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 $\mu$, an $O(\mu^2)$-competitive algorithm $\operatorname{ALG}_{\mu}$ which handles distortions up to $\mu$ 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 $\tilde{O}(\mu)$, which is a quadratic improvement over the algorithm from STOC 2021, and is nearly optimal (we show a randomized lower bound of $\Omega(\mu)$ on competitiveness).
翻译:我们考虑了在单一机器上安排时间以最大限度地减少总流时间的典型在线问题。 在STOC 2021 中,引入了强于扭曲处理时间的概念:对于每一个扭曲系数$mu$,都提出了美元(mum%2)$(美元)-竞争性算法$(operatorname{ALG ⁇ ⁇ mu)$(美元),处理高达$\mu$(美元)的扭曲。然而,使用这一结果需要先知道输入的扭曲情况,这是不切实际的。我们提出了第一个算法:对\emph{eper}扭曲输入具有竞争力的算法,因此不需要事先知道扭曲情况。此外,我们的算法的竞争性比率是$\tilde{O}(\mu)$(美元),这是对STOC 2021 的算法的四分法改进,而且几乎是最佳的(我们在竞争力上随机下下下限值$\\ omega(mu) 。