Minimizing Completion Times for Stochastic Jobs via Batched Free Times
Minimizing Completion Times for Stochastic Jobs via Batched Free Times
复制标题
DOI：
10.48550/arxiv.2208.13696
复制
发表时间：
2022-08
期刊：
影响因子：
--
通讯作者：
Anupam Gupta;Benjamin Moseley;Rudy Zhou
中科院分区：
文献类型：
--
作者：
Anupam Gupta;Benjamin Moseley;Rudy Zhou
我们研究了在$ M $相同机器上最小化的总体工作时间的经典问题，即在$ m $相同的机器上，在工作的大小随机的情况下。具体而言，每个作业的大小是一个随机变量，其分布是该算法已知的，但仅在安排工作后才揭示其实现。尽管在确定性设置中最小化总完成时间很容易，但随机问题长期以来一直是臭名昭著的：所有已知的算法的近似值比依赖于方差，或者是线性依赖于机器的数量。我们给出了一个$ \ widetilde {o}（\ sqrt {m}）$ - 随机作业的近似近似具有Bernoulli处理时间。这是此问题的第一个近似值，既独立于作业尺寸的差异，又是机器数量$ M $的均值。我们的算法是基于从最小化总完成时间到天然pan样物镜的新颖降低的，我们称之为加权空闲时间。我们希望这个空闲时间目标对于进一步改善此问题以及其他随机调度问题将很有用。
We study the classic problem of minimizing the expected total completion time of jobs on $m$ identical machines in the setting where the sizes of the jobs are stochastic. Specifically, the size of each job is a random variable whose distribution is known to the algorithm, but whose realization is revealed only after the job is scheduled. While minimizing the total completion time is easy in the deterministic setting, the stochastic problem has long been notorious: all known algorithms have approximation ratios that either depend on the variances, or depend linearly on the number of machines. We give an $\widetilde{O}(\sqrt{m})$-approximation for stochastic jobs which have Bernoulli processing times. This is the first approximation for this problem that is both independent of the variance in the job sizes, and is sublinear in the number of machines $m$. Our algorithm is based on a novel reduction from minimizing the total completion time to a natural makespan-like objective, which we call the weighted free time. We hope this free time objective will be useful in further improvements to this problem, as well as other stochastic scheduling problems.