Problem
Research questions and friction points this paper is trying to address.
online scheduling
flow time
approximate sizes
job processing
Better Late Than Never: Online Flow Time Scheduling with Online Estimates
🤖 AI Summary
研究解决了在线流时间调度问题，通过在处理过程中提供任务的粗略估计信息，提出了一种O(μ/ε)竞争比算法，改进了对任务大小和到达时间不确定性的处理。
📝 Abstract
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 $\mu$-approximate estimate of each job's processing time at some time before we complete a $(1-\varepsilon)$-fraction of its processing. Our algorithm is $O(\mu/\varepsilon)$-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 $\mu$ 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Online Scheduling
Flow Time
Approximate Sizes
Parameter-Oblivious
Competitive Algorithm
🔎 Similar Papers
No similar papers found.
