Weighted Completion Time Minimization for Unrelated Machines via Iterative Fair Contention Resolution
Weighted Completion Time Minimization for Unrelated Machines via Iterative Fair Contention Resolution
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DOI：
10.1137/1.9781611975994.170
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发表时间：
2020-01
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影响因子：
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通讯作者：
Sungjin Im;Maryam Shadloo
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文献类型：
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作者：
Sungjin Im;Maryam Shadloo
对于最小化不相关机器上的总加权完成时间的经典调度问题，我们给出了 1.488 近似值。这相对于最近突破的 $(1.5 - 10^{-7})$ 近似（STOC 2016，Bansal-Srinivasan-Svensson）和 $(1.5 - 1/6000)$ 近似的后续结果（FOCS 2017，Li）来说是一个相当大的进步。班萨尔等人。引入了一种新颖的舍入方案，首次产生强负相关性，并将其应用于调度问题以获得突破，如果能够克服长期存在的基于独立舍入的 1.5 美元近似障碍，则解决了悬而未决的问题。我们的关键技术贡献是通过迭代公平争用解决方案实现显着更强的负相关性，这是独立的利益。此前，Bansal 等人。通过 pipage 型舍入的变体获得了很强的负相关性，Li 将其用作黑匣子。
We give a 1.488-approximation for the classic scheduling problem of minimizing total weighted completion time on unrelated machines. This is a considerable improvement on the recent breakthrough of $(1.5 - 10^{-7})$-approximation (STOC 2016, Bansal-Srinivasan-Svensson) and the follow-up result of $(1.5 - 1/6000)$-approximation (FOCS 2017, Li). Bansal et al. introduced a novel rounding scheme yielding strong negative correlations for the first time and applied it to the scheduling problem to obtain their breakthrough, which resolved the open problem if one can beat out the long-standing $1.5$-approximation barrier based on independent rounding. Our key technical contribution is in achieving significantly stronger negative correlations via iterative fair contention resolution, which is of independent interest. Previously, Bansal et al. obtained strong negative correlations via a variant of pipage type rounding and Li used it as a black box.