SIAM Journal on Computing, Volume 49, Issue 3, Page 658-680, January 2020.
This paper considers minimizing the $\ell_k$-norms of flow time on a single machine offline using a preemptive scheduler for $k\geq 1$. The objective is ideal for optimizing jobs' overall waiting times while simultaneously being fair to individual jobs. This work gives the first $O(1)$-approximation for the problem, improving upon the previous best $O( \log \log P)$-approximation by Bansal and Pruhs (FOCS 09 and SICOMP 14) where $P$ is the ratio of the maximum job size to the minimum. The main technical ingredient used in this work is a novel combination of quasi-uniform sampling and iterative rounding, which is of interest in its own right.

中文翻译：

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通过迭代准均匀采样进行公平调度

SIAM计算杂志，第49卷，第3期，第658-680页，2020年1月。
本文考虑使用$ k \ geq 1 $的抢占式调度程序，使单机离线时的$ \ ell_k $-范数最小化。该目标非常适合优化作业的总体等待时间，同时又对单个作业公平。这项工作给出了问题的第一个$ O（1）$近似值，并改进了Bansal和Pruhs（FOCS 09和SICOMP 14）以前最好的$ O（\ log \ log P）$近似值，其中$ P $是最大作业大小与最小作业的比率。这项工作中使用的主要技术成分是准均匀采样和迭代舍入的新颖组合，它本身就是有趣的。