的失真的$O(μ^2)$ -竞争算法$\operatorname{ALG}_μ$。然而，使用该结果需要预先知道输入的失真，这是不切实际的。我们提出的第一个\emph{distortion-oblivious}算法：算法是竞争\emph{every}失真的\emph{every}输入，因此不需要知识的失真在前面。此外，我们的算法的竞争比是$\tilde{O}(μ)$，这是一个二次改进的算法从STOC 2021，是近最优的（我们显示了一个随机下界的$Ω(μ)$的竞争力）。
英文摘要：
We consider the classic online problem of scheduling on a single machine to minimize total flow time. In STOC 2021, the concept of robustness to distortion in processing times was introduced: for every distortion factor $μ$, an $O(μ^2)$-competitive algorithm $\operatorname{ALG}_μ$ which handles distortions up to $μ$ was presented. However, using that result requires one to know the distortion of the input in advance, which is impractical. We present the first \emph{distortion-oblivious} algorithms: algorithms which are competitive for \emph{every} input of \emph{every} distortion, and thus do not require knowledge of the distortion in advance. Moreover, the competitive ratios of our algorithms are $\tilde{O}(μ)$, which is a quadratic improvement over the algorithm from STOC 2021, and is nearly optimal (we show a randomized lower bound of $Ω(μ)$ on competitiveness).
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